ARISTOTLE'S
PRIOR AND POSTERIOR
ANALYTICS
APIZTOTEAOY2 ANAAYTIKA
ARISTOTLE’S
PRIOR AND POSTERIOR
ANALYTICS
A REVISED TEXT
WITH INTRODUCTION AND COMMENTARY
BY
W. D. ROSS
OXFORD
AT THE CLARENDON PRESS
Oxford University Press, Amen House, London E.C.4
GLASGOW NEW YORK TORONTO MELBOURNE WELLINGTON
BOMBAY CALCUTTA MADRAS KARACHI
CAPE TOWN IBADAN NAIROBI ACCRA SINGAPORE
FIRST EDITION 1949
REPRINTED LITHOGRAPHICALLY IN GREAT BRITAIN
AT THE UNIVERSITY PRESS, OXFORD
FROM CORRECTED SHEETS OF THE FIRST EDITION
1957
PREFACE
Ir is one hundred and five years since Waitz’s edition of the
Organon was published, and a commentator writing now has at his
disposal a good deal that Waitz had not. The Berlin Academy has
furnished him with a good text of the ancient Greek commentators.
Heinrich Maier's Die Syllogistik des Aristoteles supplied what
amounts to a full commentary on the Prior Analytics. Professor
Friedrich Solmsen has given us an original and challenging theory
of the relation between the Prior Analytics and the Postertor.
Albrecht Becker has written a very acute book on the Aristotelian
theory of the problematic syllogism. Other books, and articles too
numerous to be mentioned here, have added their quota of com-
ment and suggestion. Among older books we have Zabarella's fine
commentary on the Posterior Analytics, which Waitz seems not to
have studied, and Pacius' commentary on the Organon, which
Waitz studied less than it deserved.
In editing the text, I have concentrated on the five oldest Greek
manuscripts—Urbinas 35 (A), Marcianus 201 (B), Coislinianus 330
(C), Laurentianus 72.5 (d), and Ambrosianus 490 (olim L 93) (n).
Of these I have collated the last (which has been unduly neglected)
throughout in the original, and the third throughout in a photo-
graph. With regard to A, B, and d, I have studied in the original
all the passages in which Waitz's report was obscure, and all those
in which corruption might be suspected and it might be hoped that
a new collation would bring new light. Mr. L. Minio has been good
enough to lend me his report on the Greek text presupposed by
two Syriac translations some centuries older than any of our Greek
manuscripts of the Analytics, and a comparison of these with the
Greek manuscripts has yielded interesting results ; I wish to record
my sincere thanks to him for his help, as well as to the librarians
of the Bibliothéque Nationale, and of the Vatican, Marcian,
Laurentian, and Ambrosian libraries.
W. D. R.
CONTENTS
SELECT BIBLIOGRAPHY
INTRODUCTION .
I. The Title and the Plan of the AREE ;
II. The Relation of the Prior to the Posterior Analytics
III. The Pure or Assertoric Syllogism
IV. The ModalSyllogism .. .
V. Induction 5 :
VI. Demonstrative Science .
VII. The Second Book of the Posterior ΞΕ
VIII. The Text of the Analytics .
List of Manuscripts not included in the Sigla :
SIGLA
ANALYTICS : :
Text and Critical ἀρ τε 3
Conspectus of the contents
Table of the valid moods
Commentary : . τ
INDEXES
Greek index : Ε
English index , . .
ix
280
286
287
679
688
SELECT BIBLIOGRAPHY
Aldine edition: Venice, 1495.
Organum, ed. I. Pacius: Frankfurt, 1592, etc.
Aristotelis Opera, vol. i, ed. I. Bekker: Berlin, 1831.
Organon, ed. T. Waitz, 2 vols.: Leipzig, 1844-6.
Prior Analytics, ed. and trans. H. Tredennick: London, and Cambridge,
Mass., 1938.
Analytica Priora, trans. A. J. Jenkinson, and Analylica Postertora, trans.
G. R. G. Mure: Oxford, 1928.
Commentaria in Aristotelem Graeca: Alexander in Anal. Pr. 1, ed. M. Wallies:
Berlin, 1883.
Themistius quae fertur in Anal. Pr. 1 Paraphrasis, ed. M. Wallies: Berlin,
1884.
Ammonius in Anal. Pr. 1, ed. M. Wallies: Berlin, 1899.
Themistii in Anal. Post. 2 Paraphrasis, ed. M. Wallies: Berlin, 1900.
Ioannes Philoponus in Anal. Pr., ed. M. Wallies: Berlin, 1905.
Eustratius in Anal. Post. 2, ed. M. Hayduck: Berlin, 1907.
Ioannes Philoponus in Anal. Post. and Anonymus in Anal. Post. 2, ed.
M. Wallies: Berlin, 1909.
Aquinas, St. Thomas, Comment. in Arist, libros Peri Hermeneias et Post. Anal.:
Rome and Freiburg, 1882.
Becker, A.: Die arist. Theorie der Móglichkeitsschlüsse : Berlin, 1933.
Bonitz, H.: Arist. Studien, 1-4, in Sitzungsb. der kaiserl. Akad. d. Wissen-
schaften, xxxix (1862), 183-280; xli (1863), 379-434; xlii (1863), 25-109;
lii (1866), 347-423.
Bywater, I.: Aristotelia: in J. of Philol. 1888, 53.
Calogero, G.: I Fondamenti della Logica Arist.: Florence, 1927.
Colli, G.: Aristotele, Organon: Introduzione, traduzione e note. Turin, 1955.
Einarson, B. : On certain Mathematical Terms in Arist.’s Logic: in A.J.P. 1936.
33-54, 151-72.
Friedmann, I.: Arist. Anal. bei den Syrern : Berlin, 1898.
Furlani, G.: Il primo Libro dei Primi Anal. di Arist. nella versione siriaca di
Giorgio delle Nazioni, and Il secondo Libro, etc.: in Mem. Acc. Línc.,
Cl. Sc. Mor., Ser. VI, vol. v. iii and vr. iii, 1935, 1937.
Gohlke, P.: Die Entstehung der arist. Logik: Berlin, 1935.
Heath, Sir T. L.: A History of Greek Mathematics, 2 vols.: Oxford, 1921.
Heath, Sir T. L.: A Manual of Greek Mathematics: Oxford, 1931.
Heiberg, J. L.: Mathematisches 2u Arist.: in Abh. zur Gesch. d. Mathem.
Wissenschaften, 1904, 1-49.
Kapp, E.: Greek Foundations of Traditional Logic: New York, 1942.
Lee, H. D. P.: Geometrical Method and Arist.’s Account of First Principles:
in Class. Quart. 1935, 113-29.
Lukasiewicz, J.: Aristotle's Syllogistic from the Standpoint of Modern Formal
Logic : Oxford, 1951.
Maier, H.: Die Syllogistik des Arist., 3 vols.: Tübingen, 1896-1900.
Mansion, S.: Le Jugement d'existence chez Aristote: Louvain and Paris, 1946.
Miller, J. W.: The Structure of Arist. Logic: London, 1938.
Nagy, A.: Contributo per la revisione del testo degli Anal.: in Rendic. Acc.
Linc., Cl. Sc. Mor., Ser. V, vol. viii, 1899, 114-29.
x SELECT BIBLIOGRAPHY
Pacius, J.: Aristotelis Organon cum commentario analytico: Francofurti, 1597.
Solmsen, F.: Die Entwicklung der artist. Logik und Rhetorik : Berlin, 1929.
Solmsen, F. : ‘The Discovery of the Syllogism’, in Philos. Rev. 50 (1941), 410 ff.
Stocks, J. L.: The Composition of Arist.'s Logical Works: in Class. Quart. 1933,
115-24.
Waitz, T.: Varianten 2u Arist. Organon: in Philol. 1857, 726-34.
Wallies, M.: Zur Textgeschichte der Ersten Anal.: in Rhein. Mus. 1917-18,
626-32.
Wilson, J. Cook: Aristotelian Studies I: in Góttingische gelehrte Anzeiger,
1880 (1), 449-74. .
Wilson, J. Cook : On the Posstbility of a Conception of the Enthymema earlier
than that found in the Rhet. and the Pr. Anal.: in Trans. of the Oxford
Philol. Soc. 1883-4, 5-6.
Zabarella, I.: In duos Artist. Libros Post. Anal. Comment.: Venice, 1582.
Zabarella, I.: Opera Logica: Venice, 1586.
In the notes the Greek commentaries are referred to by the symbols Al.,
T., Àm,, P., E., An.
INTRODUCTION
I
THE TITLE AND THE PLAN OF THE ANALYTICS
HE Analytics are among the works whose Aristotelian
authorship is certain. Aristotle frequently refers in other
works to rà ἀναλυτικά, and these references are to passages that
actually occur in the Prior or the Posterior Analytics. He did not,
however, distinguish them as Prior and Posterior, and the earliest
traces of this distinction are in the commentary of Alexander of
Aphrodisias (fl. c. A.D. 205) on Ax. Pr. i. The distinction occurs
also in the list of Aristotelian MSS. preserved by Diogenes Laertius
(early third century A.D.), which probably rests on the authority
of Hermippus (c. 200 B.C.) ; in that list the Prior Analytics occurs
as no. 49 and the Posterior Analytics as no. 50.1 Diogenes ascribes
nine books to the Prior Analytics, and so does no. 46 in Hesychius'
list (? fifth century A.D.), but no. 134 in Hesychius' list ascribes
two books to it. The nine books may represent a more elaborate
subdivision of the extant work, but it is more likely that they were
a work falsely ascribed to Aristotle; we know from Schol. in
Arist. 33532? that Adrastus mentioned forty books of Analytics,
of which only the extant two of the Prior and two of the Posterior
were recognized as genuine.
Aristotle occasionally refers to the Prior Analytics under the
name of τὰ περὶ συλλογισμοῦ, but the title τὰ ἀναλυτικά, and later
the titles rà πρότερα ἀναλυτικά, rà ὕστερα ἀναλυτικά, prevailed. The
appropriateness of the title can be seen from such passages as
An. Pr. 4734 ἔτι δὲ τοὺς γεγενημένους ἀναλύοιμεν eis τὰ προειρημένα
σχήματα, 49318 οὕτω μὲν οὖν γίνεται: ἀνάλυσις, An. Post. g1b13 ἐν τῇ
ἀναλύσει τῇ περὶ τὰ σχήματα. The title is appropriate both to the
Prior and to the Posterior Analytics, but the object of the analysis
is different in the two cases. In the former it is syllogism in
general that Aristotle analyses; his object is to state the nature of
the propositions which will formally justify a certain conclusion.
! Under the title ἀναλυτικὰ ὕστερα μεγάλα, which presumably distinguishes
Aristotle’s work from those written by his followers.
2 Cf. Philop. in Cat. 7. 26, in An. Pr. 6. 7; Elias in Cat. 133. 15.
4985 B
2 INTRODUCTION
In the latter it is the demonstrative syllogism that he analyses ;
his object is to state the nature of the propositions which will not
merely formally justify a certain conclusion, but will also state
the facts on which the fact stated in the conclusion depends for
its existence.
The extant Greek commentaries on the Prior Analytics are (1)
that of Alexander; he commented on all four books of the
Analytics, but only his commentary on Az. Pr. i is extant; (2)
that of Ammonius (fl. c. 485) on book i; as its title (ZxóAa eis τὸ
A’ τῶν προτέρων ἀναλυτικῶν ἀπὸ φωνῆς Appwriov) implies it is a
pupil’s notes of Ammonius' lectures ; all that remains is the com-
mentary on 24?*1-25?13; (3) that of Joannes Philoponus (c. 490-
530) covering the whole work; (4) a paraphrase of the first book
which bears the name of Themistius but is not by him. It is in
the style of Sophonias’ paraphrase of the De Anima, and may be
by Sophonias (fl. c. 1300). It is put together in a very inadequate
way out of the commentaries of Alexander and Philoponus; it
covers chs. 9-46 (the end). The commentaries on the Postertor
Analytics are (1) the paraphrase of Themistius (c. 317-88) ; (2) the
commentary of Philoponus; (3) that of an anonymous commen-
tator on the second book ; (4) that of Eustratius (c. 1050-1120) on
the second book. All these commentaries have been edited in the
series of Commentaria in Aristotelem Graeca, the last by M. Hay-
duck, the rest by M. Wallies.
The arrangement of An. Pr. i is clear and straightforward.
There are three passages in which Aristotle states his programme
and sums up his results: 43316—24, 46538—47?9, 52538-5333. In these
passages— most clearly in the second—he describes the book as
falling into three main parts: (1) A study of the γένεσις τῶν συλλο-
γισμῶν, 1.6. of the figures and moods. This is contained in chs. 1-
26, where, after three preliminary chapters, Aristotle expounds in
chs. 4-7 the figures and moods of the pure syllogism, and in
chs. 8-22 those of the modal syllogism, and concludes with four
chapters summing up the characteristics of the three figures. (2) A
series of practical rules for the finding of premisses to prove each
type of conclusion ; these Aristotle gives in chs. 27-30. (3) A study
of how syllogisms are to be put into the forms of the three figures
(chs. 32-45). This is in the main a consideration of the possibilities
of error in putting into syllogistic form arguments couched in
ordinary conversational form.
Two chapters—31 and 46—fall outside this scheme. Ch. 31 is a
TITLE AND PLAN OF THE ANALYTICS 3
criticism of the Platonic method of reaching definitions by means
oí dividing a genus into species and sub-species. It has no close
connexion with what precedes or with what follows; the last
sentence of ch. 30 implies that the study of the choice of premisses
is already complete without ch. 31. Maier! may be right in holding
it to be a later addition; for in 46435-7 it seems to presuppose
Aristotle’s doctrine that a definition cannot be reached as the
conclusion of a demonstration, and thus to presuppose the dis-
cussion in An. Post. ii. 3-10. Ch. 46, on the distinction between
*B is not A’ and ‘B is not-A’, is equally unconnected with what
precedes it; the last sentence of ch. 45 implies that the study of
reduction of arguments to syllogistic form is already completed in
chs. 32-45. Maier? treats the chapter as a later addition forming
the transition from An. Pr. i to the De Interpretatione, which he
improbably (in my view) regards as among the latest of Aristotle's
surviving works ;? and the chapter has plainly a close affinity with
De Int. 10 and 14. But Maier seems to be wrong in saying that
propositions are here considered simply as isolated propositions,
not as syllogistic premisses, and that therefore the chapter belongs
to Aristotle's theory of the judgement, not to his theory of the
syllogism. The chapter begins with the statement that the ques-
tion whether 'B is not A’ means the same as 'B is not-A’ makes
a difference ἐν τῷ κατασκευάζειν ἢ ἀνασκευάζειν, and this point is
elaborated in 52324-38, where Aristotle points out that whereas
'B is not-A’ requires for its establishment a syllogism in Bar-
bara, ‘B is not A’ requires for its establishment a syllogism in
Celarent, Cesare, or Camestres. Instead of forming a transition
from An. Pr.itothe De Interpretatione, the chapter seems rather
to take account of a distinction belonging to the theory of judge-
ment and already drawn in the De Interpretatione, and to make
use of it with reference to the theory of syllogism. Nor is Maier
justified in saying that the use made in this chapter of the laws of
contradiction and excluded middle presupposes the discussion of
them in Met. Γ. After all, they had already been formulated by
Plato, and must have been familiar to Aristotle from his days of
study in the Academy. Though slightly misplaced (since it is
divided from the section on reduction of arguments to syllogistic
form by ch. 45, which deals with reduction from one figure to
another), ch. 46 is not seriously out of place. It would have been
12. b 77 ἢ. 2, 78 n. 3. 2 2, b 364 n.
3. Arch. f. d. Gesch. d. Phil. xiii (1900), 23-72.
4 INTRODUCTION
natural enough as part of the section comprised in chs. 32-45 and
dealing with possible sources of error in the reduction of argu-
ments to syllogistic form. Cf. συμβαίνει δ᾽ ἐνίοτε καὶ ἐν τῇ τοιαύτῃ
τάξει τῶν ὅρων ἀπατᾶσθαι κτλ. (46. 52514) with πολλάκις μὲν οὖν
ἀπατᾶσθαι συμβαίνει κτλ. (33. 47915) and similar expressions ib. 38,
40, 34. 48?24.
The structure of the second book is by no means so clear as
that of the first. It begins with a section (chs. 1-- 5) which brings
out what may be called properties of the syllogism, following from
its structure as exhibited in i. 4-6— viz. (1) the possibility of
drawing a fresh conclusion from the conclusion of a syllogism, or
by parity of reasoning with the original conclusion (ch. 1); (2) the
possibility of drawing true conclusions from false premisses (chs.
2-4) ; (3) the possibility of proving one premiss of a syllogism from
the conclusion and the converse of the other premiss (chs. 5-7);
(4) the possibility of proving the opposite of one premiss from the
other premiss and the opposite of the conclusion (chs. 8-10);
(s) the possibility of a particular application of the last process,
viz. reducto ad tmpossibile (chs. 11-14); (6) the possibility of
drawing a conclusion from two opposite premisses (ch. 15). The
object of these exercises in the use of the syllogism may be best
described in the words which Aristotle applies to one of them, viz.
τὸ ἀντιστρέφειν, the conversion of syllogisms (chs. 8-10). Of this
exercise he says in Top. 163%29-36 that it is useful πρὸς γυμνασίαν
Kai μελέτην τῶν τοιούτων λόγων.
From this section Aristotle passes to a rather loosely connected
section in which he exposes certain dangers that beset us in
argument. The first of these is petitio princtpis (ch. 16). The
second is ‘false cause’: when a syllogism leads to a false conclu-
sion, there must be somewhere a false premiss, but it is not easy
to detect this (chs. 17, 18). To these two topics he adds certain
others concerned with the practice of dialectical argument—hints
on how to avoid admissions which will lead to an unwelcome con-
clusion, and how to disguise one's own argument (chs. 19, 20).
To these he tacks on a chapter (21) on the question how it can
happen that, while knowing or believing one or even both of the
premisses which entail a certain conclusion, we may fail to draw
the conclusion, or even hold a belief opposite to it. His solution
turns on a distinction between universal knowledge, particular
knowledge, and actualized knowledge! which is closely akin to
! 6754-5.
TITLE AND PLAN OF THE ANALYTICS 5
the distinction drawn in An. Post. 71417-30, and may be even
later than it, since the latter passage draws only the distinction
between universal and particular knowledge.’ It will be seen that
chs. 16—21 form no organic unity. They are a series of isolated
essays grouped together for lack of organic connexion with any of
the other sections of the book.
Next comes an isolated chapter (22) which itself deals with two
unconnected subjects: (1) various rules showing under what con-
ditions the convertibility of two terms can be inferred, and (2) a
rule for comparing two objects in respect of desirability. The
present position of the chapter is probably due to the fact that
one principle laid down in it becomes the basis for the treatment
of the inductive syllogism in ch. 23 (where 68524-7 refers back to
22. 6821-5).
Finally there is a section (chs. 23-7) in which Aristotle examines
five special types of argument with a view to showing that all
methods of producing conviction by argument are reducible to
one or other of the three figures of syllogism.? Maier's arguments
for considering chs. 25 and 26 as later than 23, 24, and z7? seem to
me unconvincing.
The Postertor Analytics falls into five main parts. In i. 1-6
Aristotle states the conditions which are necessary to constitute
a demonstration, or scientific proof, and which together form the
essence or definition of demonstration. In i. 7-34 he states the
properties which a demonstration possesses by virtue of having this
essential nature. This part of the work hangs loosely together,
and contains, in particular, two somewhat detached sections—
chs. 16—18 dealing with error and ignorance, and chs. 33-4 dealing
with (a) the relation between demonstrative knowledge and
opinion and (b) that quickness of intelligence (ἀγχίνοια) which in
the absence of demonstrative knowledge of the causation of a
given effect enables us to guess its cause correctly. In ii. 1-10 he
deals with one specially important characteristic of demonstra-
tion, viz. that the demonstration that a subject has a certain
property can become the basis of a definition of the property. In
ii. 11-18 he deals with a number of special questions connected with
demonstration. Finally in ii. 19 he considers how the indemon-
strable first principles from which demonstration proceeds them-
selves come to be known.
d ! 1227-9. 2 68b9—13.
3 ji. a 453 n. 2, 472 n.
6 INTRODUCTION
II
THE RELATION OF THE PRIOR TO THE POSTERIOR
ANALYTICS
AN editor of these works is bound to form some opinion on their
relation to each other and to Aristotle's other works on reasoning,
the Topics and the Sophistict Elenchi; he may be excused from
considering the Categories and the De Interpretatione, whose
authenticity is not certain, and which do not deal with reasoning.
We may assume that the Tofics and the Sophistici Elenchi are
earlier than either of the Analytics. They move more completely
than the Analytics within the circle of Platonic ways of thinking.
They discuss many arguments in a way which could have been
immensely improved in respect of definiteness and effectiveness
if the writer had already had at his command the theory of the
syllogism, as he has in the Prior and (as will be shown) in the
Posterior Analytics; and we can hardly suppose that in writing
them he dissembled a knowledge which he already had.
It is true that the word συλλογισμός occurs occasionally in the
Topics, but in some of these passages the word has not its technical
meaning of 'syllogism', and others are best regarded as later
additions made after the Analytics had been written. Scholars
are agreed that Topics ii-vii. 2 at least are older than any part of
the Analytics. Maier! thinks that bks. i, vii. 3-5, viii, and ix (the
Sophistict Elenchi) are later additions; Solmsen thinks that only
bks. viii and ix are later ; we need not inquire which of these views
is the true one. The main question which divides scholars at
present is whether the Prior or the Posterior Analytics is the
earlier. The traditional view is that the Prior is the earlier;
Solmsen has argued that the Posterior is (as regards its main
substance) the earlier. Nothing can be inferred from the names
Prior and Posterior. Aristotle refers to both works as rà ἀναλυτικά.
Our earliest evidence for the names Prior and Posterior Analytics
is much later than Aristotle. It is possible that the names pre-
serve a tradition about the order of the writing of the two works ;
but it is equally possible that they refer to what was deemed the
logical order.
The traditional view has been best stated, perhaps, by Heinrich
Maier. He holds that what first stimulated Aristotle to thinking
about logic was the scepticism current in some of the philosophical
! ji. b 78 n. 3.
RELATION OF PRIOR TO POSTERIOR ANALYTICS 7
schools of his time—the Megarian, the Cynic, the Cyrenaic school ;
that he evolved his theory of dialectic, as it is expressed in the
Topics, with a view to the refutation of sceptical arguments.
Further, he holds that in his formulation of dialectical method
Aristotle was influenced by Plato’s conception of dialectic as con-
sisting in a twofold process of συναγωγή, the gradual ascent from
more particular Forms to the wider Forms that contained them,
and διαίρεσις, the corresponding ordered descent from the widest
to the narrowest Forms; a conception which naturally gave rise
to the doctrine of predicables which plays so large a part in the
Topics. Maier thinks further that reflection on the shortcomings
of the Platonic method of division—shortcomings to which
Aristotle more than once refers—led him to formulate the syllo-
gistic procedure in the Prior Analytics, and that later, in the
Posterior Analytics, he proceeded to deal with the more special-
ized problem of the scientific syllogism, the syllogism which, in
addition to observing the rules of syllogism, proceeds from pre-
misses which are 'true, prior in logical order to the conclusion,
and immediate'.
Solmsen's view, on the other hand, is that, having formulated
the method of dialectic in the Topics, Aristotle next formulated
the method of strict science in the Posterior Analytics, and finally
reached in the Prior Analytics the general account of the syllo-
gism as being the method lying at the base both of dialectical
argument and of scientific reasoning. Thus for the order Dialectic,
Analytic, Apodeictic he substitutes the order Dialectic, Apodeictic,
Analytic. It will be seen that the order he reaches, in which the
most general amount of method follows the two particular
accounts, is more symmetrical than that assigned in the tradi-
tional view; and it is obviously a not unnatural order to ascribe
to Aristotle's thinking. Further, he attempts to show that the
circle of ideas within which Aristotle moves in the Posterior
Analytics is more purely Platonic than that presupposed by the
Prior Analytics. And he makes a further point. He reminds us!
of what is found in the Politics. It is, as Professor Jaeger has
shown, highly probable that in the Politics the discussion of the
than the purely descriptive account of various constitutions,
many of them far from ideal, which we find in bks. iv-vi. In the
former part of the work Aristotle is still under the influence of
* p. 56.
8 INTRODUCTION
Plato's search for the ideal; in the latter he has travelled far from
his early idealism towards a purely objective, purely scientific
attitude for which all existing constitutions, good and bad alike,
are equally of interest. Solmsen traces an analogous development
from the Posterior Analytics to the Prior. In the Postertor Analy-
tics Aristotle has before him the syllogism which is most fully
scientific, that in which all the propositions are true and necessary
and the terms are arranged in the order which they hold in a tree
of Porphyry—the major term being the widest, the middle term
intermediate in extent, and the minor the narrowest; in fact, a
first-figure syllogism with true and necessary premisses. And this
alone, Solmsen thinks, is the kind of syllogism that would have
been suggested to Aristotle by meditation on Plato’s διαίρεσις,
which proceeds from the widest classes gradually down to the
narrowest. In the Prior Analytics, as in the middle books of the
Politics, he has widened his ideas so as to think nothing common
or unclean, no syllogism unworthy of attention so long as the
conclusion really follows from the premisses; and thus we get
there syllogisms with untrue or non-necessary premisses, and
syllogisms (in the second and third figures) in which the natural
order of the term is inverted.
A minor feature of Solmsen’s view is that he thinks Posterior
Analytics bk. ii later than bk. i—separated from it by the eighth
book of the Topics and by the Sophistict Elenchi—though earlier
than the Prior Analytics; and he finds evidence of the gap be-
tween the two books in the fact that while in the first book
mathematical examples of reasoning predominate almost to the
exclusion of all others, in the second book examples from the
physical sciences are introduced more and more.
There is much that is attractive in Solmsen's view, and it
deserves the most careful and the most impartial consideration.
What we have to consider is whether the detailed contents of the
two Analytics tell in favour of or against his view.
We may begin with a study of the references in each work to the
other. We must realize, of course, that references may have been
added later, by Aristotle or by an editor. We must consider each
reference on its merits, and ask ourselves (1) whether it is so
embedded in the argument that if we remove it the argument
falls to pieces, or is so loosely attached that it can easily be
regarded as a later addition. And (2) apart from the mode of the
reference, we must ask ourselves whether Aristotle is assuming
RELATION OF PRIOR TO POSTERIOR ANALYTICS 9
something which he would have no right to assume as already
proved within the work in which the reference occurs—no right
to assume unless he had proved it in a previous work ; and whether
the previous work must be, or is likely to be, that to which the
reference is given. This study of the references is a minute and
sometimes rather tedious matter, but it is a necessary, though not
the most important, part of an inquiry into the order of writing
of different works. I will pass over the references from which no
sure conclusion can be drawn—the references forward to the
Posterior Analytics in An. Pr. 24>12-14 and 43*36—; and the
possible reference in 32523, the references back to the Prior
Analytics in An. Post. 7734-5 and grbi2-14 and the possible
reference in 95>40-9622. I will take the remaining references in
order.
(1) i. 4. 25526. ‘After these distinctions let us now state by what
means, when, and how every syllogism is produced ; subsequently
we must speak of demonstration. Syllogism should be discussed
before demonstration, because syllogism is the more general;
demonstration is a sort of syllogism, but not every syllogism is a
demonstration.’ This reference (‘subsequently’, etc.) is not em-
bedded in the argument, and is easily enough detached. It cannot,
however, be neglected. We must consider with it the opening
words of the book (24210) : ‘We must first state the subject of our
inquiry: its subject is demonstration, or demonstrative science.’
We can, I believe, feel pretty sure that in these two passages
Aristotle himself is speaking. Two interpretations are, however,
possible. One is that the words belong to the original structure of
the Prior Analytics, that Aristotle’s subject all along was demon-
stration, and that the treatment of syllogism in the Prior Analy-
tics was meant to be preliminary to the study of demonstration in
the Posterior Analytics, on the ground actually given, viz. that it
is proper to examine the general nature of a thing before examin-
ing its particular nature. The other is that these two sentences
were added after Aristotle had written both works, and reflect
simply his afterthought about the logical relation between the
two. Obviously this interpretation ascribes a rather disingenuous
procedure to Aristotle. He is supposed to have first worked out a
theory of demonstration, without having discovered that demon-
stration is but a species of syllogism ; then to have discovered that
it is so, and the nature and rules of the genus to which it belongs,
and then to have said ‘let us study the genus first, because we
IO INTRODUCTION
obviously ought to study the genus before the species'. I do not
say this procedure is impossible, but I confess that it seems to me
rather unlikely.
(2) An. Post. i. 3. 35]. ‘It has been shown that the positing of
one term or one premiss... never involves a necessary consequent ;
two premisses constitute the first and smallest foundation for
drawing a conclusion at all, and therefore a foritori for the
demonstrative syllogism of science.’ The reference is to An. Pr.
34*16-21 or to 4030-7. No proof of the point is offered in the
Posterior Analytics itself. If it had not been established already,
as it is in the Prior Analytics and there alone, it would be the
merest assumption. Therefore to cut out this reference as a late
addition would involve cutting out the whole context in which
it occurs.
(3) Ib. 73*11. ‘If, then, A is implied in B and C, and B and C
are reciprocately implied in one another, it is possible, as has been
shown in my writings on syllogism, to prove all the assumptions
on which the original conclusion rested, by circular demonstra-
tion in the first figure. But it has also been shown that in the other
figures either no conclusion is possible, or at least none which
proves both the original premisses.' Not only are the two explicit
references references to An. Pr. ii. 5 and ii. 6-7, but the phrases
‘the first figure’, ‘the other figures’, which are explained only
in the Prior Analytics, are used as perfectly familiar phrases.
Evidently the whole paragraph would have to be treated by
Solmsen as a later addition; and with the omission of this Aris-
totle's disproof of the view that all demonstration is circular be-
comes a very broken-backed affair..
(4) i. 16. 8036. ‘Error of attribution occurs through these causes
and in this form only—for we found that no syllogism of universal
attribution was possible in any figure but the first’—a reference
to An. Pr. i. 5-6. The reference is vital to the argument ; further,
it is made in the most casual way ; what Aristotle says is simply
‘for there was no syllogisin of attribution in any other figure’.
We can feel quite sure that ch. 16 at least was written after the
Prior Analytics.
(5) i. 25. 86P10. ‘It has been proved that no conclusion follows
if both premisses are negative.’ This is proved only in An. Pr. i.
4-6; the assumption is vital to the proof in An. Post. i. 25.
Summing up the evidence from the references, we may say that
references (2), (3), (4), (5) show clearly that An. Post. i. 3, 16, 25
RELATION OF PRIOR TO POSTERIOR ANALYTICS 11
were written after the Prior Analytics, and that reference (x) is
more naturally explained by supposing that the Prior Analytics
was written before and as a preliminary to the Postertor Analytics.
The other references prove nothing except that Aristotle meant
the Prior Analytics to precede the Posterior in the order of
instruction.
There is, however, another way in which we can consider the
explicit references from one book to another. Many of Aristotle’s
works, taken in pairs, exhibit cross-references backward to one
another; and this must be taken to indicate either that the two
works were being written concurrently, or that a book which was
written earlier was later supplied with references back to the other
because it was placed after it in the scheme of teaching—which is
what Solmsen supposes to have happened to the Postertor Analy-
tics in relation to the Prior. But it is noticeable that no such cross-
references occur here. The references in the Prior Analytics to the
Posterior are all forward; those in the Posterior Analytics to the
Prior are all backward. If the order of writing did not correspond
to the order of teaching, we should expect some traces of the order
of writing to survive in the text; but no such traces do survive.
This is an argument from silence, but one which has a good deal
of weight.
We must now turn to consider whether, apart from actual
references, the two works give any indication of the order in
which they were written. It may probably be said without fear
of contradiction that none of the contents of the Prior Analytics
certainly presuppose the Posterior. Let us see whether any of
the contents of the Posterior Analytics presuppose the Prior.
The scrutiny, involving as it does an accumulation of small
points, is bound to be rather tedious; but it will be worth mak-
ing it if it throws any light on the question we are trying to
solve. Broadly speaking, the nature of the evidence is that
the Posterior Analytics repeatedly uses in a casual way terms
which have been explained only in the Prior, and assumes doc-
trines which only there have been proved. If this can be made
good, the conclusion is that before the Posterior Analytics was
written either the Prior must have been written, or an earlier
version of it which was so like it that Solmsen’s contention
that the philosophical logic of the Posterior Analytics was an
earlier discovery than the formal logic of the Prior falls to the
ground.
12 INTRODUCTION
First, then, we note that in An. Post. i. 2. 71>17—18 Aristotle
defines demonstration as a syllogism productive of scientific
knowledge, συλλογισμὸς ἐπιστημονικός. No attempt is made to
explain the term 'syllogism', and we must conclude that the
meaning of the term is well known, and well known because it
has been explained in the Prior Analytics.
i. 6. 74529 has a casual reference to ‘the middle term of the
demonstration’. But it is only in the Prior Analytics that it is
shown that inference must be by means of a middle term. Refer-
ences to the middle term as something already known to be
necessary occur repeatedly in the Postertor Analytics.’ Similarly,
in i. 6. 75236, 11. 77812, 19 there are unexplained references to τὸ
πρῶτον, τὸ τρίτον.
i. 9. 81>r0-14 assumes, as something already known, that every
syllogism has three terms, and that an affirmative conclusion
requires two affirmative premisses, a negative conclusion an
affirmative and a negative premiss.
An. Post. i. 13 is admitted by Solmsen to be later than the Prior
Analytics, and rightly so. For according to his general thesis the
main framework of the Posterior Analytics is based on the con-
sideration of a Platonic chain of genera and species—let them be
called A, B,C in the order of decreasing extension—and Aristotle
contemplates only the inferential connecting of C as subject
with A as predicate by means of the intermediate term B; ie.,
Solmsen conceives Aristotle as being aware, at this stage, only of
the first figure of the syllogism, and as discovering later the
second and third figures, which are of course discussed fully in the
Prior Analytics. But in this chapter? an argument in the second
figure (referred to quite familiarly in 524 as ‘the middle figure’)
forms an integral part of Aristotle’s treatment of the question
under discussion. It is of course easy to say that this is a later
addition, but the question is whether we shall not find that so
many things in the Posterior Analytics have from Solmsen's point
of view to be treated as later additions that it is sounder to hold
that the work as a whole is later than the Prior Analytics.
Again, the theme of i. r4 is that 'of all the figures the most
scientific is the first’; i.e. the whole set of figures, and the nomen-
clature of them as first, second, third, is presupposed. This quite
1 j. 6. 7429-75417; 7. 75911; 9. 7629; 11. 7798; 13. 788, 13; 15. 79*35; 19.
81517; 24. 86214; 25. 86518; 29. 8756; 33. 89414, 16; ii. 2 passim; 3. 90435; 8.
93*7; 1I passim ; 12. 95*36; 17. 99*4, 21. 2 48b13-28.
RELATION OF PRIOR TO POSTERIOR ANALYTICS 13
clearly presupposes the Prior Analytics. Not only is the distinc-
tion of figures and their nomenclature presupposed, but also the
rules, established only in the Prior Analytics, that the second
figure proves only negatives! and the third figure only particular
propositions. And further it is assumed without discussion that
arguments in the second and third figures are strictly speaking
validated only by reduction to the first figure’—precisely the
method displayed in detail in the treatment of these figures in
An. Pr. i. 5,6. It is assumed, again, in i. 15 that the minor premiss
in the first figure must be affirmative,* and that in the second
figure one premiss must be affirmative.5
An. Post. i. 17. 8020 casually uses the phrase τὸ μεῖζον ἄκρον,
which presupposes the doctrine of the syllogism stated in An. Pr.
i. 4. 523 presupposes what is shown at length in An. Pr. i. 4, that
in the first figure the minor premiss must be affirmative. 8145
refers casually to τὸ μέσον σχῆμα, the second figure, and 8145-14
relates to error arising in the use of that figure.
i. 21 says® that a negative conclusion may be proved in three
ways, and this turns out to mean ‘in each of the three figures’ ;7
the three figures are expressly referred to in 8253o-1. Once more
it is assumed that in the first figure the minor premiss must be
affirmative ;? the proof is to be found in An. Pr. i. 4.
i. 23 alludes to arguments in the moods Barbara, Celarent,
Camestres, and Cesare.?
i. 29. 87516 makes a casual reference to ‘the other figures’ ; ii. 3.
9056, 7 a casual reference to the three figures; ii. 8. 9338 a casual
reference to the first figure.
Taking together the explicit references and the casual allusions
which presuppose the Prior Analytics, we find that at least the
present form of the following chapters must be dated after that
work: i. 2, 3, 6, 7, 9, 11, 13-17, 19, 21, 23-5, 29, 33; li. 2, 3, 8, 11, 12,
17. Thus of the thirty-four chapters of the first book eighteen
explicitly (leaving out doubtful cases) presuppose the doctrine of
the syllogism as it is stated at length in the Prior Analytics. If
the Posterior Analytics was written before the Prior, we should
have to assume a very extensive rewriting of it after the Przor
Analytics had been written.
I think I should be describing fairly the nature of Solmsen's
1 49925. ? lb.27. 3 Ib.29. 4 79%17—proved in An. Pr. i. 4.
5 49620—proved in An, Pr. 1. 5. 9 gab4.
7 ΤΌ, 5-16, 16-21, 21-8. 8 Ib. 7. 9 §4631~-3, 8521-12.
I4 INTRODUCTION
argument if I said that his attempt is to prove that the philo-
sophical atmosphere of the Posterior Analytics is an early one,
belonging to the time when Aristotle had hardly emerged from
Platonism and had not yet attained the views characteristic of his
maturity. I will not pretend to cover the whole ground of Solm-
sen's arguments, but will consider some representative ones.
A great part of his case is that the preoccupation of An. Post. i
with mathematics is characteristic of an early period in which
Aristotle was still much under the influence of Plato's identifica-
tion (in the Republic, for instance) of science with mathematics.
The preoccupation is not to be denied, but it is surely clear that
at any period of Aristotle's thought mathematics must have
appeared to him to represent in its purity the ideal of strict
reasoning from indubitable premisses—with which alone, in the
Posterior Analytics, he is concerned. Throughout the whole of his
works we find him taking the view that all other sciences than
the mathematical have the name of science only by courtesy,
since they are occupied with matters in which contingency plays
a part. It is not Plato's teaching so much as the nature of things
that makes it necessary for Aristotle, as it in fact makes it neces-
sary for us, to take mathematics as the only completely exact
science.
Let us come to some of the details of the treatment of mathe-
matics in the Posterior Analytics. Solmsen claims! that Aristotle
there treats points, lines, planes, solids as constituting a chain of
Forms—an Academic doctrine professed by him in the Protrept-
cus but already discarded in the (itself early) first book of the
Metaphysics. The conception of a chain of Forms of which each
is a specification of the previous one is, of course, Platonic, but
there is no evidence that Aristotle ever thought of points, lines,
planes, solids as forming such a chain. Nor is there any evidence
that Plato did—though that question must not be gone into here.
Let us look at the Aristotelian evidence. What the Protrepticus
says? is: ‘Prior things are more of the nature of causes than
posterior things; for when the former are destroyed the things
that have their being from them are destroyed; lengths when
numbers are destroyed, planes when lengths are destroyed, solids
when planes are destroyed.' There is no suggestion that planes,
for instance, are a species of line. What is said is simply that
planes are more complex entities involving lines in their being.
τ p. 83. 2 fr. 52, p. 60. 26 Rose?.
RELATION OF PRIOR TO POSTERIOR ANALYTICS 15
This has nothing to do with a chain of Forms such as is contem-
plated in Plato's συναγωγή and διαίρεσις, where each link is a
specification of the one above it.
Now what does the Metaphysics say? In 4 1017517-21 Aristotle
mentions the same view, ascribing it to ‘some people’, but not
repudiating it for himself—though he probably would have
repudiated one phrase here used of the simpler entities, viz. that
they are ‘inhering parts’ of the more complex; for the view to
which he holds throughout his works is that while points are
involved in the being of lines, lines in that of planes, and planes
in that of solids, they are not component parts of them, since for
instance no series of points having no dimension could make up
a line having one dimension.
Met. A. 992*10—19 is a difficult passage, in which Aristotle is not
stating his own view but criticizing that of the Platonists. The
point he seems to be making is this: The Platonists derive lines,
planes, solids from different material principles (in addition to
formal principles with which he is not at the moment concerned)—
lines from the long and short, planes from the broad and narrow,
solids from the deep and shallow. How then can they explain
the presence of lines on a plane, or of lines and planes in a solid?
On the other hand, if they changed their view and treated the
deep and shallow as a species of the broad and narrow, they would
be in an equal difficulty; for it would follow that the solid is a
kind of plane, which it is not. The view implied as Aristotle's
own is that undoubtedly the planes presuppose lines, and the
solids planes, but that equally certainly the plane is not a kind of
line nor the solid a kind of plane.
Now this view is not the repudiation of anything that is said in
the Posterior Analytics. What Aristotle says! is that the line is
present in the being and in the definition of the triangle, and the
point in that of the line. But this is not to say that the triangle,
for instance, is a species of the line, but only that there could not
be a triangle unless there were lines, and that the triangle could
not be defined except as a figure bounded by three straight lines ;
ie., Aristotle is not describing points, lines, plane figures as
forming a Platonic chain of Forms at all. In fact there is no work
in which he maintains the difference of γένη more firmly than he
does in the Posterior Analytics. The theory expressed in the
Protrepticus and referred to in Met. A and 4, if it had treated the
1 73*35.
16 INTRODUCTION
line as a species of point, the plane as a species of line, etc., would
equally have treated points, lines, planes, solids as descending
species of number ;! but in Post. An. 75338-*14 he scouts the idea
that spatial magnitudes are numbers, and in consequence main-
tains that it is impossible to prove by arithmetic the propositions
of geometry.
Thus the doctrine of the Posterior Analytics is not the stupid
doctrine which treats numbers, points, lines, planes, solids as a
chain of genera and species, but the mature view characteristic
of Aristotle throughout his works, that lines, for instance, are not
points nor yet made by a mere summation of points, but yet that
they involve points in their being; and Solmsen’s reason for
placing the Postertor Analytics earlier than Met. A disappears.
Again, Solmsen treats the term ópos, which is common in the
Prior Analytics and comparatively rare in the Posterior, as the
last link in the process by which Aristotle gradually advanced
from the Platonic Form, with its metaphysical implications, to
something purely logical in its significance, the ‘Universal’ being
the intermediate link. We may, of course, grant that ‘Term’ is a
more colourless notion than ‘Form’ or even than ‘Universal’,
standing as it does for anything that may become the subject or
predicate of a statement. Solmsen is probably right in describing
the three conceptions—Form, Universal, Term—as standing in
that same order chronologically. But if so, the more evidence we
can find of the word ópos (in the sense of 'term') in the Posterior
Analytics, the later we shall have to date that work. Solmsen
speaks as if the word occurred only thrice.? But I have found
examples in i. 3. 7235, 7320; 19. 81510; 22. 8429, 36, 38; 23. 84512,
16, 27 ; 25. 8657, 24 ; 26. 87312 ; 32. 88436, ^5, 6. It is surely clear that
the notion was familiar to Aristotle when he wrote the Posterior
Analytics ; it is also clear that, whatever was the order of writing
of the Prior and the Posterior Analytics, it is only natural that the
colourless word ὅρος should occur oftener in the work devoted to
formal logic than in that from which metaphysical interests are
never absent. Further, it is at least arguable that the casual use
of the word in the Posterior Analytics as something quite familiar
presupposes the careful definition of it in An. Pr. 24516.
Again, Solmsen treats? the instances Aristotle gives of the
second kind of καθ᾽ aóró*—straight and curved as alternative
1 See the Proptrepticus passage. 2 p. 86 n. 2.
? p. 84. * 7353753.
RELATION OF PRIOR TO POSTERIOR ANALYTICS 17
necessary attributes of line, odd and even, etc., as corresponding
attributes of number—as evidence that Aristotle is still plainly
Platonic in his attitude. Might it not be suggested that the
nature of things, and not Plato, dictated this simple thought, and
that these are facts of which mathematics has still to take
account?
Take again Solmsen’s argument! to show that when he wrote
the Posterior Analytics Aristotle still believed in separately exist-
ing Platonic Forms. His only argument for this is the passage in
ii. 19. 10034-9 where.Aristotle says: ‘From experience—i.e. from
the universal now stabilized in its entirety within the soul, the
one beside the many which is a single identity within them all—
originate the skill of the craftsman and the knowledge of the man
of science.’ “The one beside the many’—this is the offending
phrase; and it must be admitted that Aristotle often attacks ‘the
one beside the many’, and insists that the universal exists only as
predicable of the many. But is the phrase capable only of having
the one meaning, and must we suppose that Aristotle always uses
it in the same sense? The passage is not concerned with meta-
physics; it is concerned with the growth of knowledge. No other
phrase in the chapter in the least suggests a belief in transcendent
Forms, and all (I would suggest) that Aristotle is referring to is the
recognition of the universal, not as existing apart from the many,
but as distinct from them while at the same time it is ‘a single
identity within them all'.: This, after all, is not the only passage
of the Posterior Analytics which refers to the Forms, and in none
of the others is their transcendent being maintained. In i. 11.
77%5 Aristotle points out that transcendent Forms are not needed
to account for demonstration, but only ‘one predicable of many’.
In i. 22. 83332 there is the famous remark: ‘The Forms we can
dispense with, for they are mere sound without sense; and even
if there are such things, they are not relevant to our discussion.’
In i. 24. 85518 he says : ‘Because the universal has a single meaning,
we are not therefore compelled to suppose that in these examples
it has being as a substance apart from its particulars—any more
than we need make a similar supposition in the other cases of
unequivocal universal predication.’
Aristotle states as the conditions of one term’s being predicable
καθ᾽ αὑτό of another that the subject term must be the first or
widest of which the predicate term can be proved, and that the
I p. 84.
4985 C
18 INTRODUCTION
predicate term must be proved of every instance of the subject
term, and illustrates this by the fact that equality of its angles to
two right angles is not a καθ᾽ αὑτό attribute of brazen isosceles
triangle, or even of isosceles triangle, nor on the other hand of
figure, but only of triangle.’ ‘The fixed order of this line'—figure,
triangle, isosceles triangle, brazen isosceles triangle (says Solmsen
on p. 87)—‘Aristotle owes without doubt to the Platonic διαί-
peots.’ But is not the fixed order part of the nature of things, and
does not Aristotle owe his awareness of it to the nature of things
rather than to Plato? We must not overdo the habit of attrib-
uting everyone’s thought to someone else’s previous thought;
there are facts that are obvious to any clear-headed person who
attends to them, and one of these is that, of the given set of terms,
triangle is the only one for which having angles equal to two right
angles is ‘commensurately universal’, neither wider nor narrower
than the subject. And if Aristotle need not have owed his insight
here to Plato, still less should we be justified in concluding that the
Posterior Analytics is early because in it Aristotle uses a chain of
Forms such as Plato might have used; for the fact is that any
logician at any time might have used it.
A whole section of Solmsen’s book? is devoted to showing the
substantial identity of Aristotle's theory of ἀρχαί with Plato’s
theory of ὑποθέσεις. There can be little doubt that Aristotle’s
theory of ἀρχαί finds its origin in Plato’s description of the method
of science, in the Republic. But the connexion is not more striking
than the difference. For one thing, Plato does not discriminate
between the different sorts of starting-point needed and used by
science. He simply says :3 ‘Those who occupy themselves with the
branches of geometry and with calculations assume the odd and
the even, and the figures, and three kinds of angles, and other
things akin to these in each inquiry ; and, treating themselves as
knowing these, they make them hypotheses and do not think fit
to give any further justification of them either to themselves or to
others.' Here, as Solmsen points out, it is not at first sight clear
whether what Plato depicts mathematics as assuming is terms or
propositions ; nor, if the latter, what kind of propositions. But I
believe Solmsen is right in supposing that what Plato is ascribing
to mathematicians is assumptions of the existence of Forms of
odd and even, triangles, etc., corresponding to the odd- or even-
numbered groups of sensible things, to sensible things roughly
* 735327743. * pp. 92-107. ? δῖος.
RELATION OF PRIOR TO POSTERIOR ANALYTICS 19
triangular in shape, etc. There is no question of assuming
definitions.
Observe now how much more developed and explicit is Aris-
totle's theory of ἀρχαί. He distinguishes first between common
principles which lie at the basis of all science, and special prin-
ciples which lie at the basis of this or that science. Among the
latter he distinguishes between hypotheses (assumptions of the
existence of certain entities) and definitions.! And finally he lays
it down explicitly that while science assumes the definitions of all
its terms, it assumes the existence only of the primary entities,
such as the unit, and proves the existence of the rest.?
Next, while Plato insists that the hypotheses of the sciences are
really only working hypotheses, useful starting-points, requiring
for their justification deduction, such as only philosophy can give,
from an unhypothetical principle, Aristotle insists that all the
first principles, common and special alike, are known on their own
merits and need no further justification. And while he retains the
name 'hypotheses' for one class of these principles, he is careful to
say of them no less than of the others that they are incapable of
being proved—not only incapable of being proved within the
science, as Plato would have agreed, but incapable of being proved
atall. The attempt to prove the special principles (which include
the hypotheses) is in one passage? mentioned but expressly said
to be incapable of success, just as the attempt to prove the com-
mon principles is in another passage* referred to merely as a
possible attempt, without any suggestion that it could succeed.
Further, while the entities which Plato describes mathemati-
cians as assuming are either Forms, or according to another
interpretation the 'intermediates' between Forms and sensible
things, the entities of which Aristotle describes mathematicians
as knowing the definition, and either assuming or proving (as the
case may be) the existence, are not transcendent entities at all
but the numbers and shapes which are actually present in sensible
things, though treated in abstraction from them.
In view of all this, valuable as Solmsen's discussion of Greek
mathematical method is, I think it does not aid his main conten-
tion, that the Posterior Analytics belongs to an early stage of
Aristotle's development in which he was still predominantly
under Plato's influence.
Solmsen claims* that the following chapters of the first book
| 22314724. 2 56*33-6. 3 46*16-25. — * 77?29-31. 5 p. 146 n. 2.
20 INTRODUCTION
are early, ‘so far as the problems found in them are concerned’:
7, 9, 17, 19 ff. (i.e. 19-23), 32, 33, and probably 24, 25, 28, 29. This
may be true, but, as we have seen, all these chapters, except 20,
22, 28, and 32, in their present form, at least, presuppose the
Prior Analytics. It may be added that ch. 22, so far from being
Platonic in tone, contains the harshest criticism of the theory of
Forms that Aristotle anywhere permits himself. The chapters
which Solmsen claims to be undoubtedly early, not merely dem
Problem nach, are 2, 3, 4-6. 7412, το. 76231-b34, 11. 7226-35. But
we have seen that ch. 2 probably presupposes the Prior Analytics,
and that ch. 3 has a definite reference to that work and involves
knowledge of the three figures. Thus we are left with chs. 4-6.
74512, 10. 76331—b34, 11. 77*26-35 as all that at the most could be
claimed with any confidence as earlier than the Prior Analytics—
just over four columns out of the thirty-seven and a half in the
book. These sections, which we might think of as earlier than the
Prior Analytics, since they make no use of the theory of syllogism,
we are not in the least bound to treat so, since the alleged Platonic
features which they are said to show are not specially Platonic at
all, but are such as might be found in almost any work of Aristotle.
After all, if the Posterior Analytics was later than the Prior, it
would be absurd to expect to find proof of this in every one of its
chapters. Since, then, a theory which makes so much of a patch-
work of the Posterior Analytics is inherently unlikely, and since
many chapters of it are much more clearly late than any are
clearly early, I prefer to regard the work, as a whole, as later than
the Prior Analytics—though I should not like to say that there
may not be some few chapters of it that were written before that
work.
But before finally committing ourselves to this view, we ought
to consider two general arguments that Solmsen puts forward.
One is this: that, having in the Topics recognized two kinds of
argument, a dialectical kind resting on τόποι and a scientific kind
resting on προτάσεις, and having discussed the first kind at length
in the Topics, the natural order would be that Aristotle should
next discuss the second kind, as he does in the Posterior Analytics,
and then and only then discuss what was common to both kinds,
as he does in the Prior Analytics. That is a natural order, but
another would have been equally natural. Already in the Topics
Aristotle shows himself well aware of the two kinds of argument.
* 83?32-5.
RELATION OF PRIOR TO POSTERIOR ANALYTICS 21
Might that awareness not have led him directly to trying to dis-
cover the form that was common to both kinds? And having got,
in the syllogism, a form that guaranteed the entailment of certain
conclusions by certain premisses, was it not natural that he should
then turn to ask what further characteristics than syllogistic
validity reasoning must possess in order to be worthy of the name
of demonstrative science? Apart from the matters of detail in
which, as I have pointed out, the Posterior Analytics presupposes
the Prior, I have the impression that throughout it Aristotle
betrays the conviction that he already has a method (viz. the
syllogism) which guarantees that if certain premisses are true
certain conclusions follow, but guarantees no more than this, and
that he is searching for a logic of truth to add to his logic of
consistency.
The second general argument of Solmsen's to which I would
refer is this. He contrasts! the assured mastery of its subject
which the Prior Analytics shows from start to finish with the
tentative, halting, repetitive manner characteristic of the Pos-
terror Analytics, and treats this as evidence of the greater maturity
of the first-named work. To this argument two answers naturally
present themselves. First, it is well known that some of Aristotle's
works have come down to us in a much more finished form than
others. For reasons which we do not know, some received much
more revision from him than others; and there is no difficulty in
seeing that the Prior Analytics was much more nearly ready for
the press, to use the modern phrase, than the Posterior. And
secondly, the nature of their subject-matters naturally leads to a
difference of treatment. The syllogism was a brilliant discovery;
but, once its principle was discovered, the detail of syllogistic
theory, the discrimination of valid from invalid syllogisms, was
almost a mechanical matter ; while the philosophical logic treated
of in the Posterior Analytics is a very difficult subject naturally
leading to hesitation, to false starts, and to repetition. Anyone
who has taught both elementary formal logic and philosophical
logic to students will at once see the truth of this, and the falsity
of treating the Posterior Analytics as immature because it treats
in a tentative way a subject which is in fact very difficult.
The connexion of the syllogism with an Ezdos-Kette is Solmsen’s
central theme ; and if he had confined himself to asserting this, and
the consequent priority, in Aristotle's thought, of the recognition
* pp. 143-4.
22 INTRODUCTION
of the first figure to that of the others, I should have agreed
heartily with him. But the Prior and the Posterior Analytics seem
to me to have the same attitude to the three figures; they both
recognize all three, and they both emphasize the logical priority
of the first figure; so that in their attitude to the figures I can see
no reason for dating the Posterior Analytics earlier than the Prior.
And in general, as I have tried to show, Professor Solmsen seems
to have under-estimated the maturity of thought in the Posterior
Analytics. He is undoubtedly right in urging that in the Posterior
Analytics there is very much which Aristotle has inherited from
Plato; but the same might be said of every one of Aristotle's
works, and the fact forms no sound reason for dating this work
specially early.
It is impossible to speak with any certainty of the date of
writing of either of the Analytics. The latest historical event
alluded to is the Third Sacred War, alluded to in An. Pr. 6912,
which can hardly have been written before 353 B.C. The allusion
to Coriscus in An. Post. 85224 takes us a little later, since it was
probably during his stay at Assos, from 347 to 344, that Aristotle
made acquaintance with Coriscus. These allusions may, no doubt,
be later additions to works written before these dates, but there
are more weighty considerations that forbid us to place the
Analytics at an earlier date. Aristotle was born in 384. We must
allow time for the writing of the early dialogues, which probably
occupied pretty fully Aristotle's twenties. We must allow time
for the writing of the Topics, not only a long work but one which
Aristotle himself describes as involving the creation of a new
τέχνη out of nothing, and as requiring much labour and much
time. The immense amount of detail involved in the writing of
the Prior Analytics must itself have occupied a considerable
period. In the Posterior Analytics Aristotle has plainly travelled
far from the Platonism of his early years. The year 347, in which
Aristotle was thirty-seven years old, is about as early a date as
can be assigned to the Posterior Analytics. It is harder to fix a
terminus ad quem. The allusion to Coriscus by no means pins the
writing of the Postertor Analytics down to the period 347-344 ; for
there are allusions to him in many of Aristotle's works, the writing
of which must have spread over a long time. There is, however,
one consideration which tells against fixing the date of the Analy-
tics much later than that period. Individual allusions in one work
! Soph. El. 183>16-184>3,
RELATION OF PRIOR TO POSTERIOR ANALYTICS 23
to another have not necessarily much weight, since they may be
later additions, but where we find an absence of cross-references
works which consistently refer back to another work are probably
later than it. There are cross-references between the Analytics
and the Topics, and if our general view be right the references in
the Topics to the Analytics must be later additions; and so is,
probably, the one reference in the De Interpretatione to the Prior
Analytics. But it is noticeable that while the Prior Analytics
are cited in the Eudemian Ethics and the Rhetoric, and the
Posterior Analytics in the Metaphysics, the Eudemian Ethics, and
the Nicomachean Ethics, there are no references backwards from
either of the Analytics to any work other than the Topics. This
points to a somewhat early date for the two Analytics, and they
may probably be assigned to the period 350-344, i.e. to Aristotle’s
late thirties. This allows for the wide distance Aristotle has
travelled from his early Platonism, while it still gives enough
time (though not too much, in view of his death in 322) for him to
write his great works on metaphysics, ethics, and rhetoric, and to
carry out the large tasks of historical research which seem to have
filled much of his later life.
ΠῚ
THE PURE OR ASSERTORIC SYLLOGISM
ARISTOTLE was probably prouder of his achievement in logic than
of any other part of his philosophical thinking. In a well-known
passage! he says: ‘In the case of all discoveries the results of
previous labours that have been handed down from others have
been advanced gradually by those who have taken them over,
whereas the original discoveries generally make an advance that
is small at first though much more useful than the development
which later springs out of them.’ This he illustrates by reference
to the art of rhetoric, and then he continues: ‘Of this inquiry, on
the other hand, it was not the case that part of the work had been
thoroughly done before, while part had not. Nothing existed at
all... . On the subject of reasoning we had nothing else of an
earlier date to speak of at all, but were kept at work for a long
time in experimental researches.'?
This passage comes at the end of the Sophistici Elenchi, which
is an appendix to the Topics; and scholars believe that these
! Soph. El. 183517-22. 2 Ib. 34-1843.
24 INTRODUCTION
works were earlier than the Prior Analytics, in which the doctrine
of the syllogism was worked out. If Aristotle was right in dis-
tinguishing his achievement in the Topics from his other achieve-
ments as being the creation of a new science or art out of nothing,
still more would he have been justified in making such a claim
when he had gone on to work out the theory of syllogism, which
we regard as the greatest of his achievements as a logician. ‘Out
of nothing’ is of course an exaggeration. In the progress of
knowledge nothing is created out of nothing; all knowledge, as he
himself tells us elsewhere,! proceeds from pre-existing knowledge.
There had been, in Greek thought, not a little reflection on logical
procedure, such as is implied for instance in Plato’s discussions of
the method of hypothesis, in the Phaedo and in the Republic. But
what Aristotle means, and what he is justified in saying, is that
there had been no attempt to develop a systematic body of thought
on logical questions. His claim to originality in this respect is
undoubtedly justified.
The question remains, what Aristotle meant to be doing in his
logical inquiries. Did he mean to provide a purely contemplative
study of the reasoning process, or to aid men in their reasoning?
In the most elaborate classification of the sciences which he offers
us (in Metaphysics E)—that into the theoretical, the practical, and
the productive sciences—logic nowhere finds a place. Yet certain
passages make it probable that he would rather have called it an
art than a science. This is in no way contradicted by the fact that
in a great part of his logical works heis offering a purely theoretical
account of inference. It is inevitable that the exposition of any
art must contain much that is purely theoretical; for without the
theoretical knowledge of the material of the art and the condi-
tions under which it works, it is impossible to provide the artist
with rules for his practical behaviour.
Aristotle's practical purpose in writing his logic is indicated
clearly by the passage of comment on his own work to which I
have already referred. ‘Our programme was’, he says,” ‘to discover
some faculty of reasoning about any theme put before us from the
most generally accepted premisses that there are.’ And again
*we proposed for our treatise not only the aforesaid aim of being
able to exact an account of any view, but also the aim of ensuring
that in standing up to an argument we shall defend our thesis in
the same manner by means of views as generally held as possible’.4
© An, Post. 7131-2. 2 Soph. El. 183437-8. 3 Ib. 18355-6.
THE PURE OR ASSERTORIC SYLLOGISM 25
And ‘we have made clear . . . the number both of the points with
reference to which, and of the materials from which, this will be
accomplished, and also from what sources we can become well
supplied with these: we have shown, moreover, how to question
or arrange the questioning as a whole, and the problems con-
cerning the answers and solutions to be used against the reason-
ings of the questioner’. And a little later he definitely refers to
logic as an art, the art which teaches people how to avoid bad
arguments, as the art of shoemaking teaches shoemakers how to
avoid giving their customers sore feet.?
This passage, it is true, is an epilogue to his treatment of
dialectical reasoning, in the Topics; but his attitude to the study
of the syllogism in Prior Analytics iis the same. That work begins,
indeed, with a purely theoretical study of the syllogism. But after
this first section? there comes another* which begins with the
words : ‘We must now state how we may ourselves always have a
supply of syllogisms in reference to the problem proposed, and by
what road we may reach the principles relative to the problem;
for perhaps we ought not only to investigate the construction of
syllogisms, but also to have the power of making them.' This
purpose of logic—the acquiring of the faculty of discovering
syllogisms—is later* again mentioned as one of the three main
themes of Prior Analytics i.
So far, then, Aristotle’s attitude to logic is not unlike his
attitude to ethics. In his study of each there is much that is pure
theory, but in both cases the theory is thought of as ancillary to
practice—to right living in the one case, to right thinking in the
other. But a change seems to come over his attitude to logic. In
the second book of the Prior Analytics, which scholars believe to
be later than the first, ch. 19 seems to be the only one that is
definitely practical. In the Posterior Analytics there seems to be
none that is so.
It is with Prior Analytics i that we shall be first concerned ; for
it is here that Aristotle, by formulating the theory of syllogism,
laid the foundation on which all subsequent logic has been built
up, or sowed the seed from which it has grown. How did Aristotle
come by the theory of the syllogism? He nowhere tells us, and
we are reduced to conjecture. Now in one passage he says that
the Platonic 'division' 'is but a small part of the method we have
! [b. 8-12. 2 Th. 18481-8. 3 i. 1-26.
4 ij. 27-30. 5 4792-5. $ 46231-3.
26 INTRODUCTION
described; for division is, so to say, a weak syllogism’; and
Heinrich Maier has fastened on the Platonic ‘division’ as the
probable source of the theory of syllogism. He thinks that re-
flection on the shortcomings of the Platonic method of division
(which Aristotle points out in detail) led him to formulate his own
theory. But there is force in Shorey’s remark’ that ‘the insistent
and somewhat invidious testing of the Platonic diaeresis by the
syllogism reads more like the polemical comparison of two finished
and competing methods than the record of the process by which
Aristotle felt the way to his own discovery’. In particular, it is
clear that syllogism has no connexion with the characteristic
element in Platonic division, viz. the recognition of species
mutually exclusive, and exhaustive of the genus; there is no
‘either . . . or’ in the syllogism as Aristotle conceives it. But there
is another element in Platonic division with which we.may well
connect the syllogism, viz. the recognition of chains of classes, in
which each class is a specification of that above it in the chain.
And, as Shorey pointed out, there is one passage in which Plato
comes very near to the principle of the syllogism. In Phaedo
104 e-105 b he says that the presence of a specific nature in an
individual introduces into it the generic nature of which the
specific nature is a specification; threeness introduces oddness
into, and excludes evenness from, any individual group of three
things. Now Aristotle’s usual mode of formulating a premiss—
the mode that is almost omnipresent in the Prior Analytics—is
to say that one thing ‘belongs to’ another. Plato is thus in germ
formulating the syllogism ‘Oddness belongs to threeness, Three-
ness belongs to this group, Therefore oddness belongs to this
group’, and the syllogism ‘Evenness does not belong to threeness,
Threeness belongs to this group, Therefore evenness does not
belong to this group'—typical syllogisms in Barbara and Celarent.
Plato is not writing logic. His interest is metaphysical; he is
working up to a proof of the immortality of the soul. But he
recognizes the wider bearings of his contention. He goes on to
say? that instead of his old and safe but stupid answer—his
typical answer in the first period of the ideal theory—to the
question what makes a body hot, viz. that heat does, he will now
give a cleverer answer, such as the answer ‘fire docs so' ; the general
principle being that the presence of a specific nature in a subject
entails the presence of the corresponding generic nature in it; i.e.,
' Class. Philology, xix. 6. 2 rosb—c.
THE PURE OR ASSERTORIC SYLLOGISM 27
he treats it as a universal metaphysical fact that the presence of
generic natures in particular things is mediated by the presence
of specific forms of these generic natures. And in his theory of
first-figure syllogisms Aristotle does little more than give a logical
turn to this metaphysical doctrine. The connexion of Aristotle’s
theory of syllogism with this passage of the Phaedo seems to be
made clear, as Shorey points out, by the occurrence not only of
the word παρεῖναι, a word very characteristic of the Theory of
Ideas, in Aristotelian passages,! to express the relation of predi-
cate to subject in the propositions of a syllogism, but also of the
more definite and unusual words ἐπιφέρειν (‘to bring in’) and
συνεπιφέρειν (‘to bring in along with itself’) to express the intro-
duction of the generic nature by the specific.’?
The occurrence of these words in the Tofics in this very special
meaning is clear evidence of the impression which the Phaedo
passage made on Aristotle's mind. But the passage does not seem
to have immediately suggested to him the theory of syllogism ;
for the Topics passages have no reference to that. We may, how-
ever, suppose that in course of time, as Aristotle brooded over the
question what sort of data would justify a certain conclusion, he
was led to give a logical turn to Plato's metaphysical doctrine,
and tosay: ‘That which will justify us in stating that C is A, or
that it is not A, is that C falls under a universal B which drags the
wider universal A with it, or under one which excludes A.’ This
is very easily translated into the language which he uses in
formulating the principle of the first figure:;? “Whenever three
terms are so related to one another that the last is contained in
the middle as in a whole, and the middle is either contained in or
excluded from' (the same alternatives of which the PAaedo takes
account) 'the first as in or from a whole, the extremes must be
related by a perfect syllogism.' And the fact that only the first
figure answers to Plato's formula is the reason why Aristotle puts
it in the forefront, describes only first-figure arguments as perfect
(i.e. self-sufficient), and insists on justifying all others by reduc-
tion to that figure. Aristotle's translation of Plato's metaphysica]
doctrine into a doctrine from which the whole of formal logic was
to develop is a most remarkable example of the fertilization of
one brilliant mind by another.
1 An. Pr. 4444, 5, 45?10; Top. 126b22, 25.
2 Cf. Phaedo 104 e 10, 105a 3, 4, d τὸ with An. Pr. 527, Top. 14416, 17, 27,
29, 30, 157223. 3 An. Pr. 25>32-5.
28 INTRODUCTION
The formulation of the dictum de omni et nullo which I have just
quoted might seem to commit Aristotle to a purely class-inclusion
theory of the judgement, and such a theory does indeed play a
part in his thought ; for it dictates the choice of the phrases major
term, middle term, minor term, which he freely uses. But it by
no means dominates his theory of the judgement. For, in the first
place, his typical way of expressing a premiss (a way that is almost
omnipresent in the Prior Analytics) is not to say 'B is included in
A’, but to say ‘A belongs to B’, where the relation suggested is not
that of class to member but that of attribute to subject. And in
the second place, it is only in the Prior Analytics that the class-
inclusion view of judgements appears at all. In the De Interpre-
latione, where he treats judgements as they are in themselves, not
as elements in a syllogism, he takes the subject-attribute view of
them; and in the Posterior Analytics, where he treats them as
elements in a scientific system and not in mere syllogisms, the
universality of judgements means the necessary connexion of sub-
ject and predicate, not the inclusion of one in the other.
We may next turn to consider how Aristotle assures himself of the
validity of the valid and of the invalidity of the invalid moods. To
begin with, he only assumes the dictum de omni et nullo, which as we
have seen guarantees the validity of Barbara and Celarent, in the
first figure. It equally guarantees the validity of Darii and Ferio,
and of this he offers no proof. But when he comes to consider other
possible moods, he has no general principle to which he appeals ; he
appeals in every case to a pair of instances from which we can see
that the given combination of premisses cannot guarantee any con-
clusion. Take, for instance, the combination All B is A, NoC is B.
We cannot infer a negative; for, while all men are animals and
no horse is a man, all horses are animals. Nor can we infer an
affirmative ; for, while all men are animals and no stones are men,
no stones are animals.! The difference of procedure that Aristotle
adopts is to a certain degree justifed. To point out that all
animals are living things, all men are animals, and all men are
living things would not show that Barbara is a valid form of
inference; while the procedure he follows with regard to the
combination All B is 4, NoC is B does show that that combination
cannot yield a valid conclusion— provided that the propositions
he states ('All men are animals', etc.) are true. Yet it is not a
completely satisfactory way of proving the invalidity of invalid
1 An. Pr. 2642-9.
THE PURE OR ASSERTORIC SYLLOGISM 29
combinations ; for instead of appealing to their form as the source
of their invalidity, he appeals to our supposed knowledge of
certain particular propositions in each case. Whereas in dealing
with the valid moods he works consistently with ABI for the
first figure, MNA for the second, ΠΡΣ for the third, and, by
taking propositional functions denoted by pairs of letters, not
actual propositions about particular things, makes it plain that
validity depends on form, and thus becomes the originator of
formal logic, he discovers the invalidity of the invalid moods
simply by trial and error. The insufficiency of the proof is veiled
from his sight by the fact that he takes it to be not a mere matter
of fallible experience, but self-evident, that all horses are animals
and no stones are animals—relying on the correctness of a system
of classification in which certain inclusions and exclusions are
supposed to be already known. He would have done better to
point to the obvious fact that the propositions 'All B is A and
No C is B’ have no tendency to show either that all or some or no
C is A or that some C is not A.
It is only syllogisms in the first figure that are directly validated
by the dictum de omni et nullo. For the validation of syllogisms in
the other two figures Aristotle relies on three other methods—con-
version, reductio ad impossibile, and éx0ecw—about each of which
something must be said.
(1) All the moods of the second and third figures but four! are
validated by means of the simple conversion of premisses in E or
I, with or without change of the order of the premisses and a
corresponding conversion of the conclusion. Cesare, for instance,
is validated by simple conversion of the major premiss; No P is
M, All S is M becomes No M is P, All S is M, from which it
follows directly that no S is P. Camestres is validated by con-
version of the minor premiss, alteration of the order of the
premisses, and conversion of the resultant conclusion; All P is M,
No S is M becomes No M is S, All P is M, from which it follows
that no P is S, and therefore that no S is P. To such validation
no objection can be taken. But in the discussion of conversion
which Aristotle prefixes to his discussion of syllogism he says?
that All B is A entails that some A is B; and he uses this form of
conversion in validating syllogisms in Darapti and Felapton. In
this he comes into conflict with a principle which plays a large
1 Viz. Cesare, Camestres, Festino, Disamis, Datisi, Ferison.
2 2527-10. 3 28417-22, 26-9.
30 INTRODUCTION
part in modern logic. In modern logic a class may be a class with
no members, and if B is such a class it may be true that all B is
A, and yet it will not be true that some A is B. In other words,
the true meaning of All B is A is said to be There is no B that is
not A, or If anything is B, it is A; and Aristotle is charged with
having illegitimately combined with this the assumption that
there is at least one B, which is needed for the justification of the
inference that some A is B.
It must be admitted that Aristotle failed to notice that Al] B is
A, as he understands it, is not a simple proposition, that it indeed
includes the two elements which modern logic has detected. But
Ishould beinclined to say with Cook Wilson! that Aristotle's inter-
pretation of All B is A isthenaturalinterpretation ofit, and that the
meaning attached to it by modern logic is more properly expressed
by the form There is no B that is not A, or If anything is B, it
is A. Aristotle's theory of the proposition is defective in that he has
failed to see the complexity of the proposition All Bis A, as he in-
terprets it ; but his interpretation of the proposition is correct, and
from it the convertibility of All Bis A into Some A is B follows.
(2) Wherever moods of the second and third figures can be
validated by conversion, Aristotle uses this method. But it is
frequently supplemented by the use of reductio ad imposstbile, and
for the moods Baroco, in the second figure, and Bocardo, in the
third, which cannot be validated by conversion, reductio becomes
the only or main method of proof. He describes it as one form of
συλλογισμὸς ἐξ b$moÜécews. His references to argument ἐξ ὑπο-
θέσεως in general, or to the kinds of it other than reductio ad im-
possibile,’ are so slight that not much need be said about it in this
1 Statement and Inference, i. 236-7. A somewhat similar point of view is
well expressed in Prof. J. W. Miller's T'he Structure of Aristotelian Logic, in
which, writing from the point of view of a modern logician, he urges that the
modern interpretation of ‘class’ is not the only possible nor the only proper
interpretation of it; that it is equally proper to interpret a class as meaning
‘those entities which satisfy a propositional function, provided that there is
at least one entity which does satisfy the function and at least one entity
which does not satisfy the function’; and that Aristotle’s system, which
adopts this interpretation (though in fact the condition ‘and at least one
entity which does not satisfy the function’ is not required for the justification
of Aristotle’s conversion of All B is A), falls into place as one part of the
wider system which modern logic has erected on its wider interpretation of
‘class’. See especially Prof. Miller's pp. 84-95. 2 40b25-6, 412378.
3 415337-Pt, 45915-20, 5o*16-b4. Aristotle's view, and the development
THE PURE OR ASSERTORIC SYLLOGISM 31
general review ; clearly it played no great part in his logical theory.
This much is clear, that he analysed it into a syllogistic and a non-
syllogistic part. If a certain proposition A is to be proved, it is
first agreed by the parties to the argument that A must be true
if another proposition B can be proved. This agreement, and the
use made of it, are the non-syllogistic part of the argument ; the
syllogistic part is the proof of the substituted proposition (τὸ
μεταλαμβανόμενον).; B having been proved, A follows in virtue of
the agreement (δι᾽ ὁμολογίας, διὰ συνθήκης, ἐξ ὑποθέσεως). E.g.,
if we want to prove that not all contraries are objects of ἃ single
science, we first get our opponent to agree that this follows if not
all contraries are realizations of a single potentiality. Then we
reason syllogistically, Health and disease are not realizations of a
single potentiality (since the same thing cannot be both healthy
and diseased),3 Health and disease are contraries, Therefore not
all contraries are realizations of a single potentiality. Then by
virtue of the agreement we conclude that not all contraries are
objects of a single science.*
Aristotle divides reductio ad impossibile similarly into two parts
—one which is a syllogism and one which establishes its point by
the use of a hypothesis The two parts are as follows: To
validate, for example, the inference involved in Baroco, All P is
M, Some S is not M, Therefore some S is not P, we say: (1) Let
it be supposed that all S is P. Then, since all P is M, all S would
be M. (2) But we know that some S is not M. Therefore, since
we know that all P is M, the other premiss used in (r)—that all S
is P—must be untrue, and therefore that some S is not P must be
true.
At first sight we might think that the ὑπόθεσις is the supposition
that all S is P (which in fact Aristotle refers to as a ὑπόθεσις) δ
But that is inconsistent with Aristotle's dissection of the argu-
ment into two parts. For that hypothesis is used in the first part,
which he expressly describes as an ordinary syllogism, while it is
the second part that he describes as reasoning ἐξ ὑποθέσεως. The
ὑπόθεσις referred to in this phrase, then, must be something
different; and the natural inference is that it is the hypothesis
that, of two premisses from which a false conclusion follows, that
from it of Theophrastus' theory of hypothetical syllogism, are discussed at
length by H. Maier (ii. a 249-87). 1 41339, 45P18. 2 41340, 50718, 25.
3 Clearly a bad reason; but the argument is only meant to be dialectical.
* 5041g~28. 5. 41323-7, 32-4, 50229~32. $ a1*32.
32 INTRODUCTION
which is not known to be true must be false, and its contradictory
true. That this, and not the supposition that all S is P, is the
ὑπόθεσις referred to is confirmed by the distinction Aristotle
draws between reductio and other arguments ἐξ ὑποθέσεως, that
while in the latter the ὑπόθεσις must be expressly agreed by the
parties, in the former this need not happen, διὰ τὸ φανερὸν εἶναι
τὸ ψεῦδος. The reference is to an assumption so obvious that it
need not be mentioned, and this must be the assumption that
premisses leading to a false conclusion cannot both be true.
There is thus an important difference between reductzo and other
arguments ἐξ ὑποθέσεως. The latter rest on a mere agreement
between two persons, and are therefore merely dialectical; the
former rests on an indisputable principle, and is therefore in-
disputably valid.
(3) Finally, in addition to one or both of these methods of
validation, Aristotle sometimes uses a third method which he
calls ἔκθεσις. Take, for instance, the mood Darapti: All S is P, All
S is R, Therefore some R is P. This must be so, says Aristotle; for
if we take a particular S, e.g. N, it will be both P and R, and
therefore some FR (at least one R) will be P.? At first sight Aris-
totle seems to be merely proving one third-figure syllogism by
means of another which is no more obviously valid. He wants to
show that if all S is P and all S is R, some R is P; and he does so
by inferring from ‘All S is P' and ‘N is S’ that N is P, and from
‘All S is R' and ‘N is S' that N is R, and finally from 'N is P' and
'N is R' that some R is P; which is just another third-figure
syllogism. If this were what he is doing, the validation would be
clearly worthless. He can hardly have meant the argument to be
taken so; yet how else could he mean it to be taken? He must,
I think, mean to be justifying the conclusion by appealing to
something more intuitive than abstract proof—to be calling for
an act of imagination in which we conjure up a particular S which
is both R and P and can see by imagination rather than by
reasoning the possession of the attribute P by one R?
Aristotle's essential problem, in the treatment of the three
figures, is to segregate the valid from the invalid moods. His pro-
cedure in doing so is open to criticism at more than one point. It
! 50232-8. The account I have given in Aristotle, 36-7, requires correction
at this point. 2 28322-6.
3 This is approximately Alexander’s explanation: ἢ οὐ τοιαύτη ἡ δεῖξις ἡ
χρῆται" ὃ yàp δι’ ἐκθέσεως τρόπος δι᾽ αἰσθήσεως γίνεται (99. 31-2).
THE PURE OR ASSERTORIC SYLLOGISM 33
most nearly approaches perfection with regard to the valid moods
of the first figure ; in dealing with them he simply claims that it is
self-evident that any two premisses of the form All B is A, All
Cis B, or No Bis A, AllC is B, or All B is A, Some C is B, or No
B is A, Some C is B, warrant a certain conclusion in each case.
But in his treatment of the invalid moods he does not point out
the formal error involved in drawing a conclusion, e.g. that of
reasoning from knowledge about part of a class to a conclusion
about the whole. He relies instead on empirical knowledge (or
supposed knowledge) to show that, major and middle term being
related in a certain way, and middle and minor term being related
in a certain way, sometimes the major is in fact true of the minor
and sometimes it is not. He thus shows that certain forms of
premiss cannot warrant a conclusion, but he does not show why
they cannot do so.
With regard to the other two figures, his chief defect is that he
never formulates for them (as modern logicians have done) dis-
tinct principles of inference just as self-evident as the dicium de
omni el nullo is for the first figure, but treats them throughout—
or almost throughout—as validated only by means of the first
figure. In fact the only points at which he escapes from the
tyranny of the first figure are those at which he uses ἔκθεσις to
show the validity of certain moods. We have seen that his con-
centration on the first figure follows from the lead given by Plato.
But it would be a mistake to treat it as a historical accident.
We must remember that Aristotle undertook the study of syllo-
gism as a stage on the way to the study of scientific method. Now
science is for him the knowledge of why things are as they are.
And the plain fact is that only the first figure can exhibit this.
Take the second figure. If we know that nothing having a certain
fundamental nature has a certain property, and that a certain
thing has this property, we can infer that it has not that funda-
mental nature. But it is pot because it has that property that it
has not that fundamental nature, but the other way about. The
premisses supply a ratio cognoscendi, but not the ratto essendi, of
the conclusion. Or take the third figure. If we know that all
things having a certain fundamental nature have a certain pro-
perty and also a certain other property, we can certainly infer
that some things having the second property also have the first ;
but the fact that certain things have each of two properties is not
the réason why the properties are compatible ; again we have only
4985 Dp
34 INTRODUCTION
a ratio cognoscendi. This is true of all arguments in the second or
third figure. Now not all arguments in the first figure give a ratio
essendi. If we know that all things having a certain property must
have a certain fundamental nature, and that a certain class of
things have that property, we can infer that they have that
fundamental nature, but we have not explained why they have it.
But with properly chosen terms a first-figure argument can
explain facts. If we know that all things having a certain funda-
mental nature must in consequence have a certain property, and
that a certain class of things have that fundamental nature, we
can know not only that but why they must have that property.
In other words, while the other two figures can serve only for
discovery of facts, the first figure can serve both for discovery and
for explanation.
There is another difference between the first figure and the
other two which helps to explain and in part to justify the pre-
dominant position that Aristotle assigns to the first figure; that is,
its greater naturalness. It is natural that a term which is subject
in a premiss should be subject in the conclusion, and that a term
which is predicate in a premiss should be predicate in the con-
clusion ; and it is only in the first figure that this happens. In the
second figure, where P and S are subjects in the premisses, one of
them must become predicate in the conclusion ; and what is more,
there is nothing in the form of the premisses to make either P or
S a more natural predicate for the conclusion than the other. In
the third figure, where P and S are predicates in the premisses,
one of them must become subject in the conclusion; and in the
form of the premisses there is nothing to suggest which of the
two terms is to become subject.
The difference between the three figures lies, according to
Aristotle, in the fact that in the first the connecting term is
predicated of the minor (i.e. of the subject of the conclusion) and
has the major (i.e. the predicate of the conclusion) predicated of
it, in the second the connecting term is predicated of both, and in
the third it is subject of both. This naturally raises the question
why he does not recognize a fourth figure, in which the connecting
term is predicated of the major and has the minor predicated of
it. The answer is that his account of the syllogism is not derived
from a formal consideration of all the possible positions of the
middle term, but from a study of the way in which actual thought
proceeds, and that in our actual thought we never do reason in the
THE PURE OR ASSERTORIC SYLLOGISM 35
way described in the fourth figure. We found a partial unnatural-
ness in the second and third figures, due to the fact that one of
the extreme terms must become predicate instead of subject in the
second figure, and one of the extreme terms subject instead of
predicate in the third; the fourth figure draws a completely
unnatural conclusion where a completely natural conclusion is
possible. From All M is P, All S is M, instead of the natural
first-figure conclusion, All S is P, in which P and S preserve their
roles of predicate and subject, it concludes Some P is S, where
both terms change their roles.
A distinction must be drawn, however, between the first three
moods of the fourth figure and the last two. With the premisses
of Bramantip (All A is B, All B is C) the only natural conclusion
is Ali A is C, with those of Camenes the only natural conclusion is
No A isC, with those of Dimaris it is Some A is C ; and if we want
instead from the given premisses to deduce respectively Some C
is A, NoC is A, SomeC is A, the natural way to do this is to draw
the natural conclusions, and then convert these. And this is how
Aristotle actually treats the matter, instead of treating Braman-
tip, Camenes, Dimaris as independent moods.' The position with
regard to Fesapo (No A is B, All B is C, Therefore some C is not
A) and Fresison (No A is B, Some B is C, Therefore some C is
not A) is different; here no first-figure conclusion can be drawn
from the premisses as they stand ; for if we change the order of the
premisses to get them into the first-figure form, we get a negative
minor premiss, which in the first figure can yield no conclusion.
To get first-figure premisses which will yield a conclusion we must
convert both premisses, and then we get in both cases No B is
A, Some C is B, Therefore some C is not A. This also Aristotle
points out.2 Thus he recognizes the validity of all the inferences
which later logicians treated as moods of a fourth figure, but
treats them, more sensibly, by way of two appendixes to his treat-
ment of the first figure.
There is a certain misfit between Aristotle's definition of syllo-
gism and his actual account of it. His definition is a definition of
the meaning of the word as it was occasionally already used in
ordinary Greek, and it is a definition which might stand as a
definition of inference in general—cevAAoywpós ἐστι λόγος ἐν ᾧ
τεθέντων τινῶν ἕτερόν τι τῶν κειμένων ἐξ ἀνάγκης συμβαίνει τῷ ταῦτα
elvai.3 But in his actual usage he limits συλλογισμός to inference
! An. Pr. 5333-12. 2 29319-26. 3 24b18-20.
36 INTRODUCTION
whose nerve depends on one particular relation between terms,
that of subject and predicate. It is now, of course, well known that
many other relations, such as that of ‘equal to’ or ‘greater than’,
can equally validly serve as the nerve of inference. The fact that
he did not see this must be traced to the fact that while he rightly
(in the Posterior Analytics) treats mathematical reasoning as the
best example of strict scientific reasoning, he did not in fact pay
close attention to the actual character of mathematical reasoning.
In a chain of mathematical reasoning there are often syllogisms
included, but there are also many links in the chain which depend
on these other relations and cannot be reduced to syllogisms. For
his examples of reasoning Aristotle depended in fact more on
non-scientific reasoning in which special relations such as that of
equality do not play a very large part, and subsumption plays a
much larger part. Yet it was not a mere historical accident, due
to the atmosphere of general and non-scientific argument in which
he was brought up, that he concentrated on the syllogism. The
truth is that while many propositions exhibit such special rela-
tions, all propositions exhibit the subject-predicate relation. If
we say A is equal to B, we say that A is related to B by the
relation of equality, but we also say that A is related to equality
to B by the subject-predicate relation. And it was only proper
that the earliest theory of reasoning should concentrate on the
common form of all judgement rather than on particular forms
which some judgements have and others have not. It is true that
often, while consideration of the general form will not justify
any inference (since a fallacy of four terms will be involved),
attention to the special form will do so. But Aristotle at least does
not make the mistake of trying to reduce the relational forms
to syllogistic form. He simply fails to take account of them ; he
does not say what is false, but only fails to say something that
is true.
There is this further to be said, that while it is possible to work
out exhaustively the logic of valid syllogistic forms, and Aristotle
in fact does so with complete success as regards the assertoric
forms of judgement (though he makes some slips with regard to
the problematic forms), it is not possible to work out exhaustively
the logic of the various relational forms of judgement. We can
point out a certain number of types, but we can never say these
are all the valid types there can be. The logic of syllogism is thus
the fundamental part of the logic of inference, and it was in
THE PURE OR ASSERTORIC SYLLOGISM 37
accordance with the proper order of things that it should be the
first to be worked out.
Aristotle not infrequently speaks as if there were other forms of
inference than syllogism—induction, example, enthymeme. But
there is an important chapter! in which he argues that if inference
is to be valid it must take the syllogistic form ; and that this was
his predominant view is confirmed when we look at what he says
about these other types. He means by induction, in different.
places, quite different things. There is the famous chapter of the
Prior Analytics in which induction is reduced to syllogistic form.?
But the induction which is so reduced is the least important kind
of induction—the perfect induction in which, having noted that
membership of any of the species of a genus involves possession
of a certain attribute, we infer that membership of the genus
involves it. More often ‘induction’ is used by Aristotle to denote
something that cannot be reduced to syllogistic form, viz. the
process by which, from seeing for instance that in the triangle we
have drawn (or rather in the perfect triangle to which this is an
approximation) equality of two sides involves equality of two
angles, we pass to seeing that any isosceles triangle must have two
angles equal. This cannot be regarded as an inference; if you
regard the first proposition as a premiss you find that the second
does not follow from it; the ‘induction’ is a fresh act of insight.
Thus the only sort of induction which Aristotle, in all probability,
regarded as strict inference is that which he reduces to syllogism.
The kind of inference which he calls example is just an induction
followed by a syllogism; and enthymeme is just a syllogism in
which the propositions are not known to be true but believed to
be probable.
There are, however, two kinds of inference which Aristotle
regards as completely valid and yet not syllogistic. One is the
non-syllogistic part of reductio ad impossibile. In connexion with
reductio he makes the remark that the propositions by which a
proposition is refuted are not necessarily premisses, and the
negative result the conclusion, sc. of a syllogism. The same
point is made in another passage, in which he points out the
existence of arguments which, while conclusive, are not syllo-
gistic; e.g. 'Substance is not annihilated by the annihilation of
what is not substance ; but if the elements out of which a thing is
made are annihilated, that which is made out of them is de-
| An. Pr. i. 23. 2 ii, 23. 3 4n. Post. 87420-2.
38 INTRODUCTION
stroyed ; therefore any part of substance must be substance’; or
again, ‘If it is necessary that animal should exist if man does, and
that substance should exist if animal does, it is necessary that
substance should exist if man does. ... We are deceived in such
cases because something necessary results from what is assumed,
since the syllogism also is necessary. But that which is necessary
is wider than the syllogism ; for every syllogism is necessary, but
not everything that is necessary is a syllogism.’ Here is a clear
recognition of inference that is conclusive but not syllogistic, and
we must regret that Aristotle did not pursue farther what he here
so clearly recognizes.
Some logicians have attacked the whole theory of syllogism on
the ground that syllogism is not a valid inference at all but a
petitio principii. Now the essence of a petitio principit is that it
assumes two propositions of which one or other cannot be known
unless the conclusion is already known; and the charge of petitio
$rincipii against the syllogism must therefore assert that either
the major premiss or the minor premiss presupposes knowledge
of the conclusion. This charge is nowhere, so far as I know, better
discussed than it is by Joseph in his Introduction to Logic?
There are two ways, as he points out, of interpreting the major
premiss of a syllogism, which would in fact reduce syllogism to a
petitio principu. If the major premiss is an empirical generaliza-
tion, we cannot know it to be true unless we already know the
conclusion. We say in the syllogism All B is A, All C is B,
Therefore all C is A; but it All B is A is an empirical generaliza-
tion we do not know it to be true unless we already know that all
C is A. On the other hand, if All B is A is merely an explanation
of the sense in which the name for which B stands is being used,
we have no right to say All C is B unless we already know that
all C is A. Thus on one interpretation of the major premiss, that
premiss commits a petitio principii ; and on another interpretation
of the major premiss, the minor premiss commits one. The value
of syllogism thus depends on the major premiss's being neither
an empirical generalization nor a verbal definition (or partial
definition). It depends in fact on its being both a priori and
synthetic; and of course the possibility of our knowing such
propositions has been severely attacked by the Positivist school.
But it has outlived such attacks in the past and is likely to do so
again. The arguments brought in support of the attack are not
1 An, Pr. 47222-3535. 2 278-82.
THE PURE OR ASSERTORIC SYLLOGISM 39
very strong, and for my own part I think they cannot stand up
against criticism.' It seems probable that Aristotle's theory of
syllogism will not founder in a sea of discredit, but will always be
regarded as the indispensable foundation of formal logic.
Aristotle nowhere defends the syllogism against the charge of
petitio principii, which we first find in Sextus Empiricus ;? but he
would have had his own defence. He would have had to admit
that the form of the major premiss, ‘All B is A’ or ‘A belongs to
all B’, is compatible with its being either an empirical generaliza-
tion or a nominal definition of B, and that when it is either of
these, the syllogism is a petitio principii. But he would have
pointed out that in dealing with a certain type of subject-matter
(e.g. in mathematics) a universal truth may be ascertained by
the consideration of even a single instance—that the generic
universal is different from the enumerative. You may know by a
universal proof that all triangles have their angles equal to two
right angles, without having examined every triangle in the
world,? and even without having examined the various species of
triangle. Again, to the objection that we have no right to say
that all C is B unless we know it to have all the attributes of
B, including A, he would have replied by his distinction of prop-
erty from essence. Among the attributes necessarily involved
in being B he distinguishes a certain set of fundamental attributes
which is necessary and sufficient to distinguish B from everything
else ; and he regards its other necessary attributes as flowing from
and demonstrable from these. To know that C is B it is enough
to know that it has the essential nature of B—the genus and the
differentiae ; it is not necessary to know that it has the properties
of B. Thus each premiss may be known independently of the
conclusion, and neither premiss need commit a petitio principti.
The objector might then say that the premisses taken together
commit a petitio principii, that we cannot know both without
already knowing the conclusion. To this Aristotle would have
replied by a distinction between potential and actual knowledge.
In knowing the premisses we potentially know the conciusion ;
but to know anything potentially is not to know it, but to be
in such'a state that given one further condition we shall pass
immediately to knowing it. The further condition that is needed
! Such, for instance, as is brought against them by Dr. Ewing in Proc. of
Arist. Soc. x1 (1939-40), 207-44.
2 Pyrrh, Hypot. 195-203. 3 An. Pr, 6738-21.
40 INTRODUCTION
in order to pass from the potential to the actual knowledge of the
conclusion is the seeing of the premisses in their relation to each
other: οὐ yàp ἐπίσταται ὅτι τὸ A τῷ Γ᾽, μὴ συνθεωρῶν τὸ καθ᾽
ékárepov,! one does not know the conclusion without contemplating
the premisses together and seeing them in their mutual relation'.
Thus while both premisses together involve the conclusion (with-
out which inference would be impossible), knowledge of them does
not presuppose knowledge of the conclusion; inference is a real
process, an advance to something new (ἕτερόν τι τῶν κειμένων) ,2
the making explicit of what was implicit, the actualizing of
knowledge which was only potential?
IV
THE MODAL SYLLOGISM
ARISTOTLE does not in the Prior Analytics tell us what he means
by a 'necessary premiss' ; he treats as self-evident the distinction
between this and one which only professes to state a mere fact.
The test he applies is simply the presence or absence of the word
ἀνάγκη. But while the distinction between a necessary and an
assertoric premiss is this purely grammatical one, as soon as the
question of validity arises we must take account of the fact that
a necessary proposition is true only if what it states is a neces-
sary fact; and there is for Aristotle a most important distinc-
tion between a necessary fact and a mere fact. In his choice of
examples, in An. Pr. i. g-11 he seems sometimes to be obliterating
this distinction. Consider for instance 305-6. To show that, in
the first figure, premisses of the form EJ” warrant only an asser-
toric, not an apodeictic, conclusion he takes the example
'(a) No animal is in movement.
(b) Some white things are necessarily animals.
But it is not a necessary fact that some white things are not in
movement.' And then consider ib. 33-8. To show that, in the
second figure, premisses of the form A"E warrant only an asser-
toric, not an apodeictic, conclusion he takes the example
'(c) Every man is necessarily an animal.
(d) Nothing white is an animal.
But it is not a necessary fact that nothing white is a man.'
It looks as if in (b) Aristotle were treating it as a necessary
fact that some white things are animals, and in (4) treating it
as a fact that nothing white is an animal. But he is not to be
1 An. Pr. 67236-7. 2 24%19. 3 67412-b11, An. Post. 7124-58, 86922-9.
THE MODAL SYLLOGISM 4I
accused of inconsistency here. He is not saying that some white
things are necessarily animals and then that nothing white is an
animal. These are simply illustrative propositions; he is merely
saying that if propositions a and 5 were true, it might still not be
necessary that some white things should not be in movement,
and that if propositions c and d were true, it might still not be
necessary that nothing white should be a man.
His examples, then, throw no light on the question what kinds
of facts he regards as necessary, and what kinds as not necessary.
But we should be justified in supposing that he draws the dis-
tinction at the point where he draws it in the Posterior Analytics,
where he tells us that the connexion between a subject and any
element in its definition (i.e. any of the classes to which it essen-
tially belongs, or any of its differentiae), or again between a sub-
ject and any property which follows from its definition, is a
necessary connexion, while its connexion with any other attribute
is an accidental one.
The most interesting feature of Aristotle's treatment of apo-
deictic syllogisms is his doctrine that certain combinations of
an apodeictic and an assertoric premiss warrant an apodeictic
conclusion. The rule he lays down for the first figure is that an
apodeictic major and an assertoric minor may yield such a con-
clusion, while an assertoric major and an apodeictic minor cannot.
The rules for the other two figures follow from those for the
first (since for Aristotle the validity of these figures depends
on their reducibility to the first), and need not be separately
considered.
We know from Alexander! that the followers of Eudemus and
Theophrastus held the opposite doctrine, that if either premiss is
assertoric the conclusion must be so, just as if either premiss is
negative the conclusion must be so, and if either premiss is par-
ticular the conclusion must be so, and that they summed up their
view by saying that the conclusion must be like the ‘inferior pre-
miss’. Nothing is really gained by the comparison; the question
must be considered on its own merits. The arguments on which
Theophrastus relied were two in number: (1) 'If B belongs to all
C, but not of necessity, the two may be disjoined, and when B is
disjoined from C, A also will be disjoined from it.’ Or, as the
argument is put elsewhere by Alexander, since the major term is
imported into the minor through the middle term, the major
1 124. 8—127. 16. 2 124. 18-21.
42 INTRODUCTION
cannot be more closely related to the minor than the middle is.!
(2 He pointed to examples, quite comparable to those which
Aristotle uses to prove Ais point:
(a) Every man is necessarily an animal, and it might be true at
some time that everything that was in movement was a
man ; but it could not be true that everything in movement
was necessarily an animal.
(b) Every literate being necessarily has scientific knowledge, and
it might be true that every man was literate; but it could
not be true that every man mecessarily has scientific
knowledge.
(c) Everything that walks necessarily moves, and it might be
true that every man was walking; but it could not be true
that every man was necessarily in movement.?
We need not concern ourselves with an attempt that was made
to water down Aristotle’s view so as to free it from these objec-
tions—an attempt which, Alexander points out, is a complete
misunderstanding of what Aristotle says.’ Aristotle bases his case
on the general statement ‘since A of necessity belongs, or does not
belong, to B, and C is one of the B’s, evidently to C too A will
necessarily belong, or necessarily not belong’.* I.e. he takes it as
self-evident that if A is necessarily true of B, it is necessarily true
of everything of which B is in fact true.
A further light is thrown on Aristotle’s reasoning, by what he
says of one of the combinations which he describes as nof yielding
an apodeictic conclusion—the combination All B is A, Some C
is necessarily B. This, he says, does not yield an apodeictic con-
clusion, οὐδὲν yàp ἀδύνατον συμπίπτει, ‘for it cannot be established
by a reductio ad impossibile .5 He clearly held that in the cases
where an apodeictic conclusion does follow, it can be established
by a reducto. The cases are four in number: A"A A^, E"AE^,
AP?II", E^IO". In principle all four cases raise the same problem,
and it is only necessary to consider 4^4 4"—"'A]l B is necessarily
A, All C is B, Therefore all C is necessarily A. For if some C were
not necessarily A, then since all C is B, some B would not neces-
sarily be A.’
The reductio syllogism gives a conclusion which contradicts the
original major premiss, and the contradiction seems to establish
the original conclusion. And, further, by using the reductio Aris-
! 124. 31-125. 2. 2 A]. 124. 24-30. 3 125. 3-29.
4 An, Pr. 3021-3. 5 3obr-s.
THE MODAL SYLLOGISM 43
totle seems to get round the prima facie objection to the original
syllogism, that it has a premiss ‘weaker’ than the conclusion it
draws; for the reductio syllogism is not open to this objection.
Yet Aristotle’s doctrine is plainly wrong. For what he is seeking
to show is that the premisses prove not only that all C is A, but
also that it is necessarily A just as all B is necessarily A, i.e. by a
permanent necessity of its own nature; while what they do show
is only that so long as all C is B, it is A, not by a permanent
necessity of its own nature, but by a temporary necessity arising
from its temporarily sharing in the nature of B.! It is harder to
point out the fallacy in the reducto, but it can be pointed out.
What Aristotle is in effect saying is that three propositions cannot
all be true—that some C is not necessarily A, that all C is B, and
that all B is necessarily A ; and if ‘necessarily A’ meant the same
in both cases this would be so. But in fact, if the argument is to
prove Aristotle’s point, ‘necessarily’ in the first proposition must
mean 'by a permanent necessity of C's nature', and in the third
proposition 'by a permanent necessity of B's nature', and when
the propositions are so interpreted we see that the three proposi-
tions may all be true together. Thus the veductzo fails, and with
it what Alexander rightly recognizes as the strongest argument
for Aristotle's view.?
Aristotle's treatment of problematic syllogisms depends, of
course, on his conception of the meaning of the word ἐνδέχεται,
which occurs in one or both of the premisses of a problematic
syllogism. This conception we have to gather from four passages
of considerable difficulty, none perhaps intelligible without assis-
tance from one or more of the others—25337—525, 32316—522, 33525-
33, 3635-37231. I have considered these passages in connexion
with one another in my note on 25337-^19; the general upshot is
all that need be mentioned here.
In all his treatment of problematic syllogisms Aristotle recog-
nizes two and only two senses of ἐνδεχόμενον. In a loose sense it
means 'not impossible', but in its strict sense it means 'neither
impossible nor necessary'. These are, indeed, the only meanings
which the word could be said naturally to bear. But in each of
the two senses the word has two applications. That which is
! Aristotle recognizes the distinction, in the words οὐκ ἔστιν ἀναγκαῖον ἁπλῶς,
ἀλλὰ τούτων ὄντων ἀναγκαῖον (3032-3), but unfortunately does not apply it
impartially to all combinations of an apodeictic with an assertoric premiss.
2
127. 3-14.
44 INTRODUCTION
known or thought to be necessary may be said a fortiori to be
possible in the loose sense; and that which, without being known
or thought to be necessary, is known or thought to be not impos-
sible, may be said to be possible in the loose sense. And again,
that which has a natural tendency to be the case or to happen,
and is the case or happens in most instances, may be said to be
possible in the strict sense; and that whose being the case or
happening is a matter of pure chance may be said to be possible
in the strict sense. This latter distinction is one to which Aristotle
attaches much importance; he says for instance that while
science may deal with that which happens for the most part, as
well as with that which is necessary, it cannot profitably deal with
that which is a matter of pure chance. But while this distinction
is of great importance in its own place, and is mentioned in the
Prior Analytics! it plays no part in Aristotle's treatment of the
problematic syllogism ; it is in fact more pertinent to the Postertor
Analytics, which is concerned with science, than to the Prior
Analytics, which is concerned simply with valid syllogism. In
his treatment of this, Aristotle always takes ἐνδέχεται in a premiss
as meaning ‘is neither impossible nor necessary’; where the only
valid concluston is one in which ἐνδέχεται means ‘is not impossible’,
he is as a rule careful to point this out.
For the understanding of the chapters on problematic syllo-
gism, two further points must be kept in mind: (1) Aristotle
points out a special form of ἀντιστροφή (what I have called comple-
mentary conversion) which is valid for propositions that are
problematic in the strict sense:
‘That all B should be A is contingent’ entails ‘That no B should
be A is contingent’ and ‘That some B should not be A is con-
tingent'.
"That no B should be A is contingent’ entails ‘That all B should
be A is contingent’ and ‘That some B should be A is con-
tingent’.
‘That some B should be 4 is contingent’ entails ‘That some B
should not be A is contingent’, and vice versa.?
This form of conversion (whose validity follows from the strict
sense of ἐνδέχεται) is often used by him in the reduction of proble-
matic syllogisms.
(2) He also points out? that while the rules for the convertibility
of propositions using ἐνδέχεται in the loose sense, and of proposi-
1 32b3-22; cf. 25b14-15. 2 32429-35. 3 3635-37831.
THE MODAL SYLLOGISM 45
tions stating conjunctions of subject and attribute to be possible
in the strict sense, are the same as the rules for the convertibility
of assertoric and apodeictic propositions (A propositions con-
vertible per accidens, E and I propositions simply, O propositions
not at all), a proposition of the form ‘That no B should be A is
contingent’ does not entail ‘That no A should be B is contingent’.
This follows from the fact that since (i) ‘For every B, being A is
contingent’ entails (ii) ‘For every B, not being A is contingent’, and
(iii) ‘For every A, not being B is contingent’ entails (iv) ‘For every
A, being B is contingent’, therefore if (ii) entailed (iii), (i) would
entail (iv), which plainly it does not. On the other hand, both ‘For
every B, not being A is contingent’ and ‘For some B’s, not being
A is contingent’ entail ‘For some A’s, not being B is contingent’.
This apparent divergence from the general principle that uni-
versal negative propositions are simply convertible, and partic-
ular negative propositions not convertible, has from early times
awakened suspicion. Alexander tells us' that Theophrastus and
Eudemus rejected both the dicta stated in our last paragraph and
the doctrine of the complementary conversion of propositions
asserting possibility in the strict sense. Maier, following Theo-
phrastus and Eudemus, has a long passage? in which he treats the
dicta of our last paragraph as an aberration on Aristotle’s part,
and tries to explain how he came to commit it. But Alexander
defends the master against the criticism of his followers, and he is
right. If Aristotle’s reasoning is carefully followed, he is seen to
be completely justified. Those who have criticized him have done
so because they have not completely grasped his conception of
strict possibility, i.e. of contingency, in which the contingency of
B’s being A and the contingency of its not being A are logically
equivalent. This once grasped, it follows at once that if the state-
ment of a universal affirmative possibility is (as everyone admits)
only convertible per accidens, so must be the statement of a
universal negative possibility. And this is no divergence from the
general principle that while A propositions are only convertible
per accidens, E propositions are convertible simply ; for ‘For every
B, being A is contingent’ and ‘For every B, not being A is contin-
gent’ are, as Aristotle himself observes,} both affirmative proposi-
tions. A statement which denses the existence of a possibility is
not a problematic statement at all, but a disjunctive statement
asserting the existence either of necessity or of impossibility.
! 169. 8-13, 220. 9-221. 5. 2 2. a 37-47. 3 25b19-24, 3251-3.
46 INTRODUCTION
If these general features of Aristotle’s theory of the problematic
proposition are kept in mind, it becomes not too difficult to follow
his detailed treatment of syllogisms with one or both premisses
problematic, in An. Pr. i. 14-22. Of all the valid syllogisms of this
type, few escape his notice; of those that do not need comple-
mentary conversion for their validation, none does, but of those
that require such conversion several are omitted'—no doubt
because, having mentioned the possibility of such validation in
many cases, he does not think it necessary to mention it in all.
The method of reduction of syllogisms which he adopts is in a few
cases inconclusive, but these occasional flaws do not prevent the
discussion from being a most remarkable piece of analysis. The
fact that Theophrastus denied the convertibility of ἐνδέχεται παντὶ
τῷ Β τὸ A ὑπάρχειν with ἐνδέχεται μηδενὶ τῷ Β τὸ A ὑπάρχειν shows
that he was interpreting ἐνδέχεται not in its strict Aristotelian
sense but in that which Aristotle calls its looser sense, as meaning
not ‘neither impossible nor necessary’ but ‘not impossible’. Thus
Aristotle and Theophrastus were considering entirely different
problems, each a problem well worthy of study. Methodologically
Theophrastus chose the better path, by attempting the simpler
problem. Aristotle’s choice of problem was probably dictated by
metaphysical rather than logical considerations. For him the dis-
tinction between the necessary and the contingent was of funda-
mental importance, identical in its incidence with that between
the world of being and the world of becoming. On the one side lay
a world of universals linked or separated by unchanging connexions
or exclusions, on the other a world of individual things capable
of now possessing and again not possessing certain attributes.
Another of Aristotle’s contentions which scandalized Theo-
phrastus? was the contention that certain combinations of an
apodeictic with a problematic premiss yield an assertoric con-
clusion—which ran counter to Theophrastus’ doctrine that the
conclusion can never state a stronger connexion than that stated
in the weaker premiss. For the first figure (and the rules for the
other figures follow from that for the first figure) Aristotle’s rule
is that when a negative apodeictic major premiss is combined with
an affirmative problematic minor premiss, a negative assertoric
conclusion follows; that ‘All B is necessarily not A’ and ‘For all
C, being B is contingent’ entail ‘No C is A’, and that ‘All B is
necessarily not A’ and ‘For some C, being B is contingent’ entail
! See instances in the table at facing p. 286. 2 Al. 173. 32-174. 3.
THE MODAL SYLLOGISM 47
‘Some C is not A’.' His proof of the first of these entailments
(and that of the other follows suit) is as follows: ‘Suppose that
some C is A, and convert the major premiss. Then we have All
A is necessarily not B, Some C is A, which entail Some C is
necessarily not B. But ex hypothesi for all C, being B is contingent.
Therefore our supposition that some C is A was false, and No C
is A is true.' It will be seen that Aristotle tries to validate the
inference by veductio to a syllogism with an apodeictic and an
assertoric premiss, and an apodeictic conclusion; and we have
already? seen reason to deny the validity of such an inference.
Aristotle is at fault, and Theophrastus' doctrine that the conclu-
sion follows in its nature the weaker premiss is vindicated.
V
INDUCTION
THE chief method of argument recognized by Aristotle apart from
syllogism is induction; in one passage! he says broadly ἅπαντα
πιστεύομεν 7) διὰ συλλογισμοῦ 7) ἐξ ἐπαγωγῆς, and in others* the same
general distinction is implied. And since syllogism is the form in
which demonstration is cast, a similar broad opposition between
induction and demonstration is sometimes* found. The general
distinction is that demonstration proceeds from universals to
particulars, induction from particulars to universals.®
The root idea involved in Aristotle's usage of the words ἐπάγειν
and ἐπαγωγή is not (as Trendelenburg argued) that of adducing
instances, but that of leading some one from one truth to another.”
So far as this goes, ordinary syllogism might equally be described
as ἐπαγωγή, and ἐπάγειν is occasionally used of ordinary syllogism.?
And in general Aristotle clearly means by ἐπαγωγή not the
adducing of instances but the passage from them to a universal
conclusion. But there are occasional passages in which ἐπακτικός,9
énaxrikós,!? and emaywyn" are used of the adducing of instances;
and it seems to be by a conflation of these two usages that
ἐπαγωγή comes to be used habitually of leading another person
on by the contemplation of instances to see a general truth.
1 3697-15, 34-9. 2 pp. 41-3. 3. An. Pr. 68915.
* 4233, 68>32-7; An. Post. 7195-11. 5' An, Post. 91P34-5, 92335-br.
6 Br340-br, Top. 105913. 7 See introductory note to An. Pr. ii. 23.
8 An. Post. 71321, 24.
9 77>35 and perhaps Met. 1078b28. 10 Phys, 210b8.
τ Cat. 1337, Top. 108b1o, Soph. El. 174337, Met. 104836.
48 INTRODUCTION
With one exception to be mentioned presently, Aristotle no-
where offers any theory of the nature of induction, and the word
ἐπαγωγή cannot be said to have been with him a term of art as
συλλογισμός is. He uses the word to mean a variety of mental
processes, having only this in common, that in all there is an
advance from one or more particular judgements to a general one.
At times the advance is from statements about species to state-
ments about the genus they belong to;! at times it is from indi-
viduals to their species;? and since induction starts from sense-
perception, induction from species to genus must have been
preceded by induction from individuals to species. Again, where
the passage is from species to genus, Aristotle sometimes* passes
under review all (or what he takes to be all) the species of the
genus, but more often’ only some of the species.
Where a statement about a whole species is based on facts about
a mere selection of its members, or an inference about a whole
genus on facts about a mere selection of its species, it cannot be
reasonably supposed that there is a valid inference, and in the one
passage where Aristotle discusses induction at length, he says
that induction to be valid must be from all the καθ᾽ ἕκαστα. What
then does he suppose to happen when this condition is not ful-
filled? In most cases he evidently thinks of the argument as a
dialectical argument, in which knowledge about the particulars
tends to produce the corresponding belief about the universal,
without producing certainty. Syllogism is said to be βιαστικώ-
τερον than induction,’ and this implies that induction is not cogent
proof. True, he often says that the conclusion is δῆλον or φανερὸν
ἐκ τῆς ἐπαγωγῆς; but the more correct expression is πιστὸν ἐκ τῆς
ἐπαγωγῆς. A distinction must, however, be drawn. In most of
Aristotle's references to induction, not merely is it not suggested
that it produces knowledge ; there is no suggestion that knowledge
of the universal truth even follows upon the use of induction. But
in certain passages we are told that the first principles of science,
or some of them, come to be known by means of induction:
! eg. An, Pr. 68>18-21, Top. 105*13-16, Met. 104813554.
2 eg. Rhet. 1398332-brg.
5. An. Post, 81338-bg. * eg. An. Pr. 6820-1, Met. 10555510.
5 eg. Top. 105*13-16, 113>15-114%6; Phys. 210*15-b9; Part. An. 646%24-30;
Met. 1025°6-13, 1048235-b4. $ An. Pr. ii. 23. 7 Top. xos*16-19.
3. De Caelo, 276714; cf. Top. 10353, Phys..224>30, Meteor. 378514, Met.
106714.
INDUCTION 49
δῆλον δὴ ὅτι ἡμῖν τὰ πρῶτα ἐπαγωγῇ γνωρίζειν ἀναγκαῖον : τῶν ἀρχῶν
αἱ μὲν ἐπαγωγῇ θεωροῦνται, αἱ δ᾽ αἰσθήσει, αἱ δ᾽ ἐθισμῷ τινί, καὶ ἄλλαι δ᾽
ἄλλως : εἰσὶν ἄρα ἀρχαὶ ἐξ ὧν ὁ συλλογισμός, ὧν οὐκ ἔστι συλλογισμός '
ἐπαγωγὴ apa.! Now Aristotle considers that, in the mathematical
sciences at least, knowledge of derivative propositions can be
reached, and that this can happen only if the ultimate premisses
from which the proof starts are themselves known. But these are
not themselves known by proof; that is implied in calling them
ultimate. Here, then, under the heading of induction he clearly
contemplates a mental process which is not proof, yet on which
knowledge supervenes. Take the most fundamental proposition of
all, that on which all proof depends, the law of contradiction, How
do we come to knowit? By seeing, Aristotle would say, that some
particular subject B cannot both have and not have the attribute
A, that some particular subject D cannot both have and not have the
attribute C, and so on, until the truth of the corresponding general
proposition dawns upon us. And so, too, with the ἀρχαί proper toa
particular science. The induction here is not proof of the principle,
but the psychological preparation upon which the knowledge of
the principle supervenes. The knowledge of the principle is not
produced by reasoning but achieved by direct insight—vois dv εἴη
τῶν dpydv.2 This is in fact what modern logicians call intuitive
induction. And this is far the most important of the types of
induction which Aristotle considers.
The general principle, in such a case, being capable of being
known directly on its own merits, the particular examples serve
merely to direct our attention to the general principle; and for a
person of sufficient intelligence one example may be enough. At
the very opposite extreme to this application of induction stands
the application which Aristotle considers in the one passage in
which he describes induction at some length, A. Pr. ii. 23. He
here studies the kind of induction which really amounts to proof
and can be exhibited as a syllogism, ὁ ἐξ ἐπαγωγῆς συλλογισμός.
In this αἰ the particulars must be studied, in order that the general
principle should be proved. Induction is said to be 'the connecting
of one extreme syllogistically with the middle term through the
other extreme’. This seems at first sight inconsistent with the very
notions of extreme and middle term. The explanation is not far
to seek. He contemplates a situation in which certain species C,,
C,, etc., have an attribute A because of their membership of a
1 An. Post. 100°3, E.N. 10983, 1139529. 2 An. Post. 10012.
4985 E
50 INTRODUCTION
genus B. The demonstrative syllogism would run ‘All B is A;
C,, Cy, etc., are B; therefore they are A.’ The inductive syllogism
runs 'C,, C,, etc., are A; C,, C,, etc., are B, and this proposition
is convertible (i.e. all B is either C, or Cg, etc.) ; therefore all B is
A.’ Cand A are still called the extremes and B the middle term,
because that is what they are in the demonstrative syllogism, and
in the nature of things.
It is strange that in the one considerable passage devoted to
induction Aristotle should identify it with its least valuable form,
perfect induction. The reason is to be found in the remarks which
introduce the chapter. Filled with enthusiasm for his new-found
discovery the syllogism, he makes the bold claim that all argu-
ments—dialectical, demonstrative, or rhetorical—are carried out
in one or other of the three syllogistic figures. Not unnaturally,
therefore, he selects just the type of induction which alone can be
cast in the form of a valid syllogism ; for it is plain that whenever
the named C’s fall short of the whole extension of B, you cannot
validly infer from ‘C,, Cy, etc., are 4 ; C4, C, etc., are B' that all
B is A.
Nor is perfect induction entirely valueless. If you know that
C,, Cs, etc., are A, and that they are B, and that they alone are B,
you have all the data required for the knowledge that all B is A;
but you have not yet that knowledge; for the drawing of the
conclusion you must not only know these data, but you must also
think them together (συνθεωρεῖν) ,ἷ and it is this, as in all syllogism,
that makes a real advance in knowledge possible.
To sum up, then, Aristotle uses ‘induction’ in three ways. He
most often means by it a mode of argument from particulars
which merely tends to produce belief in a general principle, with-
out proving it. Sometimes he means by it the flash of insight by
which we pass from knowledge of a particular fact to direct
knowledge of the corresponding general principle. In one passage
he means by it a valid argument by which we pass from seeing that
certain species of a genus have a certain attribute, and that these
are allthe species of the genus, to seeing that the whole genus has it.
We can now see why it is that Aristotle describes syllogism as
πρότερος καὶ γνωριμώτερος than induction, while induction is ἡμῖν
€vapyéarepos,* or demonstration as being ἐκ προτέρων καὶ γνωριμω-
Tépuv ἁπλῶς, induction as being ἐκ προτέρων καὶ γνωριμωτέρων
ἡμῖν. All knowledge starts with the apprehension of particular
t An, Pr. 67337. 2 68b35-7. 3 An. Post. 7226-30.
INDUCTION 51
facts, which are the most obvious objects of knowledge. But
Aristotle is convinced that if a particular subject C has an attri-
bute 4, it has it not as being that particular subject but in virtue
of some attribute B which it shares with other subjects, and that
it is more really intelligible that all B is A than that C, a par-
ticular instance of B, is A. To pass from the particular fact that
C is A to the general fact that all B is A is not to understand why
all B is A; but to pass, as we may then proceed to do, from
knowing that all B is A to knowing that C, a particular B, is A,
is to understand why C is A.
Having in An. Pr. ii. 23 shown how induction, in one of its
forms, viz. perfect induction, can be reduced to syllogistic form,
Aristotle proceeds in the remainder of the book to treat of other
modes of argument reducible to syllogistic form—example, reduc-
tion, objection, enthymeme ; but these are not of sufficient general
importance to need discussion here.
VI
DEMONSTRATIVE SCIENCE
As the Prior Analytics present Aristotle’s theory of syllogism, the
Posterior Analytics present his theory of scientific knowledge.
This, rather than ‘knowledge’ simply, is the right rendering of his
word ἐπιστήμη ; for while he would not deny that individual facts
may be known, he maintains that ἐπιστήμη is of the universal.
Syllogistic inference involves, no doubt, some scientific know-
ledge, viz. the knowledge that premisses of a certain form entail
a conclusion of a certain form. But while formal logic aims simply
at knowing the conditions of such entailment, a logic that aims
at being a theory of scientific knowledge must do more than this;
for the sciences themselves aim at knowing not only relations
between propositions but also relations between things, and if the
conclusions of inference are to give us such knowledge as this,
they must fulfil further conditions than that of following from
certain premisses. To this material logic, as we might call it in
opposition to formal logic, Aristotle now turns; to the statement
of these further conditions the first six chapters of Aw. Post. i
are devoted.
Aristotle begins by pointing out that all imparting or acquisi-
tion of knowledge by reasoning starts from pre-existing know-
ledge; and this passage from knowledge to knowledge is what
52 INTRODUCTION
occupies almost the whole of the Posterior Analytics. There
remains the question whether the knowledge we start from is
innate or acquired, and if acquired, how it is acquired; and to
that question Aristotle turns in the last chapter of the second
book. But about the nature of this original knowledge he says at
once! that it is of two kinds. There is knowledge of facts and
knowledge of the meaning of words. The first he illustrates by
the knowledge of the law of excluded middle; the second by the
knowledge that ‘triangle’ means so-and-so. He adds that there
are certain things (e.g. the unit) about which we know not only
that the word by which we designate them means so-and-so, but
also that something answering to that meaning exists. And else-
where? he expands this by observing that while we must know
beforehand the meaning of all the terms we use in our science, we
need know beforehand the existence of corresponding things only
when these are fundamental subjects of the science in question.
The instances he gives suggest—and there is much in what
follows to support the suggestion—that he has mathematics in
mind as furnishing the primary example of science (or rather
examples, for in his view arithmetic and geometry are essentially
different sciences). It was inevitable that this should be so; for
the mathematical sciences were the only sciences that had been
to any degree developed by the Greeks when Aristotle wrote. In
Euclid, who wrote about a generation later, we find recognized
the two types of preliminary knowledge that Aristotle here men-
tions; for Euclid's ὅροι answer to Aristotle's ‘knowledge of the
meaning of words’, and his κοιναὶ ἔννοιαι answer approximately to
Aristotle’s ‘knowledge of facts’; though only approximately, as
we shall see later. Now Euclid’s Elements had predecessors, and
in particular it seems probable that the Elements of Theudius*
existed in Aristotle's time. But we know nothing of its contents,
and it would be difficult to say whether Aristotle found the
distinction of two kinds of knowledge already drawn by Theudius,
or whether it was Aristotle's teaching that led to the appearance
of the distinction in Euclid.
Aristotle turns next5 to what is in fact a comment on his own
statement that all knowledge gained by way of reasoning is gained
from pre-existing knowledge. What his comment comes to is this,
that when knowledge that a particular member of a class has a
I 71311-17, 2 46332-6. 3 pp. 56-7.
* Cf. Heath, Greek Mathematics, i. 320-1. 5 71417-b8,
DEMONSTRATIVE SCIENCE 53
certain attribute is gained by way of reasoning, the major premiss
must have been known beforehand, but the recognition of the
particular thing as belonging to the class and the recognition of it
as having that attribute may be simultaneous. ‘That every
triangle has its angles equal to two right angles we knew before;
that this figure in the semicircle is a triangle, one grasped at the
very moment at which one was led on to the conclusion." This
implies, of course, that the knowledge that all triangles have this
property was not knowledge that each of a certain number of
triangles has the property plus the knowledge that there are no other
triangles—was knowledge not of an enumerative but of a generic
universal. If he did not know a thing to exist, how could he know
that it has angles equal to two right angles? One has knowledge
of the particular in a sense, i.e. universally, but not in the un-
qualified sense’ ;? or, as he puts it elsewhere,’ in knowing the
major premiss one was potentially, but only potentially, knowing
the conclusion. This important distinction had already been
stated, in a more elaborate form, in An. Pr. ii. 21.
We think we have scientific knowledge of a fact, Aristotle pro-
ceeds,* when we think we know its actual cause to be its cause, and
the fact itself to be necessary. Our premisses must have two
intrinsic characteristics. They must be true, and this distinguishes
the scientific syllogism from all those correct syllogisms which
proceed from false premisses (for which cf. An. Pr. ii. 2-4). But
not all inferences from true premisses are scientific ; secondly, the
premisses must be primary or immediate, since a connexion that
is mediable can be known only by being mediated. And besides
having these intrinsic characteristics they must stand in a certain
special relation to the conclusion ; they must be ‘more intelligible
than and prior to and causes of the conclusion . . . causes because
we know a fact only when we know its cause; prior, because they
are causes ; known before, not only in the sense that we know what
the words mean but also in the sense that we know they stand for
a fact. These, while named as three separate conditions, are
clearly connected. 'Prior' and 'better known' state two charac-
teristics both of which follow from the premisses' being causes,
ie. statements of the ground on which the fact stated in the
conclusion depends. Both ‘prior’ and ‘better known’ are used in
a special, non-natural sense. Aristotle would not claim that the
! JIÀIg-2I. * [b. 26-9. 3 86322-9.
* 4199-16. 5 Tb. 19-33.
54 INTRODUCTION
facts stated in the premisses are necessarily prior in time; for in
mathematics there is no temporal succession between ground and
consequent. Aristotle would even go farther and say that a
fact (or a combination of facts) which precedes another fact can
never be the complete ground of the other, since the time-lapse
implies that the earlier fact can exist without the later fact’s
doing so.' ‘Prior’ therefore must mean ‘more fundamental in the
nature of things’. And again ‘more known’ does not mean ‘more
familiar’, nor ‘foreknown’ ‘known earlier in time’. For he goes on
to say that ‘the same thing is not more known by nature and more
known to us. The things that are nearer to sense are more known
to us, those that are farther from sense more known without
qualification. Now the things that are most universal are farthest
from sense, and individual things nearest to it." In a demonstratio
potissima all three terms are actually of equal universality; but
nevertheless when we say All B is A, All C is B, Therefore all C
is A, in the minor premiss we are using only the fact that all C is
B, and not the fact that all B is C, so that notionally the major
premiss is wider than the conclusion, and therefore (Aristotle
would say) less known fo «s. In saying this, he is pointing to the
fact that is brought out in the final chapter of the Posterior
Analytics—that the ultimate premisses of demonstration are
arrived at by intuitive induction from individual facts grasped by
sense; while in saying that the premisses are more known by
nature he is saying that the universal fact is more intelligible than
the individual fact that is deduced from it; and this is so; for if
all C is A because all B is A and all C is B, we wndersiand all C's
being A only by grasping the more fundamental facts that all B
is A and allC is B. Thus the two senses of ‘more known’ are ‘more
familiar', which is applicable to the conclusion, and 'more in-
telligible', which is applicable to the premisses. In demonstration
we are not passing from familiar premisses to a less familiar con-
clusion, but explaining a familiar fact by deducing it from less
familiar but more intelligible facts.
One thing in this context that is puzzling is the statement that
the premisses must be προγινωσκόμενα, which clearly refers to
temporal precedence and might seem to contradict the statement
that the conclusions are more familiar to us. But the two state-
ments are not inconsistent; for even if the premisses have been
reached by induction from particular instances, it need not be
! Zn. Post. ii. 12. 2 71634-7245, 3 71531; cf. 72228.
DEMONSTRATIVE SCIENCE 55
from the instances to which the conclusion refers, and even if it
is so, within the syllogism the knowledge of the conclusion appears
as emerging from the knowledge of the premisses and following it
in time.
Aristotle adds one further qualification of the ἀρχαί of science;
they must be ofxefat.!. This must be understood as meaning not
‘peculiar’ to the science in question (for Aristotle includes among
the ἀρχαί axioms which extend beyond the bounds of any one
science), but 'appropriate' to it. What he is excluding is the
μετάβασις ἐξ ἄλλου yévovs,? the use (as in dialectic) of premisses
borrowed from here, there, and everywhere.
Aristotle turns now?'to distinguish the various kinds of premiss
that scientific demonstration needs. There are, first of all, ἀξιώ-
para (also called κοινά or κοιναὶ dpxai), the things one must know
if one is to learn anything, the principles that are true of all things
that are. The only principles ever cited by Aristotle that strictly
conform to this account are the laws of contradiction and of
excluded middle,* but it is to be noted that he also includes under
ἀξιώματα principles of less generality than these but applying to
all quantities, e.g. that if equals be taken from equals, equals
remain.’ Even these are κοινά as compared with assumptions
pecular to arithmetic or to geometry.
Secondly, there are θέσεις, necessary for the pursuit of one
particular science, though not necessary presuppositions of all
learning. These fall into two groups: (1) ὑποθέσεις, assumptions
of the existence of certain things, and (2) ὁρισμοί, definitions,
which, since they are co-ordinated with ὑποθέσεις and not de-
scribed as including them as elements, must be purely nominal
definitions of the meaning of words, and are, indeed, so described
in 71814-15. The same passage adds that while with regard to
some terms (e.g. triangle in geometry) only the meaning must be
assumed, with regard to others (e.g. unit in arithmetic)® the exis-
tence of a corresponding entity must also be assumed. Aristotle's
view is that the meaning of all the technical terms used in a
science and the existence of the primary subjects of the science
must be assumed, while the existence of the non-primary terms
(ie. of the attributes to be asserted of the subjects) must be
proved.?
1 4296. ? 75938, 3 72*14-24.
4 71914, 77*10-12, 30, 88br. 5 76941, 620, 7733021.
$ Cf. magnitude in geometry, 76736. 7 76%32-6.
56 INTRODUCTION
With regard to these assumptions, he makes two important
points elsewhere, One is that where an assumption is perfectly
obvious it need not be expressly stated.! The second is that a
science does not assume the axioms in all their generality, but
only as applying to the subject-matter of the science?—on the
principle of not employing means that are unnecessary to our end.
Aristotle is not so clear as might be wished with regard to the
function of the axioms in demonstration. He describes them as
e€ dv, starting-points. In another passage he says demonstra-
tions are achieved διά re τῶν κοινῶν Kal ἐκ τῶν ἀποδεδειγμένων,"
apparently distinguishing the function of the axioms from that of
any previously proved propositions that form premisses for a
later proposition. Their function is more obscurely hinted at in
883, where it is said that propositions are proved through (διά)
the axioms, with the help of (μετά) the essential attributes of the
subjects of the science. On the other hand, he says that no proof
expressly assumes the law of contradiction, unless it is wished to
establish a conclusion of the form ‘S is P and not non-P'.5 This
would point to the true view that the axioms, or at least the com-
pletely universal axioms, serve not as premisses but as laws of
being, silently assumed in all ordinary demonstrations, not pre-
misses but principles according to which we reason.
There were writers of Elements of Geometry before Aristotle—
Hippocrates of Chios in the second half of the fifth century, Leon
in the first half of the fourth, and Theudius of Magnesia, who was
roughly contemporary with Aristotle. Unfortunately we have no
details about what was included in the Elements written by these
writers. What can be said, however, is that there is a considerable
affinity between Aristotle’s treatnient and Euclid’s treatment of
the presuppositions of geometry, so that it is highly probable that
Euclid, writing a generation after Aristotle, was influenced by
him.$ Euclid’s xowai ἔννοιαι answer pretty well to Aristotle's
κοιναὶ ἀρχαί or ἀξιώματα, but the significance of κοιναί is different
in the two cases. In κοιναὶ ἀρχαί it means ‘not limited to one
science',? and the instances Aristotle gives are either common to
1 5691621, 77?10-12. 2 46437-b2, 3 75442, 7614, 77227, 8808,
4 76bI0, 5. 77*10-12.
$ On the relation of Aristotle’s ἀρχαί to those of Euclid cf. Heath, The
Thirteen Books of Euclid’s Elements, i. 117-24. In referring to Euclid's axioms
and postulates, I refer to the restricted list given in Heiberg’s edition and
Heath’s translation. 7 72%14-17.
DEMONSTRATIVE SCIENCE 57
all things that are (the laws of contradiction and excluded middle)
or at least common to the subject-matter of arithmetic and
geometry (‘if equals be taken from equals, equals remain’). In
κοιναὶ ἔννοιαι, kowat means ‘common to the thought of all men’,
and the phrase is derived not from xowal dpyai but from a phrase
which Aristotle uses in the Metaphysics'—ras κοινὰς δόξας ἐξ dv
ἅπαντες δεικνύουσιν. Euclid’s κοιναὶ ἔννοιαι include neither of
Aristotle’s axioms of supreme generality. They do include axioms
common to arithmetic and geometry (‘things which are equal to
the same thing are also equal to one another’, ‘if equals be added
to equals, the wholes-are equal’, ‘if equals be subtracted from
equals, the remainders are equal’, ‘the whole is greater than the
part’), and one which is κοινή in the second sense but not in the
first, being limited to geometry—‘things which coincide with one
another (ie. which can be superimposed on one another) are
equal to one another'.
Euclid's ὅροι answer exactly to Aristotle's ὁρισμοί (which Aris-
totle elsewhere often calls ὅροι). Like Aristotle, Euclid included
definitions not only of the fundamental terms of the science—
point, line, surface—but also of attributes like straight, plane,
rectilinear. The underlying theory is Aristotle's theory, that
geometry must assume nominal definitions of all its technical
terms, alike those in whose case the existence of corresponding
entities is assumed, and those in whose case it must be proved.
Euclid states no presuppositions answering to Aristotle’s ὑπο-
θέσεις, assumptions of existence; it is reasonable to suppose that
he silently assumes the existence of entities corresponding to the
most fundamental of the terms he defines. Aristotle's treatment is
in this respect preferable. He admits:that when an assumption is
perfectly self-evident it need not be expressly stated; he is right
in saying that even when it is not expressly stated, the presupposi-
tion of the existence of certain fundamental entities is a distinct
and necessary type of presupposition.
On the other hand, Euclid recognizes a type of presupposition
which does not answer to anything in Aristotle—the αἴτημα or
postulate. The word occurs in Aristotle, but not as standing for
one of the necessary presuppositions of science. When a teacher
or disputant assumes without proof something that is provable,
and the learner or other disputant has no opinion or a contrary
opinion on the subject, or indeed when anything provable is
1 99628 ; cf. 997221.
58 INTRODUCTION
assumed without proof (the alternatives show that Aristotle is
not using αἴτημα as a technical term, but taking account of a
variation in its ordinary usage), that is an αἴτημα. In neither
case is this a proper presupposition of science. Euclid's αἰτήματα
are a curious assemblage of two quite distinct kinds of assumption.
The first three are assumptions of the possibility of performing
certain simple constructions—‘let it be demanded to draw a
straight line from any point to any point, to produce a finite
straight line continuously in a straight line, to describe a circle
with any centre and distance’. The last two are of quite a different
order—‘that all right angles are equal to one another’ and ‘that,
if a straight line falling on two straight lines make the interior
angles on the same side less than two right angles, the two
straight lines, if produced indefinitely, meet on that side on which
are the angles less than two right angles'—the famous postulate of
parallels. "
The first three postulates are not propositions at all, but de-
mands to be allowed to do certain things; and as such they
naturally find no place among the fundamental propositions
which Aristotle is seeking to classify. No doubt the demand to be
allowed to do them involves a claim to be able to do them if one
is allowed ; an improper claim, since in fact no one can, strictly
speaking, draw or produce a straight line, or describe a circle.
All that the geometer really needs is permission to reason about
that which he has drawn, as if it were a straight line or a circle.
And on this Aristotle says what is really necessary when he points
out that the geometer is guilty of no falsity when he so reasons,
and that the supposition, fiction if you will, that what he has
drawn is a straight line or circle forms no part of his premisses but
only serves to bring his reasoning home to the mind of his hearer.?
When we come to the last two of Euclid's postulates, the situa-
tion is quite different. The fourth states a self-evident proposition
whose right place would be among the κοιναὲ ἔννοιαι, a proposition
quite analogous to the κοινὴ ἔννοια that figures which coincide are
equal. On the famous fifth postulate it would ill become me to
dogmatize against the prevailing trend of modern mathematical
theory ; but I venture to regard this also as axiomatic.
Aristotle's recognition of axioms, definitions, and hypotheses as
three distinct types of assumption needed by science is sound, so
far as it goes, but it needs supplementation. To begin with, he
! 165324. 2 76639-7733.
DEMONSTRATIVE SCIENCE 59
should have recognized the distinction between the axioms that
are applicable to all things that are, and those that are applicable
only to quantities, ie. to the subject-matter of arithmetic and
geometry. Secondly, he should have recognized among the prin-
ciples peculiar to one science certain which are neither definitions
nor assumptions of the existence of certain entities—such pro-
positions as Euclid's fourth axiom, that things which coincide are
equal, and his fourth and fifth postulates. Among these principles
he should have included such assumptions as that every number
is either odd or even, every line either straight or curved, which
in another passage! he includes among the assumptions of science.
In recognizing the existence of such self-evident propositions as
these, Aristotle is recognizing an important difference between the
mathematical and the inductive sciences. In the latter the alterna-
tive attributes, one or other of which a certain subject must have,
can only be discovered empirically; in the former they can be
known intuitively. And finally, a closer scrutiny of the actual
procedure of geometry would no doubt have shown him that it
uses many other assumptions which are involved in our intuition
of the nature of space, e.g. (to borrow an example from Cook
Wilson) that the diagonals of a quadrilateral figure which has not
a re-entrant angle must cross within the figure.
It is not unusual to describe Aristotle as lacking in mathe-
matical talent ; but there are at least three things which show the
falsity of such a view. One is his discussion of the presuppositions
of science (which means for him primarily the foundations of
mathematics) ; this, though far from perfect, is almost certainly
a great advance on anything that preceded it. Another is his
masterly and completely original discussion, in the sixth book of
the Physics, of the whole problem of continuity. A third is the
brilliant passage in the Metaphysics? in which he anticipates
Kant’s doctrine that the construction of the figure is the secret
of geometrical discovery. He did not make original mathematical
discoveries; but few thinkers have contributed so much as he to
the philosophical theory of the nature of mathematics.
Aristotle’s firm insistence that there must be starting-points of
proof which neither need nor admit of proof enables him! to set
aside two theories that evidently had some vogue in his day—
theories which assumed in common that knowledge can only be
1 2455-12. 3 yo51 421-33. 3 Ch. 3.
60 INTRODUCTION
got by proof. On this assumption some based the conclusion that
knowledge is impossible since no proof proves its own premisses ;!
while others held that knowledge is possible but is got by reasoning
in a circle, proving a conclusion from premisses and these premisses
from the conclusion.? Aristotle refutes the latter view at some
length? by pointing out in detail the futility of circular argument.
He next points out* that that which is to be known scientifically
must be incapable of being otherwise, and that therefore the
premisses from which it is proved must also be necessary. But
before drawing out the implications of this he proceeds to dis-
tinguish three relations which may exist between a predicate and
a subject, and must exist if the proposition is to be truly scientific.
(1) The first is that the predicate must be κατὰ παντός, true of
every instance of the subject. Universality in this merely enumera-
tive sense is the minimum requirement. (2) The second is that the
one term must be καθ᾽ αὑτό, essential to the other. He dis-
tinguishes four senses of καθ᾽ αὑτό, but the last two are irrelevant
to his present inquiry and are introduced only for the sake of
completeness. The first two senses have this in common, that a
term A which is καθ᾽ αὑτό to a term B must belong to B as an
element in its essential nature. They differ in this, that A is καθ᾽
αὑτό to B in the first sense when A is an essential element in the
definition of B, and in the second sense when B is an essential
element in the definition of A. The underlying idea is that in the
essential nature of anything there are two layers—a complex of
fundamental attributes (genus and differentiae) which form the
core of its being and by reference to which it is defined, and a
complex of consequential attributes which are its properties and
can be defined only by reference to it. Propositions which are
examples of the first kind of καθ᾽ αὑτό relation are definitions or
partial definitions, which form suitable premisses of demonstra-
tion ; with regard to the second kind of καθ᾽ αὑτό relation, Aristotle
no doubt means, though he fails to point out clearly, that pro-
positions like ‘every angle is either right, acute, or obtuse’ occur
among the premisses of geometry, and propositions like ‘the angle
in the semicircle is right’ among its conclusions.
The instances Aristotle gives of these two kinds of καθ᾽ αὐτό
relation call for two comments. (2) Terms that are καθ᾽ αὑτό in
the first sense are said to belong (ὑπάρχειν) to their subjects.
ὑπάρχειν is a non-technical and ambiguous word. Line belongs to
! g2b7-15. 2 Ib. 15-18. 3 Ib. 25-73?20. * 2392144.
DEMONSTRATIVE SCIENCE 61
triangle as being its boundary, point to line as being its terminus;
but more often it is an attvibute that he describes as being in this
sense καθ᾽ αὑτό to its subject. And if we wish to express the rela-
tion of line to triangle and of point to line in terms of a relation
between an attribute and a subject, we may say that a triangle is
necessarily ‘bounded by lines’, and a line necessarily ‘terminates
in points'. (b) The examples Aristotle gives here of terms that are
καθ᾽ αὑτό to others in the second sense are pairs of terms that are
alternatively predicable of their subjects (e.g. straight and curved) ;
but there is no reason why he might not have cited larger groups of
terms that are alternatively predicable of their subjects, or for that
matter single terms that are necessarily predicable of their subjects.
(3) But it is not enough that the predicate should be true,
without exception and necessarily, of its subject. It must also be
true of it # αὐτό, of it precisely as itself, not of any wider whole.
Aristotle applies this distinction to both kinds of καθ᾽ αὑτό rela-
tion.! As applied to the first kind it would mean that only pro-
positions ascribing to a subject its final differentia are suitable
premisses of demonstration, for only these are simply convertible.
But it is doubtful if he would have stressed this point. What he
has mainly in mind is to assert that the conclusion of a demon-
stration? must have terms that are equal in denotation or 'com-
mensurately universal’, though he allows that in a looser sense a
proposition whose predicate is not commensurately universal
may be demonstrated. If we merely show that a subject always
and necessarily has a certain attribute, we have not yet reached the
ideal of demonstration; we do this only when we show that a
subject has a property in virtue of its whole nature, so that
nothing else can also have it. This is the severe ideal of demon-
stration which Aristotle sets up. In the next chapter* he points
out various circumstances in which, while there is a 'sort of proof',
there is not genuine proof because there is not a perfect fit
between the subject and the predicate of our conclusion. Greek
mathematics, he says, had at one time been defective because it
proved that if A is to B asC is to D, A is to C as B is to D, not
universally of all quantities but separately for numbers, lines,
solids, and times, but had later remedied this defect.5 In Euclid®
we find the universal proposition actually proved.
¥ 9329-32. 2 5451-2. 3 Ib. 2. *i 5.
5 74*17-25. Such advance from particular to general proofs is in fact con-
stantly happening in all the sciences. $ Bks. v, vi.
62 INTRODUCTION
Aristotle has already said! that since it is the object of science
to prove conclusions that state necessary facts, its premisses also
must state necessary facts, but he has not supported this dictum
by argument. Instead, he turned aside to state the conditions
which any proposition must fulfil if it is to be necessary—viz.
that it be enumeratively true, and that it state a connexion which
is καθ᾽ αὑτό (for the third characteristic, that it enunciate a con-
nexion which is ἢ αὐτό, commensurately universal, while it is a
characteristic of a perfectly scientific proposition, is not a prece-
dent condition of its being necessary). He now turns to prove the
proposition stated without proof in 73221-4. He supports it by a
variety of probable arguments, but his most cogent argument is
that stated in 74526-32. If a proposition is provable, one cannot
know it scientifically unless one knows the reason for its being
true. Now if A is necessarily true of C, but B, the middle term
one uses, is not necessarily true of C (or, for that matter, if 4 is
not necessarily true of B), one cannot be knowing why C is A.
For obviously C's being something which it is not necessarily
cannot be the cause of its being something which it is necessarily.
It is, of course, possible to infer a necessary fact from non-
necessary premisses, as it is possible to draw a true inference from
false premisses, but as in the latter case the conclusion cannot be
known to be true, in the former the fact cannot be known to be
necessary ; but the object of science is to know just that. On the
other hand, just as if the premisses are known to be true the
conclusion is known to be true, so if the premisses are known to
be necessary the conclusion is known to be so. Thus the requisite
and sufficient condition of the conclusion's being known to be
necessary is that our premisses be known to be necessary,” or in
other words that we know their predicates to be connected with
their subjects by one or other of the two καθ᾽ αὑτό relations.?
The first corollary which Aristotle deduces* from the account
just given of the nature of the premisses of scientific reasoning is
that there must be no μετάβασις ἐξ ἄλλου γένους, no proving of
propositions in one science by premisses drawn from another
science. No science has a roving commission; each deals with a
determinate genus. The subject of each of its conclusions must
be an entity belonging to that genus; the predicate must be an
attribute that is καθ᾽ αὑτό to such a subject; but two terms of
which one is καθ᾽ αὑτό to the other obviously cannot be properly
I 73?21-4. 2 9531-17. 3 Tb. 28-37. as Pa
DEMONSTRATIVE SCIENCE 63
linked by a middle term that is not in such a relation to them.
Thus a geometrical proposition cannot be proved by arithmetic,!
nor vice versa ;? for the subject of geometry is spatial magnitudes,
i.e. continuous quanta, and that of arithmetic is numbers, i.e.
discrete quanta.?
At the same time, Aristotle allows the possibility of μετάβασις
from one genus to another, when the genera are 'the same in some
respect'.* What he has in mind is the possibility of using mathe-
matical proofs in sciences that are intermediate between mathe-
matics and physics, what he elsewhere$ calls rà φυσικώτερα τῶν
μαθημάτων, since their subject-matters are subordinate to those
of a mathematical science. Optics is in this sense subordinate to
geometry, and harmonics to arithmetic. He elsewhere says much
thesame about astronomy? and mechanics.? Consider, for instance,
optics. Optics studies rays of light, which are lines 'embodied' in
certain matter; and in virtue of their being lines they obey
geometrical principles, and their properties can be studied by the
aid of geometry without any improper transition being involved.
But elsewhere? Aristotle adds a refinement, by distinguishing
within these sciences a mathematical part and a physical or
observational part, the latter being subordinate to the former as
that is to geometry or arithmetic. Here it is the business of the
observer to ascertain the facts, and that of the mathematician to
discover the reasons for them.!?
The second corollary which Aristotle draws!! from his account
of the premisses of science is that there cannot, strictly speaking,
be demonstration of perishable facts, i.e. of a subject's possession
of an attribute at certain times. Aristotle is taking account of the
fact that there are not only mathematical sciences stating eternal
and necessary connexions between subjects and attributes, but
also quasi-mathematical sciences which prove and explain tem-
porary but recurring facts, as astronomy explains why the moon
is at times eclipsed. There is an eternal and necessary connexion
between a body's having an opaque body interposed between it
and its source of light, and its being eclipsed, and the moon some-
! 25*38-9. 2 15b13-14. 3 Cat, 4520-5, Met. 10202714.
* 7558-9. 5 Phys. 194*7. 5 75914-17.
7 Phys. 193925-33, Met. 107353-8.
8 76422-5, 78535-9, Met. 1078*314-17. 9 78639-79413.
9 For a full discussion of Aristotle’s views about these intermediate sciences
cf. Mansion, Introd. à la Phys. Aristotélicienne, 94-101. 11 7521-30,
64 INTRODUCTION
times incidentally has the one attribute because it sometimes in-
cidentally has the other.’ The proof that it has it is eternal inas-
much as its object is a recurrent type of attribute, but inasmuch
as the subject does not always have this attribute the proof is
particular.2 The fact explained is an incidental and non-eternal
example of an eternal connexion.
The third corollary? is that the propositions of a science cannot
be proved from common principles (i.e. from principles which
apply more widely than to the subject-matter of the science), any
more than they can be proved from alien principles. For it is
plain that there will be some subject to which the predicate of our
conclusion applies commensurately, and that subject and not
something wider must be the middle term of our proof, if our
premisses are to be commensurately universal. In consequence,
Aristotle rejects the ideal, adumbrated by Plato in the Republic,
of a master-knowledge which will prove the ἀρχαί of the special
sciences ; each science, he holds, stands on its own basis, and its
appropriate premisses are known by their own self-evidence.
Zabarella argues* that Aristotle is not attempting to show that
metaphysics cannot prove the ἀρχαί of the sciences, but only that
they cannot prove their own ἀρχαί; but there is nothing here or
elsewhere in Aristotle to justify this view. In the Metaphysics
itself it is nowhere suggested that metaphysics can do this, and it
would be inconsistent with the underlying assumption of that
work, that metaphysics is the study of τὸ dv # ov, of being only in
respect of its most universal characteristics. Zabarella’s interpre-
tation is, I think, only a projection of his own somewhat Platonic
view into Aristotle. It is natural enough that Plato should have
been scandalized by the spectacle of several sciences starting from
separate dpyai, and should have been fired by the ideal of a single
unified system of knowledge. But it is significant that neither
Plato nor anyone else has ever had any success in realizing such
an ideal, while mathematics offers a clear example of a science
which, starting from premisses which it holds to be self-evident,
succeeds in reaching a unified body of knowledge which covers
one large sphere of being. The search for a single all-explaining
principle seems to be a product of the equally mistaken desire to
have proof of everything. If we cannot have proof of everything
(so its advocates seem to say), since the ultimate premisses of any
ward συμβεβηκός 75925. 2 Ib. 33-5. 3 Ch. 9.
* In duos Aristotelis lib. Post. An. Comm. 44.
DEMONSTRATIVE SCIENCE 65
proof are obviously themselves not proved, let us at least have as
few unproved principles as possible, and if possible only one. But
there is really nothing more scandalous in a plurality of unproved
premisses than in a single one.
In maintaining that proof must be from the proper principles
of the science in question, Aristotle might seem to be contradicting
his inclusion of the κοινὰ ἀξιώματα among the premisses of a
science. In ch. ro he meets this difficulty by pointing out! that a
science does not assume the κοινὰ ἀξιώματα in their generality,
but only in so far as they are true of the subjects of the science in
question, this being all that is necessary for its purpose.
Aristotle draws an interesting distinction between three types
of error which may arise in the attempt at scientific proof.? In the
first place, we may sin against the principle that our premisses
must be true.’ In trying to prove a geometrical proposition we
may use premisses that are geometrical in the sense that their
terms are geometrical terms, but ungeometrical in the sense that
they connect these terms incorrectly (e.g. by assuming that the
angles of a triangle are not equal to two right angles). In the
second place we may sin against the principle that our proof must
be syllogistically correct.* In this case our premisses may be in the
full sense geometrical, but we misuse them. In the third place we
may sin against the principle that proof in any science must be
drawn from premisses appropriate to the science.5 In this case
our premisses are not geometrical at all. Aristotle adds that error
of the second kind is less likely to arise in mathematics than in
dialectical reasoning, because any ambiguity in terms is easily
detected when we have a figure to look at. 'Is every circle a
figure? If we draw one, we see that this is so. Are the epic poems
a circle? Clearly not'—i.e. not in the literal sense in which every
circle is a figure.
With this distinction of three types of error we may compare
a later section of the Posterior Analytics, i. 16-18. Paralogism—
reasoning not in accordance with the rules of syllogism—is not
there mentioned, probably because it has been fully considered in
the Prior Amalytics. The first kind of error discussed in the
present chapter, 6 ἐκ τῶν ἀντικειμένων συλλογισμός (e.g. reasoning
from incorrect geometrical assumptions), is described in chs. 16
and 17 under the title ἄγνοια ἡ κατὰ διάθεσιν, ignorance which
1 26337-b2. 2 77b16-33. 3 Cf. 71b19-21, 25-6.
* Cf. ib. 18. 5 Cf. ch. 7. 6 They were often called ὁ κύκλος,
4985 F
66 INTRODUCTION
involves a definite though mistaken attitude towards geometrical
principles. The third kind discussed in the present chapter, 6 é£
ἄλλης τέχνης, that which in the absence of even incorrect geo-
metrical opinions attempts to prove a geometrical proposition
from premisses borrowed from another science, is by implication
called ἄγνοια ἡ κατ᾽ ἀπόφασιν, and in ch. 18 such ignorance of a
whole sphere of reality is described as due to the absence of one of
the senses ; and this is in accordance with Aristotle’s general view
that the principles of all the sciences are derived by generalization
from sensuous experience.”
The chapter with which we are dealing? contains one further
important point, not made elsewhere. A science grows, says
Aristotle, not by interpolation of new middle terms, but by one or
other of two methods, both of them methods of extrapolation. If
we already know that C is A because B is A and C is B we can (1)
add the premiss 'D is C' and thus get the new conclusion that D
is A, or (2) we can add the premisses that D is A and E is D, and
thus get the conclusion that E is A; ie. we may extrapolate
either vertically or horizontally. The dictum that a science grows
by extrapolation might at first sight seem to contradict what
Aristotle says elsewhere,* that ‘packing’ or interpolation {(πύκνω-
σις) is the method of science; but there is no real contradiction.
We have not science at all till interpolation has been completed,
till we have replaced all provable premisses by premisses that need
no proof. But once this has been done, extrapolation comes by
its own and provides for the growth of the science.
Aristotle has pointed out’ three types of error which do not
yield knowledge at all. In ch. 13 he passes to consider less gross
forms of error, which lead to something that may in a loose sense
be called knowledge, but falls short of demonstratio botissima.
When we commit them, we may reach knowledge that a fact is so,
but not knowledge of why it is so. In the first place, we may sin
against the principle that our premisses should be immediate.$
If D is A because B is A,C is B, and D is C, and we reason Ὁ is A,
D isC, Therefore D is A', i.e. if'C is A' is provable and we assume
it without proof, we shall not know why D is A, nor indeed in the
strict sense know that D is Á, but we shall at least have reached
a true opinion, and have to some extent reached it by correct
means. Secondly, we may sin against the principle that our
1 49b25. 2 jj. 19. 3 i. 12. 4 8433-5.
5 In ch. 12. $ 78223-6, cf. 71b19-21, 26-9.
DEMONSTRATIVE SCIENCE 67
premisses must be γνωριμώτερα kai πρότερα Kai αἴτια τοῦ συμπε-
pdopatos.' Suppose we reason: ‘Heavenly bodies that do not
twinkle must be relatively near to us, Planets do not twinkle,
Therefore planets must be relatively near to us.’ Then our
premisses are true, our reasoning is syllogistically correct, and we
reach a true opinion about the state of the facts. But it is not the
case that because the planets do not twinkle they are near to us,
but that because they are near they do not twinkle. We have
clearly not reached knowledge of the actual ground of the fact we
state in our conclusion.
In this case the converse of our major premiss is true, and we
can therefore replace the defective syllogism by the syllogism
'Heavenly bodies that are near to us do not twinkle, The planets
are near to us, Therefore the planets do not twinkle', and then we
shall know both the fact stated in our conclusion and the ground
of its truth, and our reasoning will be truly scientific. But in
other cases our major premiss may ot be convertible; then we
have an unscientific syllogism which cannot be immediately re-
placed by a scientific one.
Thirdly, we may sin against the principle that our premisses
must be true 4 αὐτό.2 This happens when the middle term ‘is
placed outside’, i.e. occurs as predicate of both premisses, as when
we say ‘All breathing things are animals, No wall is an animal,
Therefore no wall breathes'. Here we reason as if not being an
animal were the cause of not breathing, and imply that being an
animal is the cause of breathing; but plainly being an animal is
not the cause of breathing, since not all animals breathe. The
precise or adequate cause of breathing is possession of a lung;
being an animal is an inadequate cause of breathing, and not being
an animal a super-adequate cause of not breathing. In saying, in
effect, 'Nothing that is not an animal breathes', we have used a
premiss which, while true κατὰ παντός and καθ᾽ αὑτό, is not true jj
αὐτό; for it is not precisely qua not being an animal, but qua not
possessing a lung, that that which does not breathe does not
breathe.
Having thus pointed out in ch. 13 the failure of a second-figure
argument to give the true cause of an effect, Aristotle goes on in
ch. 14 to point out that in general the first figure is the figure
appropriate to science. He appeals to the fact that the sciences
actually use this much more than the other figures, and he gives
τ 78826-br3, cf. 7 1519-22, 29-7245. 2 2813-31, cf. 73525-7433.
68 INTRODUCTION
two reasons for its superiority: (1) that it alone can establish a
definition, since the second figure cannot prove an affirmative, nor
the third a universal, conclusion; and (2) that even if we start
with a syllogism in the second or third figure, if its premisses
themselves need to be proved we must fall back on the first, since
the affirmative premiss which a second-figure syllogism needs
cannot be proved in the second figure, and the universal premiss
which a third-figure syllogism needs cannot be proved in the third.
Aristotle has in ch. 3 shown, and has repeatedly thereafter
assumed, that there must be immediate premisses, neither needing
nor admitting of proof. He now! makes the important point that
among these there must be negative as well as affirmative pre-
misses, and points out clearly the kind of terms that must occur
in them. If either A or B is included in a wider class in which the
other is not included, the proposition No B is A cannot be im-
mediate. For (1) if A is included in C and B is not, No B is A can
be established by the premisses All A is C, No BisC. (2) If B is
included in D and A is not, No B is A can be established by the
premisses No A is D, All B is D. (3) If A is included in C and B
in D, No B is A can be established by the premisses All 4 is C,
No B isC, or by the premisses No A is D, All B is D. The only
type of immediate negative proposition which Aristotle seems to
consider is that in which one category is excluded from another,
as when one says 'No substance is a quality'. The types of pro-
position he does not consider are those whose terms are (1) two
infimae species falling under the same proximate genus, (2) two
alternative differentiae, or (3) two members of the same tnfima
species. In the first case the differentia possessed by one and not
by the other can be used as middle term to prove the exclusion of
one species from the other. In the second case Aristotle would
have to admit that the two differentiae exclude one another
directly, just as two categories do. The third case would not
interest him, because in the Posferior Analytics he is concerned
only with relations between universals. His consideration of the
problem is incomplete, but both his insistence that there are
immediate negative premisses and his insistence that propositions
in which one category is excluded from another are immediate
are important pieces of logical doctrine.
He now? embarks on a discussion, much more elaborate than
any that has preceded, of the question whether there are im-
1 Ch. 15. 2 Chs. 19-22.
DEMONSTRATIVE SCIENCE 69
mediate premisses, not needing nor admitting of proof. A dialec-
tician is satisfied if he can find two highly probable premisses of
the form All B is A, AllC is B; he then proceeds to infer that all
C is A. But a scientist must ask the question, ‘Are All B is A,
AIC is B, really immediate propositions ; am I not bound to look
for a middle term between B and A, and one between C and B?'
Aristotle divides the problem into three problems: (1) If thereisa
subject not predicable of anything, a predicate predicable of that
subject, and a predicate predicable of that predicate, is there an
infinite chain of propositions in the upward direction, a chain in
which that which is predicate in one proposition becomes subject
in the next? (2) If there is a predicate of which nothing can be
predicated, a subject of which it is predicable, and a subject of
which that subject is predicable, is there an infinite chain in the
downward direction, in which that which is subject in one pro-
position becomes predicate in the next? (3) Is there an infinite
chain of middle terms between any two given terms?!
He first? establishes that if questions (1) and (2) are to be
answered in the negative, question (3) must also be so answered.
This is obvious, because if between two terms in a chain leading
down from a predicate, or in a chain leading up from a subject,
there is ever an infinite number of middle terms, there is neces-
sarily an infinite number of terms in the whole chain; this must
be so, even if between some of the terms no middle term can be
inserted.
Next! Aristotle proves that if a chain having an affirmative
conclusion is necessarily limited at both ends, a chain having a
negative conclusion must also be limited at both ends. This fol-
lows from the fact that a negative can only be proved in one or
other of the three figures: (a) No Bis A, AIL C is B, Therefore no
Cis A; (b) All A is B, NoC is B, Therefore no C is A; (c) No B is
C (or Some B is not C), All B is A, Therefore some A is not C.
Now if in (a) we try to mediate the negative premiss, this will be
by a prosyllogism: No D is A, All Bis D, Therefore no B is A.
Thus with each introduction of an intermediate negative premiss
we introduce a new affirmative premiss; and therefore if the
chain of affirmative premisses is limited, so is the chain of negative
premisses; there must be a term of which 4 is directly deniable.
A similar proof applies to cases (δ) and (c).
Aristotle now* turns to his main thesis, that a chain of affirma-
τ 81530-8258. 2 Ch. 20. 3 Ch. 21. * Ch. 22.
70 INTRODUCTION
tive premisses must be limited both in the upward and in the
downward direction. He first offers arguments which he describes
as dialectical,! but which we must not pass over, because they
contain so much that is characteristic of his way of thinking. He
starts? with the true observation that if definition is to be possible,.
the elements in the definition of a thing must be limited in number.
But clearly propositions other than definitions occur in scientific
reasoning, and he therefore has to attempt a wider proof. He
prefaces this by laying down a distinction between genuine
predication and another kind of assertion. He discusses three
types of assertion: (1) ‘that big thing is a log’, or ‘that white thing
is a log’; (2) ‘that white thing is walking’, or ‘that musical thing is
white’; (3) ‘that log is big’, or ‘that log is white’, or ‘that man is
walking’; and analyses them differently. (1) When we say ‘that
white thing is a log’, we do not mean that ‘white’ is a subject of
which being a log is an attribute, but that being white is an
attribute of which that log is the subject. And (2) when we say
‘that musical thing is white’ we do not mean that ‘musical’ is a
subject of which being white is an attribute, but that a certain
man who has the attribute of being musical has also that of being
white. In neither case do we think of our grammatical subject
as being a metaphysical subject, or of our grammatical predicate
as being a metaphysical attribute of that subject. But when (3)
we say ‘that log is white’ we understand our subject to be a meta-
physical subject underlying or possessing the attribute of being
white. Aristotle recognizes only assertions of type (3) as predica-
tions proper, and describes the others as predications κατὰ συμ-
βεβηκός, as statements which are possible only as incidental
consequences of the possibility of a proper predication.
This distinction is open to serious criticism. It is evident that
the form of words 'that white thing is a log' or 'that musical thing
is white' is not only a perfectly proper statement, but in certain
circumstances the only appropriate statement. When we say
‘that white thing is a log’, our meaning would be quite im-
properly conveyed by the words 'that log is white'; 'that white
thing' is not only the grammatical but the logical subject—that
about which something is asserted—and what is predicated of it
is just that it is a log. Aristotle is either confusing the logical
distinction of subject and predicate—a distinction which depends
on our subjective approach to the matter in hand—with the
! 8427. 2 82037.
DEMONSTRATIVE SCIENCE 71
metaphysical distinction of subject (or substrate) and attribute,
or else, while aware of the difference, he is saying that only that
is proper predication in which the metaphysical subject and attri-
bute are made respectively logical subject and predicate; which
would be just as serious an error as a confusion of the two dis-
tinctions would be."
It may be added that his mistake is made more easy by the
Greek usage by which a phrase like τὸ λευκόν may stand either for
‘the white thing’ or for ‘white colour’. For the speaker of a
language in which τὸ λευκόν ἐστι ξύλον might mean ‘white colour
is a log', it becomes easy to suppose that the statement is an
improper statement. It may be said too that while as a general
logical doctrine what Aristotle says here is indefensible, there is
some justification for his restricting predication as he does, in the
present context. For the Postertor Analytics is a study of scientific
method, and he is justified in saying? that the sort of proposition
which the sciences use is normally one in which an attribute is
predicated of a substance. But to this it must be added that the
mathematical sciences habitually assert propositions of which the
subject is not a substance but an entity (such as a triangle) which
is thought of as having a nature of its own in consequence of
which it has the attribute that is predicated of it, as substances
have attributes in consequence of their intrinsic nature. Aristotle
is, in effect, recognizing this when he later describes the unit as
οὐσία aberos and the point as οὐσία θετός.3
Among proper predications Aristotle proceeds* to distinguish
definitions and partial definitions (ὅπερ ἐκεῖνο 7) ὅπερ ἐκεῖνό τι
onpatver) from those which assert of subjects συμβεβηκότα, among
which he includes not only accidents but also attributes that are
καθ᾽ αὑτό in the second sense,5 i.e. properties. In any case the
chain of predication must be finite, since the categories, under
onc or other of which any predicate of a given subject must fall,
are finite in number, and so are the attributes in any category.®
There is only one type of case, he points out, in which a thing is
predicated of itself; viz. definition, in which a thing designated
by a name is identified with itself as described by a phrase. In
every other case the predicate is an attribute assigned to a subject
and not itself having the nature proper to a subject, i.e. not a
! There is a penetrating criticism of Aristotle's doctrine in J. Cook Wilson,
Statement and Inference, 1. 159-66. 2 83320-I, 34-5.
? 87236. * 83324. * Cf. pp. 60-1. © 83br2-15.
72 INTRODUCTION
self-subsistent thing. Every chain of predication is terminated in
the downward direction by such a thing, an individual substance.
Upwards from this stretches a finite chain of essential attributes,
terminating in a summum. genus or category, and a finite chain of
συμβεβηκοτά, some of which are predicated of the subject strictly
ἡ αὐτό, just as being that subject, while others are predicated
ἡ αὐτό of some element in the nature of the subject (i.e. of some
species to which it belongs), and thus related καθ᾽ αὑτό but not
ἡ αὐτό to the subject. Any chain of συμβεβηκότα, no less than any
chain of definitory attributes, terminates in a category, ‘which
neither is predicated of anything prior to itself, nor has anything
prior to itself predicated of it'—because there 15 nothing prior to it.'
The second dialectical argument? for the finiteness of the chain
of predication is a simple one, running as follows: anything that
is the conclusion from a chain of propositions can be known only
if it is proved; but if the chain is infinite it cannot be traversed,
and its conclusion cannot be proved. Thus to suppose the chain
of predication to be infinite runs counter to our confidence that,
in mathematics at least, we know the conclusions of certain trains
of reasoning to be true, and not merely to be true if the pre-
misses are.
Aristotle now? turns to the proof which he describes as analyti-
cal—analytical because it rests on a consideration not of predica-
tion in general, but of the two kinds of predication which in
ch. 4 have been described as being proper to science, those in which
we predicate of a subject some element in its definition, and those
in which we predicate of a subject some attribute in whose
definition the subject itself is included. If we had an infinite chain
of predicates, each related to its subject in the second of these
ways, we should have a predicate B including in its definition its
subject A, a predicate C including in its definition its subject B,
.. . and therefore the term at infinity would include in its defini-
tion an infinite number of elements. If, again, we had an infinite
chain of predicates, each related to its subject in the first of the
two ways, the original subject would include in its definition an
infinite number of elements. Each of these two consequences
Aristotle rejects as impossible, on the ground that, since any
term is definable, no term can include an infinite number of
elements in its essential nature.
It would seem plausible to say that if two subjects have the
! 83Pr7-31. 2 Ib. 32-8436. 3 8438.
DEMONSTRATIVE SCIENCE 73
same attribute, it must be by virtue of some other attribute
which they have in common. But Aristotle is quick to point out!
that this would involve an infinite chain of predication. If, when
C and D both have the attribute A, this must be because they
both have the attribute B, it will be equally true that if they
both have the attribute B, this must be because they both have
a further attribute in common, and so ad infinitum. The true
ὁδὸς ἐπὶ τὰς ἀρχάς is one that terminates not, as Plato supposed,
in a single ἀρχὴ ἀνυπόθετος, but in a variety of immediate proposi-
tions, some affirmative, some negative. In seeking the ground of
an affirmative proposition we proceed by packing the interval
between our minor term and our major, never inserting a middle
term wider than our major. B is A because BisC, Cis D... Y
is Z, Z is A, the ultimate premisses being known not by reasoning
but by intuition (voós). If the proposition we seek to prove is a
negative one, we may proceed in either of three ways. (1) Suppose
that no B is A because no C is A andall B isC ; then if we want to
prove that no C is A, we may do so by recognizing that no D is A
and all C is D; and so on. We never take in a middle term which
includes our major term A. (2) Suppose that no E is D because
all D is C and no E is C; then if we want to prove that no E isC,
we may do so by recognizing that all C is F and no E is F ; and
so on. We never take in a middle term included within our
minor, E. (3) Suppose that no E is D because no D is C and all E
is C ; then if we want to prove that no D is C, we may do so by
recognizing that no C is F and all D is F ; and so on. We never
take a middle term that either includes our major, or is included
in our minor.
From this consideration of the necessity for immediate pre-
misses, Aristotle passes? to compare three pairs of types of proof
in respect of 'goodness', i.e. of intellectual satisfactoriness. Is
universal or particular proof the better? Is affirmative or nega-
tive proof the better? Is ostensive proof or reductio ad impossibile
the better? On the first question, he first? states various dialec-
tical arguments purporting to show particular proof (i.e. proof
proceeding from narrower premisses) to be better than universal,
then‘ refutes these, and offers5 dialectical arguments in favour of
the opposite view, and finally offers what he considers the most
conclusive arguments in support of it, viz. (1) that if we know a
t Ch. 23. 2 Chs. 24-6. ? 85420-b3,
* 8553-22. 5 Ib, 23-86221. $ Ib. 22-30.
74 INTRODUCTION
universal proposition such as ‘Every triangle has its angles equal
to two right angles’, we know potentially the narrower proposi-
tion ‘Every isosceles triangle has its angles equal to two right
angles’, while the converse is not true; and (2) that a universal
proposition is apprehended by pure νόησις, while in approaching
a particularization of it we have entered on a path which termi-
nates in mere sensuous perception. His consideration of the merits
of affirmative as compared with negative proof,! and of ostensive
proof as compared with reductio,? is of less general interest.
Turning? from the comparison of particular proofs to that of
whole sciences, Aristotle points out that one science is more
precise than another, more completely satisfactory to the intellect,
if it fulfils any one of three conditions. In the first place, a science
which knows both facts and the reasons for them is superior to a
so-called science which is a mere collection of unexplained facts.
In the second place; among genuine sciences a pure science, one
that deals with abstract entities, is superior to an applied science,
one that deals with those entities embodied in some kind of
'matter' ; pure arithmetic, for instance, is superior to the applica-
tion of arithmetic to the study of vibrating strings. In the third
place, among pure sciences one that deals with simple entities is
superior to one that deals with complex entities; arithmetic,
dealing with units, which are entities without position, is superior
to geometry, dealing with points, which are entities with position.
It is noteworthy that, while Aristotle conceives of demonstra-
tion in the strict sense as proceeding from premisses that are
necessarily true to conclusions that are necessarily true, he recog-
nizes demonstration (in a less strict sense, of course) as capable of
proceeding from premisses for the most part true to similar con-
clusions.* That which can never be an object of scientific know-
ledge is a mere chance conjunction between a subject and a
predicate. And, continuing in the same strain,’ he points out that
to grasp an individual fact by sense-perception is never to know
it scientifically. Even if we could see the triangle to have its
angles equal to two right angles, we should still have to look for a
demonstration to show why this is so. Even if we were on the
moon and could see the earth thrusting itself between the moon
and the sun, we should still have to seek the cause of lunar
eclipse. The function of perception is not to give us scientific
knowledge but to rouse the curiosity which only demonstration
! Ch. 25. * Ch. 26. 3 Ch. 27. * Ch. 30. 5 Ch. 31.
DEMONSTRATIVE SCIENCE 75
can satisfy. At the same time some of our problems are due to
lack of sense-perception; for there are cases in which if we per-
ceived a certain fact we should as an immediate consequence,
without further inquiry, recognize that and why it must be so in
any similar case. To quickness in divining the cause of a fact, as
an immediate result of perceiving the fact, Aristotle assigns the
name of ἀγχίνοια.
VII
THE SECOND BOOK OF THE POSTERIOR ANALYTICS
THE second book of the Posterior Analytics bears every appearance
of having been originally a separate work. It begins abruptly,
with no attempt to link it on to what has gone before; even the
absence of a connective particle in the first sentence is significant.”
Further, there is one fact which suggests that the second book is a
good deal later than the first. In the first book allusions to mathe-
matics are very frequent, and it might almost be said that Aris-
totle identifies science with mathematics, as we might expect a
student of the Academy to do; the only traces of a scientific
interest going beyond mathematics and the semi-mathematical
sciences of astronomy, mechanics, optics, and harmonics are the
very cursory allusions to physics and to medical science in 77441,
b41-7845, 88214-17, P12. In the second book allusions to mathe-
matics are relatively much fewer, and references to physical and
biological problems much more numerous; cf. the references to
the causes of thunder? and of the rising of the Nile,* to the
definition of ice,5 to the properties of different species of animals
and to analogical parts of animals,’ to the causes of deciduousness?
and of long life,? and to medical problems.!?
The subject of the first book has been demonstration ; the main
subject of the second book, with which the first ten chapters are
concerned, is definition. Aristotle begins by distinguishing four
topics of scientific inquiry, τὸ ὅτι, τὸ διότι, εἰ ἔστι, τί ἐστι. The
difference between τὸ ὅτι and εἰ ἔστι turns on the difference
between the copulative and the existential use of ‘is’; the two
τ Ch. 34.
? Apart from the Metaphysics, the only other clear cases in Aristotle of
books (after the first) beginning without such a particle are Phys. 7, Pol. 3, 4.
3. 93322-5, 57-12, 9433-9, P32-4. + 9g8*31-4. 5 gg*16-21.
© 9823-19. 7 Tb. 20-3. 3 b. 36-616, 533-8, 99323-9.
? 9955-8. 1 9458-21, 9726-7.
76 INTRODUCTION
questions are respectively of the form ‘Is A B?’ and of the form
‘Does A exist?’ If we have established that A is B, we go on to
ask why it is so; if we have established that A exists, we go on to
ask what it is.
Aristotle proceeds in ch. 2 to say that to ask whether A is B, or
whether A exists, is to ask whether there is a middle term to account
for A’s being B, or for A’s existing, and that to ask why A is B, or
what 4 is, is to ask what this middle term is. But there are reasons
for supposing that this is an over-statement of Aristotle’s mean-
ing. He never, so far as I know, makes the question whether a
certain substance exists turn on the question whether there is a
middle term to account for its existence, nor the question what
acertain substance is turn on the question what that middle term
is; and it would be strange if he did so. The question whether a
certain substance exists is to be decided simply by observation ;
the question what it is is to be answered by a definition stating
simply the genus to which the substance belongs, and the differen-
tia or differentiae that distinguish it from other species of the
genus. It is really of attributes that Aristotle is speaking when he
says that to ask whether they exist is to ask whether there is a
cause to account for them, and that to ask what they are is to ask
what that cause is. And when we are considering an attribute,
the question whether it exists is identified with the question
whether this, that, or the other substance possesses it, and the
question what it is is identified with the question why this, that,
or the other substance possesses it. ‘What is eclipse? Depriva-
tion of light from the moon by the interposition of the earth. Why
does eclipse occur, or why does the moon suffer eclipse? Because
its light fails through the earth’s blocking it off.”
In ch. 3 Aristotle passes to pose certain questions regarding the
relation between demonstration and definition. How is a defini-
tion proved? How is the method of proof to be put into syllo-
gistic form? What is definition? What things can be defined?
Can the same thing be known, in the same respect, by definition
and by demonstration? Ina passage which is clearly only dialec-
tical? he argues that not everything that can be demonstrated
can be defined, that not everything that can be defined can be
demonstrated, and, indeed, that nothing can be both demonstrated
and defined. Dialectical arguments directed against various pos-
sible methods of attempting to prove a definition, and tending to
! go*15-18. 2 b3-91811.
SECOND BOOK OF POSTERIOR ANALYTICS 77
show the complete impossibility of definition, are offered in chs.
4-7. In ch. 8 Aristotle turns to examining critically these dialec-
tical arguments. As a clue to the discovery of the true method of
definition, he adopts the thesis already laid down,! that to know
the cause of a substance's possessing an attribute is to know the
essence of the attribute. Suppose that we know that a certain
event, say, eclipse, exists. We may know this merely κατὰ cupBe-
βηκός (e.g. by hearsay) without knowing anything of what is
meant by the word, and in that case we have not even a starting-
point for definition. But suppose we have some knowledge of the
nature of the event, e.g. that eclipse is a loss of light. Then to ask
whether the moon suffers eclipse is to ask whether a cause capable
of producing it (e.g. interposition of the earth between the moon
and the sun) exists. If, starting with a subject C and an attribute
(or event) A, we can establish a connexion between C and A by a
series of intermediate propositions such as 'that which has the
attribute B, necessarily has the attribute A, that which has the
attribute B, necessarily has the attribute B, . . . that which
has the attribute B, necessarily has the attribute B, ,, C
necessarily has the attribute B,’, then we know both that
and why C has the attribute 4. If at some point we fail to
reach immediacy, e.g. if we have to be content with saying
‘C actually (not necessarily) has the attribute B,’, we know that
C has the attribute 4 but not why it has it. Aristotle illus-
trates the latter situation by this example: A heavenly body
which produces no shadow, though there is nothing between us
and it to account for this, must be in eclipse, The moon is thus
failing to produce a shadow, Therefore the moon is in eclipse.
Here the middle term by the use of which we infer the existence
of eclipse plainly cannot be the cause of eclipse, being instead a
necessary consequence of it; it does not help us to explain why
the moon is in eclipse, and therefore does not help us to know what
eclipse is. But the discovery, by this means, that eclipse exists
may set us on inquiring what cause does exist that would explain
the existence of eclipse, whether it is the interposition of an opaque
body between the moon and its source of light, or a divergence of
the moon from its usual path, or the extinction of fire in it. If we
find such a cause to exist, it becomes the definition of eclipse;
eclipse is the interposition of the earth between the moon and the
sun. And if we can in time discover the presence of a cause which
T 9o*14-23.
78 INTRODUCTION
will account for the earth’s coming between the moon and the
sun, that will serve as a further, even more satisfactory, definition
of eclipse.! We never get a syllogism having as its conclusion
“eclipse is so-and-so’, but we get a sorites by which it becomes
clear what eclipse is—a sorites of the form ‘What has B,
suffers eclipse, What has B, has B, ... What has B, has B,_,,
The moon has B,, Therefore the moon suffers eclipse'. Our final
definition would then be ‘eclipse is loss of light by the moon in
consequence of the sequence of attributes B,, B, ,,. . . Bs, By’.
This type of definition can of course be got only when 4 is an
attribute that has a cause or series of causes. But there are also
things that have no cause other than themselves, and of these we
must simply assume, or make known by some other means (e.g.
by pointing to an example) both that they exist and what they
are. This is what every science does with regard to its primary
subjects, e.g. arithmetic with regard to the unit.?
There are thus three types of definition :? (1) A verbal definition
stating the nature of an attribute or event by naming its generic
nature and the substance in which it occurs, e.g. 'eclipse is a loss
of light by a heavenly body'—a definition which sets us on to
search for a causal definition of the thing in question. (2) A causal
definition of such a thing, e.g. ‘eclipse of the moon is a deprivation
of light from the moon by the interposition of the earth between
the moon and the sun'. Such a definition is 'a sort of demonstra-
tion of the essence, differing in form from the demonstration'.*
Le., the definition packs into a phrase the substance of the
demonstration "What has an opaque body interposed between it
and its source of light is eclipsed. The moon has an opaque body
so interposed, Therefore the moon suffers eclipse.’ A definition
of type (1), on the other hand, contains a restatement only of the
conclusion of the demonstration. (3) A definition of a term that
needs no mediation, i.e. of one of the primary subjects of a
science.
Aristotle now passes from the subject of definition to consider
a number of special questions relating to demonstration.5 It is
unnecessary to enter here into the difficulties of ch. 11, one of the
most difficult chapters in the whole of Aristotle. He introduces
here a list of types of αἰτίαν which differs from his usual list by
containing, in addition to the formal, the efficient, and the final
T gabr2-14. 2 Ch. 9. 3 Ch. ro. 4 9491-2.
5 These occupy Chs. 11-18.
SECOND BOOK OF POSTERIOR ANALYTICS = 79
cause, not the material cause but τὸ τίνων ὄντων ἀνάγκη τοῦτ᾽ εἶναι.
That this is not another name for the material cause is shown by
two things. For one thing, the material cause could not be so
described ; for Aristotle frequently insists that the material cause
does not necessitate its effect, but is merely a necessary precondi-
tion of it. And secondly, the example given is as remote as pos-
sible from the typical examples of the material cause which he
gives elsewhere. How, then, is this departure from his usual list
of causes to be explained? We may conjecture that it was due
to Aristotle's recognition of the difference between the type of
explanation that is appropriate in the writing of history or the
pursuit of natural science and that which is appropriate in mathe-
matics. In history and in natural science we are attempting to
explain events, and an event is to be explained (in Aristotle's
view) by reference either to an event that precedes it (an efficient
cause) or to one that follows it (a final cause). In mathematics
we are dealing with eternal attributes of eternal subjects, and
neither an efficient nor a final cause is to be looked for, but only
another eternal attribute of the same eternal subject, some attri-
bute the possession of which by the subject can be more directly
apprehended than its possession of the attribute to be explained.
This eternal ground of an eternal consequent is thus introduced
here instead of the material cause which we find elsewhere in
Aristotle’s account of causation. A reference to the material
cause would indeed be out of place here; for the analysis of the
individual thing into matter and form is a purely metaphysical
one of which logic need take no account, and in fact the word ὕλη
and that for which it stands are entirely absent from the Organon.
It is not easy to see how the efficient cause, the final cause, and
the eternal ground are related, in Aristotle's thought, to the formal
cause. But we have already found him stating the definition or
formal cause of eclipse to be 'deprivation of light from the moon
by the interposition of the earth', where the efficient cause
becomes an element in the formal cause and is by an overstate-
ment said to be the formal cause.! And similarly here he identifies
the formal cause of the rightness of the angle in the semicircle
with its being equal to the half of two right angles, i.e. with the
ground on which it is inferred.? And again, where an event is to
be explained by a final cause, he would no doubt be prepared to
identify the formal cause of the event with its final cause. We
1 9356-7. 509 ga*28-35.
80 INTRODUCTION
have here in fact the doctrine that is briefly adumbrated in
Metaphysics 1041227—30—$avepóv τοίνυν ὅτι ζητεῖ τὸ αἴτιον" τοῦτο δ᾽
ἐστὶ τὸ τί ἦν εἶναι, ὡς εἰπεῖν λογικῶς, ὃ ἐπ᾽ ἐνίων μέν ἐστι τίνος
ἕνεκα, οἷον ἴσως ἐπ᾽ οἰκίας ἢ κλίνης, ἐπ᾽ ἐνίων δὲ τί ἐκίνησε πρῶτον"
αἴτιον yap καὶ τοῦτο. The doctrine is that the cause of the inherence
of a πάθος in a substratum (e.g. of noise in clouds) or of a quality
in certain materials (e.g. of the shape characteristic of a house in
bricks and timber) is always—to state the matter abstractly
(Aoyixds)—the τί ἦν εἶναι or definition of the union of substratum
and πάθος, or of materials and shape. But in some cases this
definition expresses the final cause—e.g. a house is defined as a
shelter for living things and goods ;! in other cases the definition
expresses the efficient cause—e.g. thunder is a noise in clouds
produced by the quenching of fire.?^ In yet other cases, he here
adds, the formal cause expresses the eternal ground of an eternal
attribute. In other words, the formal cause is not a distinct cause
over and above the final or efficient cause or the eternal ground,
but is one of these when considered as forming the definition of
the thing in question. The one type of cause that can never be
identical with the formal cause is the material, and hence the
material cause is silently omitted from the present passage.
Aristotle goes on in ch. 12 to point out a difficulty which arises
with regard to efficient causation. Here, he maintains, we can
infer from the fact that an event has occurred that its cause must
have occurred previously, but we cannot infer from the fact that
a cause has occurred that its effect must have occurred. For
between an efficient cause and its effect there is always an interval
of time, and within that interval it would not be true to say that
the effect has occurred. Similarly we cannot infer that since a
certain efficient cause has taken place, its effect will take place.
For it does not take place in the interval, and we can neither say
how long the interval will last, nor even whether it will ever end.
Aristotle is clearly conscious of the difficulty which everyone must
feel if he asks the question why a cause precedes its effect ; for it
is hard to see how a mere lapse of time can be necessary for the
occurrence of an event when the other conditions are already
present; this is a mystery which has never been explained.
Aristotle confesses his sense of the mystery when he says ém-
σκεπτέον δὲ τί τὸ συνέχον ὥστε μετὰ τὸ γεγονέναι τὸ γίνεσθαι ὑπάρχειν
ἐν τοῖς πράγμασιν.3 This much, he adds, is clear, that the com-
τ Met. 1043416, 33. % An. Post. 938, 945. 3 gsbr-35.
SECOND BOOK OF POSTERIOR ANALYTICS 81
pletion of one process, being momentary, cannot be contiguous
to the completion of another, which is also momentary, any more
than one point can be contiguous to another, nor one continuous
process contiguous to the completion of another, any more than
a line can be contiguous to a point. For the fuller treatment of
this subject he refers to the Phystcs, where it is in fact treated
much more fully.! It is reasonable to infer that this chapter
either was written after that part of the Physics, or at least
belongs to about the same period of Aristotle's life.
It being impossible to infer from the occurrence of a past event
that a later past event has occurred, Aristotle concludes that we
can only infer that an earlier past event must have occurred ; and
similarly, it being impossible to infer that if a future event occurs
a later future event must occur also, we can only infer that if a
future event is to occur an earlier future event must occur. In
either case the implied assumption is that for the occurrence of an
event there are needed both a set of particular circumstances and
a lapse of time whose length we cannot determine, so that we can
reason from the occurrence of an event to the previous occurrence
of its particular conditions but not vice versa.
In ch. 13 Aristotle returns to the subject of definition. He has
stated his theory of definition; he now gives practical advice as
to how definitions are to be arrived at. But here he is concerned
not with the definition of events, like eclipse or thunder, but with
the definition of the primary subjects of a science. If we wish to
define the number three, for instance, we collect the various
attributes each of which is applicable to all sets of three and to
certain other things as well, but all of which together belong only
to sets of three. Three is (1) a number, (2) odd, (3) prime, (4) not
formed by the addition of other numbers.? It is noticeable that
Aristotle does not follow the prescription laid down in the Meta-
$hysics,? that each differentia must be a further differentiation of
the previous differentia, so that a definition is complete when the
genus and the final differentia have been stated ; and in fact the
number two satisfies conditions (3) and (4) but not condition (2).
The present passage may be compared with that in the De
Partibus* in which he rejects, so far as biology is concerned, the
Platonic method of definition by successive dichotomies, as failing
to correspond to the complexity of nature.
! In Bk.G. 2 For the Greeks, one was not a number but an ἀρχὴ ἀριθμοῦ,
3 103829-21. * 1. 2-3.
4985 G
82 INTRODUCTION
This passage is, however, followed by one! in which he assumes
that each of the differentiae included in a definition will be a
differentiation of the previous differentia. The latter passage
must almost certainly date back to an earlier period in which
Aristotle was still accepting the Platonic method of definition.
He concludes with a passage in which he points out the danger of
assuming that a single term necessarily stands for a single species,
and recommends that, since wider terms are more likely to be
ambiguous than narrower ones, we should move cautiously up
through the definition of narrower terms to that of wider.
Aristotle assumes? that, generally speaking, ordinary language
will provide us with names for the genera and species which form
the subjects of a science. When we have established the existence
of such a chain of genera and species, the right order (he continues)
of attacking the problem of discovering the properties of the genus
and of its species is to discover first the properties of the whole
genus, for then we shall know both that and why the species
possess these properties, and need only consider what peculiar
properties they have and why they have them. But we must be
prepared to find that sometimes common language fails to provide
us with names for the species. Greek has no name for the class of
horned animals, but we must be prepared to find that they form
a real class, whose possession of certain other attributes depends
on their having horns. Or again we may find that the possession
of certain common attributes by different species of animals
depends on their having parts which without being the same have
an analogous character, as the spine in fishes and the pounce in
squids are analogous to bone in other animals. We may find that
problems apparently different find their solution in a single middle
term, e.g. in ἀντιπερίστασις, reciprocal replacement, which in fact
Aristotle uses as the explanation not only of different problems
but of problems in different sciences. Or again we may find
that the solution of one problem gives us part of the solution
of another, by providing us with one of two or more middle
terms.?
Aristotle now* turns to the problem of plurality of causes. We
may find a complete coincidence between two attributes, e.g. (in
trees) the possession of broad leaves and deciduousness, or between
two events, e.g. the interposition of the earth between the sun
and the moon and lunar eclipse, and in such a case the presence of
* g6b15-97b6. 2 Ch. 14. * Ch. 15. * Ch. 16.
SECOND BOOK OF POSTERIOR ANALYTICS 83
either attribute or event may be inferred from that of the other—
though, since two things cannot be causes of one another, only
one of the two inferences will explain the fact it establishes. But
may there not be cases of the following type—such that attribute
A belongs to D because of its possession of attribute B, and to E
because of its possession of attribute C, A being directly and
separately entailed both by B and by C? Then, while the posses-
sion of B or of C entails the possession of A, the possession of A
will not presuppose the possession of B nor the possession of C,
but only the possession of either B or C. Or must there be for
each type of phenomenon a single commensurate subject, all of
which and nothing but which suffers that phenomenon, and a
single commensurate middle term, which must be present wherever
the phenomenon is present?
Aristotle offers his solution in an admirable chapter! in which
he does justice both to the general principle that a single effect
must have a single cause, and of the facts that seem to point to
a plurality of causes. He distinguishes various cases in which a
plurality of things have or seem to have an attribute in common.
At one extreme is the case in which there is not really a single
attribute but different attributes are called by the same name;
we must not look for a common cause of similarity between colours
and between figures, for similarity in the one case is sensible
similarity and in the other is proportionality of sides and equality
of angles. Next there is the case in which the subjects, and again
the attributes, are analogically the same; i.e. in which a certain
attribute is to a certain subject as a second attribute is to a second
subject. In this case the two middle terms are also analogically
related. Thirdly there is the case in which the two subjects fall
within a single genus. Suppose we ask, for instance, why, if A
is to B as C is to D, A must be to C as B is to D, alike when the
terms are lines and when they are numbers ; we may say that the
proportion between lines is convertible because of the nature of
lines and that between numbers because of the nature of numbers,
thus assigning different causes. But we can also say that in both
cases the proportion is convertible because in both cases we have
a proportion between quantities, and then we are assigning an
identical cause. The attribute, the possession of which is to be
explained, is always wider than each of the subjects that possess
it, but commensurate with all of them together, and so is the
' Ch. 17.
84 INTRODUCTION
middle term. When subjects of more than one species have a
common attribute there is always a middle term next to each
subject and different for each subject, and a middle term next
to the attribute and the same for all the subjects, being in fact
the definition of the attribute. The deciduousness of the various
deciduous trees has one common cause, the congelation of the sap,
but this is mediated to the different kinds of tree by different
proximate causes. Any given attribute will have one immediate
cause A ; but things of the class D may have A because they have
B, and things of the class E may have it because they have C;
because of the difference of nature between class D and class E
they may require different causes of their possession of 4 and of
the consequent attribute. But things of the same species, having
no essential difference of nature, require no such differing causes
of their possession of A and of its consequent. Leaving aside the
question of the possession of a common attribute by different
species, and considering only the possession of an attribute by a
single species, we may say that when species D possesses an attri-
bute C, which entails B, which entails A, C is the cause of D's
having B, and therefore of its having A, that B is the cause of
C's entailing A, and that B's own nature is the cause of its
entailing A.!
Aristotle now? comes to his final problem ; how do we come to
know the first principles, which as we have seen cannot be known
by demonstration, being presupposed by it? The questions he
propounds are (1) whether they are objects of ἐπιστήμη or of some
other state of mind, and (2) whether the knowledge of them is
acquired or inborn; and he attacks the second question first. It
would be strange if we had had from birth such a state of mind,
superior to scientific knowledge (of which it is the foundation),
without knowing that we had it ; and it is equally difficult to see
how we could have acquired such a state if we had no knowledge
to start with. We must therefore have from birth some faculty
of apprehension, but not one superior either to knowledge by
demonstration or to knowledge of first principles. Now in fact
all animals have in sense-perception an innate discriminative fa-
culty. In some, no awareness of the object survives the moment
of perception; in others such awareness persists, in the form of
memory; and of those that have memory, some as a result of
! Ch. 18. ? Ch. 19.
SECOND BOOK OF POSTERIOR ANALYTICS 85
repeated memories of the same object acquire ‘experience’. From
experience—from the ‘resting’ in the mind of the universal, the
identical element present in a number of similar objects but
distinct from them—art and science take their origin, art con-
cerned with bringing things into being, and science with that
which is. Thus the apprehension of universals neither is present
from the start nor comes from any state superior to itself; it
springs from sense-perception. In a famous simile’ Aristotle
likens the passage from individual objects to universals, and to
wider universals, to the rallying of a routed army by one stout
fighter who gradually gathers to him others. The process is made
possible by the fact that while the object of perception is always
an individual, it is the universal in the individual that is perceived,
‘man, not the man Callias’.?
The discussion started from the question how we come to know
the universal propositions which lie at the basis of science: it has
diverged to the question how we come to apprehend universal
concepts like ‘animal’. Aristotle now returns to his main theme
by saying that just as we reach universal concepts by induction
from sense-perception, so we come to know the first principles
of science. Just as the perception of one man, while we still re-
member perceiving another, leads to the grasping of the universal
‘man’, so by perceiving that this thing, that thing, and the other
thing are never white and black in the same part of themselves,
we come to grasp the law of contradiction ; and so with the other
πρῶτα of science.
Aristotle now? turns to the other main question propounded in
the chapter; what is the state of mind by which we grasp the
πρῶτα The only states of mind that are infallible are scientific
knowledge and intuitive reason; the first principles of science
must be more completely apprehended than the conclusions from
them, and intuitive reason is the only state of mind that is
superior to scientific knowledge. . Therefore it must be intuitive
reason that grasps the first principles. This is the faculty which is
the starting-point of knowledge, and it isit that grasps the starting-
point of the knowable, while the combination of it and scientific
knowledge (the combination which is in the Ethics called σοφία)
grasps the whole of the knowable.*
This chapter is concerned only with the question how we come
! I00312-13. 2 Tb. 17-51. 3 1375.
* With this chapter should be compared Met. A. 1.
86 INTRODUCTION
to know the first principles on which science is based. Aristotle’s
answer does justice both to the part played by sense-perception
and to that played by intuitive reason. Sense-perception supplies
the particular information without which general principles could
never be reached ; but it does not explain our reaching them ; for
that a distinct capacity possessed by man alone among the
animals is needed, the power of intuitive induction which sees
the general principle of which the particular fact is but onc
exemplification. Aristotle is thus neither an empiricist nor a
rationalist, but recognizes that sense and intellect are mutually
complementary. The same balance is found in the account which
he gives of the way in which science proceeds from its first prin-
ciples to its conclusions. Sense-perception, he says, supplies us
with the facts to be explained, and without it science could not
even make a beginning. Its problem is that of bridging the gulf
between the particular facts of which sense-perception informs us
and the general principles by which they are to be explained. He
is often charged with having proceeded too much a Priori in his
pursuit of natural science, and he cannot be acquitted of the
charge, but his fault lay not in holding wrong general views on the
subject, but in a failure to apply correctly his own principles. His
theory is that it is the business of sense-perception to supply
science with its data; the ὅτε must be known before we begin the
search for the διότι,2 and ἀπόδειξις is thought of by him not as the
arriving by reasoning at knowledge of particular facts, but as
the explanation by reasoning of facts already known by sense-
perception. This is no doubt the true theory. But he failed in two
respects, as anyone in the infancy of science was bound to fail.
The 'facts' with which he started were not always genuine facts;
they were often unjustifiable though natural interpretations of the
facts which our senses really give us. And, on the other hand,
some of the first principles on which he relied as being self-
evident were not really so. His physics and his biology yield many
examples of both these errors. Yet he must be given the credit
for having at least seen the general position in its true light—that
it is the role of science to wait on experience for the facts to be
explained, and use reason as the faculty which can explain them.
Of the further function of reason—that of reasoning from facts
known by experience to those not yet experienced—he has little
conception.
1 81238-bo, ? 89b29-31.
THE TEXT OF THE ANALYTICS 87
VIII
THE TEXT OF THE ANALYTICS
FoR the purpose of establishing the text I have chosen the five
oldest of the MSS. cited by Waitz. These are (1) Urbinas 35
(Bekker’s and Waitz's A), of the ninth or early tenth century; (2)
Marcianus 201 (Bekker's and Waitz's B), written in 955; (3)
Coislinianus 330 (Bekker’s and Waitz's C), of the eleventh
century; (4) Laurentianus 72.5 (Waitz’s d), of the eleventh cen-
tury; (5) Ambrosianus 490 (formerly L 93) (Waitz’s n), of the
ninth century. Where we have so unusual an array of old MSS.,
it is unlikely that very much would be gained by exploring the
vast field of later MSS.
We may look, in the first place, at the relative frequency of
agreements between the readings of these five MSS. There are
two long passages for which the original hand of all the five is
extant, and I have made a count of the agreements in these
passages, 31218-49226 and 694-8222, which together amount to
between a third and a half of the whole of the Analytics. The
figures for the groupings of consentient readings are as follows:
ABCd 399, ABCn 173, ABdn 199, ACdn 78, BCdn 70.
ABC 18, ABd 68, ABn 19, ACd 13, ACn 6, Adn 12, BCd 4, BCn
17, Bdn 11, Cdn rg.
AB 2o, AC 7, Ad 26, Ans, BC 8, Bd 5, Bn 17, Cd 14, Cn 60, dn 14.
A alone 78, B alone 88, C alone 235, d alone 185, n alone 416.
Summing the agreements of MSS. two at a time we get:
AB 896, AC 694, Ad 795, An 492, BC 689, Bd 756, Bn 506, Cd 597,
Cn 423, dn 403.
We notice first that the agreements of four MSS. are much more
numerous than the agreements of three only, or of two only.
Either the variations are due to casual errors in single MSS., or
there is a family of four MSS. and a family of only one, or there is
a combination of these two circumstances. The fact that a// the
groups of four are large, compared with the groups of three or of
two, shows that casual errors in single MSS. play a large part in
the situation. But when we look more closely at the groups of
four, we find that one group, ABCd, is twice aslarge as that which
is nearest to it in size, and more than five times as large as the
smallest. Either, then, n is particularly careless, or it represents
a separate tradition, or both these things are true. Now individual
variations in one MS. from the others may, when they are wrong,
88 INTRODUCTION
imply either carelessness in the writing of the MS. or careful
following of a different tradition. But when they are right
this must be due to the following of a different, and a right,
tradition.
We must therefore look next to see how our MSS. compare in
respect of correctness, in passages where the true reading can be
established on grounds of sense or grammar or of Aristotelian
usage. Within the two long passages already mentioned I have
found B to have the right reading 4o1 times, A 389 times, C 363
times, n 339 times, d 337 times; the earlier editors Bekker and
Waitz are evidently justified in considering À and B the most
reliable MSS. Bekker gives the preference to A; Waitz gives it
to B, and his opinion is endorsed by Strache in his edition of the
Topics. At the same time it is noteworthy that the other three
MSS. fall so little behind A and B in respect of accuracy.
The value of a MS., however, does not depend only on the
number of times in which it gives an evidently correct reading,
but also on the number of times it is alone in doing so. I have
made a note of the passages, throughout the Analytics, in which
a certainly (or almost certainly) correct reading is found in one MS.
only (ignoring the very numereus insertions by later hands). The
results are as follows:
A alone has the right reading in 92*32, 947, 95235, 100?1;
B alone in 31232, 44734~5, 45°3, 46528, 47221, 59326, 65229, 67218,
7o*r, 75°34, 87538, 94°30, 35, 99°33;
C alone in 28531, 29528, 30531, 325, 47214, 5138, 5258, 19, 54535,
5629, 6555, 66314, 67537, 69520, 7332, 33, 7478, 8122;
d alone in 27*9, 33325, 4812, 49536, 70°32, 7256, 88227, 94322, ^16;
n alone in 34338, P18, 31, 35°13, 39522, 44*4, 6, 46°39, 4732, 11, I9,
49529, 52*1, 54337, 57524, 58?25, b33, 6210, 23, 64>30, 73?20,
14322, 38, 75519, 28, 7751, 7852-3, 31, 35, 8034, Bahr, ro, 12,
84719, 32, 533, 8525, 26, 28, b8, 15, 86220, 37, 39, ^17, 87218, 24,
8847, 10, 15, 20, 21, Pr1, 16, 89227, go#19, 24, 27, P1, 9153, 30,
92*11, 27, 34, ^27, 93°31, 35, 36, Pt1, 13, 31, 36, 9516, 56, 25, 37,
96°15, g8*ri, 12, 26, 32, 38 (specially important because n
comes to our aid where there is a lacuna in A, B, and d, and
the original hand of C is lacking), 20, 23, 38, 9935, 25, >r1, 19.
Thus, while there are only four passages in which A alone has the
true reading, there are fourteen in which B has it, eighteen in
which C has it, nine in which d has it, and no fewer than eighty-
~ nine in which n has it. It follows, then, that the very numerous
THE TEXT OF THE ANALYTICS 89
variations of n from the other MSS. are not always due to care-
lessness on the part of the writer of the MS. or of one of its ances-
tors, but are often the result of its following a different, and a
right, tradition; we have clear evidence of there being two
families of MSS. represented by ABCd and by n.
Next, we note that A and B agree a good deal more often than
any other pair of MSS., and we may infer that they are the most
faithful representatives of their family. B is both more often
right, and more often alone in being right, than A; and n agrees
more often with B than with any of the other three MSS. ; we may
therefore infer that B is the best representative of its family. B
and n, then, are the most important MSS. It follows, too, that
any agreement of n with any of the other MSS. is prima-facie
evidence of the correctness of the reading in which they agree.
Much new light has recently been cast on the text of the Prtor
Analytics by the researches of Mr. L. Minio into two ancient
Syriac translations. The older of these (which he denotes by the
symbol 77) is a translation of i. 1-7, not improbably by Proba, a
writer of the middle of the fifth century ; it is extant in eight MSS.,
of which the oldest belongs to the eighth or ninth century. The
other (denoted by I") is a complete translation by George, Bishop
of the Arabs, and belongs to the end of the seventh or the begin-
ning of the eighth century ; it is found in one MS. of the eighth or
ninth century.
Minio's critical apparatus shows only the divergences of Γ΄ ἀπά
IT from the text of Waitz, and since Waitz's text is based mainly
on A and B, the comparative rarity of the appearance of A and B
in his apparatus does not prove that the Syriac translations agree
less with them than with the other MSS. ; it is quite likely that a
complete apparatus would show that they agree more closely with
these two Greek MSS. than with any others. Further, the transla-
tion IT covers only a part of the Prior Analytics for which we have
not the original hand of n, but a text in a later hand. What
Minio’s collation does show, however, is two things: (1) the large
measure of agreement of both translations with C, (2) the large
measure of their agreement with the late Greek MS. m.
From the point at which the original hand of n begins (31218),
the most striking feature of Minio’s collation is the very large
number of agreements of I' with n. Its correspondences with C,
though not so numerous as those with n, are fairly numerous.
Minio ranks the MSS. ABCmn in the order nBCAm as regards
go INTRODUCTION
their affinity, and with this I agree, except that it would seem
that if Waitz’s citations of m were complete, it might be seen to
have more affinity with Γ᾽ than any of the other MSS.
The readings of Γ and Π, when they do not agree with any of
the best Greek MSS., do not seem to me very important ; in many
cases the apparent divergences may be due simply to a certain
freedom in translation, or to errors in translation. For this
reason, and to avoid overburdening the apparatus, I have ab-
stained from recording such readings. In passages in which no
Greek MS. affords a tenable reading, I have not found that I'
or IT comes to our aid. Again, I have refrained from record-
ing the readings of Γ and IT where Minio expresses some doubt
about them. But where there is no doubt about their readings,
and where these agree with any of the chief Greek MSS., I have
recorded them, as providing evidence that the reading of the Greek
MS. goes back to a period some centuries earlier than itself. It is
particularly interesting to note that n, which on its own merits I
had coine to consider as representing a good independent tradi-
tion, is very often supported by the evidence of Γ΄.
I may add Minio's summary of the position as regards the
Categories, which he has very carefully studied:
‘(a) The Greek copies current in the Vth to VIIth centuries!
agreed between themselves and with the later Greek tradition on
most essential features ;
*(b) they varied between themselves in many details; most of
these old variants are preserved also in one or more later Greck
MSS, and a large proportion of the variants which differentiate
these later copies go back to the older texts;
“ἡ Waitz's choice of B... . as the best Greek MS is confirmed to
be on the whole right; but
'(d) other MSS appear to represent a tradition going back at
least to the Vth-VIth century, especially n . . ., and in a smaller
degree C and e...;
'(e) in a few instances the older tradition stands unanimous
against the Greek MSS; and
'(f) in the instances coming under (4) and (e) there is no apparent
reason to prefer the later to the older evidence.’
"The frequent coincidence', continues Minio, 'between the Greek
MS n and Boethius confirms what had already been pointed out by
Ὁ. Schüler, K. Kalbfleisch and G. Furlani on the importance of
! i.e. those on which Boethius' translation was based.
THE TEXT OF THE ANALYTICS 9I
this MS, which is perhaps the oldest we possess. They even
exaggerated the extent of its similarity to the older texts. It is
true that it agrees with them on many points against the other
Greek MSS, but it is not true that it is nearer to them than B is,
since it has a great number of variants differentiating it from all
older texts. It 15, however, interesting to notice that the impor-
tance of n as preserving old features was emphasized also in regard
to the De Interpret. by K. Meiser and J. G. E. Hoffmann who found
striking examples of this fact while examining the Latin and
Syriac versions of this treatise.'
I have still to consider the contribution of the Greek commen-
tators to the establishment of the text. Alexander is more than
6oo years nearer to Aristotle than the earliest Greek MS. of the
Analytics, Themistius 500, Ammonius about 4oo, Simplicius 300;
it might perhaps be expected that the commentators should be
of primary importance for the text of Aristotle. But we must be
careful. Support for a reading derived from the commentaries is
of very different degrees:
(1) Sometimes the course of the commentary makes it clear
what reading the commentator had before him. Such sup-
port I designate by Al (Alexander), Am (Ammonius), An
(Anonymus), E (Eustratius), P (Philoponus), T (Themistius).
(2) Sometimes the commentator introduces a citation which is
evidently meant to be exact. But even so he may not be
quoting quite exactly, or the citation as it reaches us may
have been influenced by the text of Aristotle used by the
copyist from the commentator's MS. Such support I
designate by Ale, etc.
(3) Sometimes the commentator introduces a careless citation,
paraphrasing the sense of the text he had before him.
(4) The lernmata I designate by All, etc.
It is agreed among scholars that the lemmata were written not.
by the commentators, but by copyists; and the copyists respon-
sible for our MSS. of the commentators are as a rule later than the
writers of our five old MSS. The lemmata are therefore almost
valueless as support for a reading against the evidence of our MSS.,
and not worth very much as support for one variant as against
another. For obvious reasons the loose quotations also have little
importance. I have included lemmata in the apparatus only to
show that there is some support for a reading found in only one,
92 INTRODUCTION
or in none, of our MSS. To make more mention of them than this
would be to overload the apparatus with needless information.
The first two of the four kinds of evidence, on the other hand,
have great importance, and the first kind has much more than the
second, because it can hardly have been influenced by the MSS.
of Aristotle used by the copyists of the commentaries. But even
when we know that a commentator had a certain reading, it by
no means follows that that reading is what Aristotle wrote; in
many places the commentators plainly had an inferior text.
Nevertheless, of the 134 places cited above in which the plainly
right reading is found in only one MS., there are 69 in which that
reading finds support in one or more of the commentators. In
addition, there is a certain number of passages in which the first
hands of all our five MSS. go astray, while one or more of the
commentators has the right reading. Those that I have noted will
be found at 30514, 36223, 44538, 45°14, 46217, 8217, 83524, 8688, b27,
88>29, 89*13, gobro, 16, 92324, 3o (bis), 31, "9, 93924, 94*34, 35,
95°34, 97°14, 33, 9856. In addition there are a few passages in which
a commentator has a reading that has claims on our acceptance
not by reason of intrinsic superiority but because the commen-
tator is a much earlier authority than many of our MSS. . These
are found at 24529, 2622, 38521.
In our two test passages (31218-49226, 694-8222) the following
agreements occur:
A = Al 20 times = Alc8 = P 21 Ξε Pes — T4 Total 58
B .22 9 29 2 2 66
ς 20 II 32 II 5 88
d 17 9 27 8 4 65
n 3o 12 29 9 9 89
It is surprising that the two MSS. hitherto reckoned the best show
the least agreement with the commentators ; but the total number
of agreements is probably too small to warrant any very definite
conclusion, and the agreements throughout the Analytics should
be taken as the basis for any conclusions to be drawn. It is
interesting, however, to find some confirmation of the possession
of an old and good tradition by n.
Our original hypothesis that, with five MSS. of so early a date,
we have little need to take account of later MSS. is confirmed
if we consider the very small number of passages in which a
clearly right reading is found only in a later MS. or MSS., or in
a later hand in one of the old MSS. The only instances I have
THE TEXT OF THE ANALYTICS 93
noted will be found at 26*32 (f), 66>10 (mn*), 82617 (MP), 83°14
(DM), 84533 (D), 87424 (c?), 88622 (DM), 89°13 (DP), 9o^ro (c?P*),
6 (Mn?E), 92431 (B*E), *o (DAn-E), 943 (D), 34 (CP), 35 (DP).
LIST OF MANUSCRIPTS NOT INCLUDED IN THE SIGLA
A 1,2 — Zn. Pr. 1, 115 A 3, 4 = An, Post. I, II
Ambrosianus 124 (B 103), saec. xiii
$5 231 (D 43) ,, xiv (A r, mutilus)
» 237 (D 54) , xiii (A 1 (pars), 2, 3 (pars))
» 255(D82) ,, xiii
» 344 (F 67) » xvi (A 3 4)
525 (M 71, Waitzii q), saec. xiv and xv
Βοάϊείαπυς, Baroccianus 87, saec. xv
3$
35 +s 177 , Xxiiiineuntis
a Laudianus 45 ,, XV
» » 46 » xiv
» Seldenianus 35 ,, xiv
^ Miscellaneus 261 xv (A r. 1-9)
Bononiensis (Bibl. Univ.) 3637, sa saec. xiv (A 1, mutilus)
Escurialis ® III. 1o, saec. xiii and xv (A 1-4, A 1 mutilus)
Gennensis F VI. 9, saec. xv-xvi (À 1)
Gudianus gr 24, saec. xiii
Laurentianus 72, 3 (Waitzii e), anni 1383 (palimpsestus)
" 72, 4, saec, xiii
» 72,10 ,, xiv (A I, 2)
is 72, 12 (Waitzii T), saec. xiii
» 72, 19, saec. xiv (A I. 1-7)
» 87,16 ,, xiii (A 1 (pars))
” 89, 77 » xvi
5 Suppl. 55 (88. 39), saec. xiv (A 1, mutilus)
Conventi suppressi 192, saec. xiv (À r, 2)
Lipsiensis (Bibl. Sanatoria) 7, saec. xv (À 1, 2)
Marcianus 202, saec. xiv-xv
$5 203 ,, xiv
» 204 (Waitzii o), saec. xiv
» App IV. 53 (Bekkeri Nb, Waitzii L), saec. xii
Monacensis 222, saec. xiv (À 2-4) ‘
» 34» XV (A 3,4)
Mutinensis 118 (II D r9), anni 1400
E: 149 (II E 16), saec. xv (A 3, 4)
5 189 (III Fir) ,, xiv-xv-xvi
Neapolitanus III D 3o, saec. xv
» NID gr , xiv
» HID32 , xv(AA4)
94 INTRODUCTION
Neapolitanus III D 37 saec. xiv (A 1)
Oxoniensis, Coll. Corporis Christi 104, saec. xv (A 3, 4)
E Coll. Novi 225, saec. xiv
3 Coll. Novi299 ,, xv
Parisinus 1843, saec. xiii
» 1845 4, xiv
» GM o χὶν (Α τ, 2)
» 1841 ,, xvi(A 3,4)
» 1897 A, saec. xiii
» 1919, anni 1442 (A 1, 2, 4)
ἣν 1971, saec. xiii
5 1972 4, xiv
» 1974 yy XV
" 2020 4, XV
a 2030 ,, xvi (AI, 2)
$s 2051 ,, xiv (At, 2)
5 2086 ,, xiv
5 2120 , xvi
s Coislinianus 167, saec. xiv
» » 323.» xiv(Ar2)
p » 327] , Χὶν
iss Suppl. 141, saec. xvi
» » 245 » xiv
4 » 644 » xiv
Toletanus 95-8
Vaticanus 110, saec. xiii-xiv (A 1, 2)
» 199 , xiv (A 1, 2)
ὃ; 241 (Bekkeri I, Waitzii K), saec. xiii
3 242, saec. xili-xiv
» 243 » xiii-xiv
» 244 » xum
35 245 ,, ΧΙ (A 1-4 (A 4 mutilus))
» 247 (Waitzii E), saec. xiii-xiv (A 1)
55 1018, saec. xv-xvi (A 1, 2)
» 1294
» 1498
» 1693
m Ottobonianus 386, saec. xv (A 1)
Ἢ Palatinus 34 saec. xiv A 1, 2 (ἃ 2 mutilus)
» » 74 » XV
5 5 78 4, xv exeuntis
» » 159,anni 1442
» ” 255, Saec. XV
ὃς Reginensis 107, saec. xiv
” » 116 »» xiv
5; "ἡ 190 ,, xvi (A 1-4 (A 2 mutilus))
" Urbinas 56, saec. xvi (A 1, 2, mutili)
MANUSCRIPTS NOT INCLUDED IN THE SIGLA 95
Vindobonensis 41, saec. xv-xvi (A 1, mutilus)
» 94
δέ 155 4, xvi exeuntis (A 3, 4)
» 230 (A I, 2)
3» Suppl. 59, saec. xiv (À 1, 2, mutili)
” ” 60 » XV
APIZTOTEAOYZ
ANAAYTIKQN
SIGLA
An.Pr. 24510-31917 codices ABCd
31418-49226 ABCdn
49227-6994 ABCn
69>4-An. Post. 8222 ABCdn
An. Post. 8282-10017 ABdn
A (Bekkeri atque Waitzii) = Urbinas 35, saec. ix vel x ineuntis
B (Bekkeri atque Waitzii) = Marcianus 201, anni 955
C (Bekkeri atque Waitzii) = Coislinianus 330, saec. xi
d (Waitzii) = Laurentianus 72. 5, saec. xi
n (Waitzii) = Ambrosianus 400 (olim L 93), saec. ix
I' — Georgii traductio Syriaca
I| = Probae traductio Syriaca
Al = Alexander in An. Pr. i
Am = Ammonius in An. Pr. i
An = Anonymus in An. Post. ii
E = Eustratius in An. Post. ii
P = Philoponus in An. Pr. et Post.
T — Themistius in An. Post.
Ale, Ame, Anc, Ec, Pe = Alexandri, etc., citatio
All, Am], An!, El, Pi = Alexandri, etc., lemma
RARO CITANTUR
D (Bekkeri atque Waitzii) — Coislinianus 157, saec. xiv medii
F (Waitzii) — Vaticanus 209, saec. xiv
M (Waitzii) = Marcianus App. iv. 51
a (Waitzii) = Angelicus 42 (olim C 3. 13), saec. xiv
c (Waitzii) = Vaticanus 1024, vetustus
f (Waitzii) = Marcianus App. iv. 5, saec. xiv
i (Waitzii) — Laurentianus 72. 15, saec. xiv
m (Waitzii) = Ambrosianus 687 (olim Q 87), saec. xv
p (Waitzii) = Ambrosianus 535 (olim M 89), saec. xiv
u (Waitzii) = Basileensis 54 (F ii. 21), saec. xii
ANAAYTIKQN IIPOTEPQN A.
IT, ^ » ^ x , * ’ 7 ‘ € , Ld 4 s
ρῶτον εἰπεῖν περὶ τί kai τίνος ἐστὶν ἡ σκέψις, ὅτι περὶ 24
ἀπόδειξιν καὶ ἐπιστήμης ἀποδεικτικῆς: εἶτα διορίσαι τί
ἐστι πρότασις καὶ τί ὄρος καὶ τί συλλογισμός, καὶ ποῖος
, ‘ ^ > , A A ^ , ^ ? Ld
τέλειος kai motos ἀτελής, μετὰ δὲ ταῦτα τί τὸ ἐν ὅλῳ εἶ-
ναι ἢ μὴ εἶναι τόδε τῷδε, καὶ τί λέγομεν τὸ κατὰ παντὸς
ἢ μηδενὸς κατηγορεῖσθαι. 15
IT, rd ' ^ , M rd ‘ ^ > ,
ρότασις μὲν οὖν ἐστὶ λόγος καταφατικὸς ἢ ἀποφατικός
, s 4. δὲ - 06A "^ , , a 19 a
Twos κατά τινος" οὗτος δὲ ἢ καθόλου 7) ἐν μέρει ἢ ἀδιόριστος.
λέγω δὲ καθόλου μὲν τὸ παντὶ ἢ μηδενὶ ὑπάρχειν, ἐν μέρει
δὲ τὸ τινὲ ἢ μὴ τινὶ 7) μὴ παντὶ ὑπάρχειν, ἀδιόριστον δὲ τὸ
ὑπάρχειν ἣ μὴ ὑπάρχειν ἄνευ τοῦ καθόλου ἢ κατὰ μέρος, οἷον 20
τὸ τῶν ἐναντίων εἶναι τὴν αὐτὴν ἐπιστήμην ἣ τὸ τὴν ἡδονὴν μὴ εἴ-
, / , M ec > ^ , ^
vat ἀγαθόν. διαφέρει δὲ ἡ ἀποδεικτικὴ πρότασις τῆς διαλε-
~ σ t * » ‘ ^ » , ^ > ΄
κτικῆς, ὅτι ἡ μὲν ἀποδεικτικὴ λῆψις θατέρου μορίου τῆς ἀντιφά-
, > ᾽ ^ , a ? A, , δ ἘΞ , € bt
σεώς ἐστιν (o) yàp ἐρωτᾷ ἀλλὰ λαμβάνει ὁ ἀποδεικνύων), ἡ δὲ
διαλεκτικὴ ἐρώτησις ἀντιφάσεώς ἐστιν. οὐδὲν δὲ διοίσει πρὸς τὸ 25
γενέσθαι τὸν ἑκατέρου συλλογισμόν: καὶ yap 6 ἀποδεικνύων
καὶ ὁ ἐρωτῶν συλλογίζεται λαβών τι κατά τινος ὑπάρχειν
ἢ μὴ ὑπάρχειν. ὥστε ἔσται συλλογιστικὴ μὲν πρότασις ἁπλῶς
κατάφασις ἢ ἀπόφασίς τινος κατά τινος τὸν εἰρημένον τρό-
> M , γι » xX T ‘ ^ -^ $ > ^
mov, ἀποδεικτικὴ δέ, ἐὰν ἀληθὴς ἦ καὶ διὰ τῶν ἐξ ἀρχῆς 30
ὑποθέσεων εἰλημμένη, διαλεκτικὴ δὲ πυνθανομένῳ μὲν ἐρώ- 24>
> ων , * - ^ 7
τησις ἀντιφάσεως, συλλογιζομένῳ δὲ λῆψις τοῦ φαινομένου
καὶ ἐνδόξου, καθάπερ ἐν τοῖς Τοπικοῖς εἴρηται. τί μὲν οὖν ἐστὶ
, ' , , M ^ > *. *
πρότασις, kai τί διαφέρει συλλογιστικὴ καὶ ἀποδεικτικὴ καὶ
διαλεκτική, δι’ ἀκριβείας μὲν ἐν τοῖς ἑπομένοις ῥηθήσεται,
πρὸς δὲ τὴν παροῦσαν χρείαν ἱκανῶς ἡμῖν διωρίσθω τὰ νῦν. 15
"Opov δὲ καλῶ eis dv διαλύεται ἡ πρότασις, olov τό τε κατη-
γορούμενον καὶ τὸ καθ᾽ οὗ κατηγορεῖται, προστιθεμένου [ἢ διαι-
ρουμένου] τοῦ εἶναι 7j μὴ εἶναι. συλλογισμὸς δέ ἐστι λόγος ἐν
T , ee , ES " > > 0; ,
ᾧ τεθέντων τινῶν ἕτερόν τι τῶν κειμένων ἐξ ἀνάγκης συμβαί-
24310 ἐστὶν om. C? 11 ἐπιστήμην ἀποδεικτικήν Al 17 ttvos* codd.
AlAmP : +7 τινος ἀπό τινος AmY? : καί τινος ἀπό τινος PY? 29 ἢ ἀπόφασίς
om. C! rwos?-+- +7 τινος ἀπό τινος Amv? Ὁ17 προστιθεμένου C'i AlcPe :
ἢ προστιθεμένου ABCdT ἢ διαιρουμένου seclusi: habent codd. AlAmP:
xai διαιρουμένου IT 18 ἢ C AL Am*P* : καὶ ABd 19 τινῶν... ἀνάγκης
C ALAmP, fecit d: tt... ἀνάγκης fecit A: τῶν κειμένων om. B!
ANAAYTIKQN IIPOTEPON A
20 veu TH ταῦτα εἶναι. λέγω δὲ τῷ ταῦτα εἶναι τὸ διὰ ταῦτα
, 4 a A ~ , M 4 L4
συμβαίνειν, τὸ δὲ διὰ ταῦτα συμβαίνειν τὸ μηδενὸς ἔξωθεν
ὅρου προσδεῖν πρὸς τὸ γενέσθαι τὸ ἀναγκαῖον. τέλειον μὲν οὖν
~ * A A LÀ 7 ^ ^
καλῶ συλλογισμὸν τὸν μηδενὸς ἄλλου προσδεόμενον παρὰ τὰ
εἰλημμένα πρὸς τὸ φανῆναι τὸ ἀναγκαῖον, ἀτελῆ δὲ τὸν προσ-
25 δεόμενον ἢ ἑνὸς ἢ πλειόνων, ἃ ἔστι μὲν ἀναγκαῖα διὰ τῶν
ὑποκειμένων ὅρων, οὐ μὴν εἴληπται διὰ προτάσεων. τὸ δὲ ἐν
ὅλῳ εἶναι ἕτερον ἑτέρῳ καὶ τὸ κατὰ παντὸς κατηγορεῖσθαι
θατέρου θάτερον ταὐτόν ἐστιν. λέγομεν δὲ τὸ κατὰ παντὸς
κατηγορεῖσθαι. ὅταν μηδὲν ἦ λαβεῖν [τοῦ ὑποκειμένου]
» T , , , ' ^ ^ ^ € ré
3o καθ᾽ ob θάτερον od λεχθήσεται" kai TO κατὰ μηδενὸς ὡσαύτως.
a > ' \ ^ / ΄ » ^ ^ tos ^ ^3
25 Ἐπεὶ δὲ πᾶσα πρότασίς ἐστιν ἢ τοῦ ὑπάρχειν T) τοῦ ἐξ 2
> , € , -^ ^ ᾽ ὃ Ψ' of e , ^ δὲ M
ἀνάγκης ὑπάρχειν ἢ τοῦ ἐνδέχεσθαι ὑπάρχειν, τούτων δὲ ai
μὲν καταφατικαὶ αἱ δὲ ἀποφατικαὶ καθ᾽ ἑκάστην πρόσρησιν,
, A ~ ~ ^ 2 ^ « M ,
πάλιν δὲ τῶν καταφατικῶν καὶ ἀποφατικῶν ai μὲν καθόλου
5 αἱ δὲ ἐν μέρει αἱ δὲ ἀδιόριστοι, τὴν μὲν ἐν τῷ ὑπάρχειν κα-
θόλου στερητικὴν ἀνάγκη τοῖς ὅροις ἀντιστρέφειν, οἷον εἰ μηδε-
, c Ν 3 , νῶν 93» A $t w € ὔ b A
μία ἡδονὴ ἀγαθόν, οὐδ᾽ ἀγαθὸν οὐδὲν ἔσται ἡδονή: τὴν δὲ κατη-
A Li , A , ^ ΕΣ + , > ? >
yopucjv ἀντιστρέφειν μὲν ἀναγκαῖον, οὐ μὴν καθόλου ἀλλ᾽ ἐν
/ > ^ * A > , A 2 06 f 5o
μέρει, olov εἰ πᾶσα ἡδονὴ ἀγαθόν, Kai ἀγαθόν τι εἶναι ἡδο-
10 vrjy: τῶν δὲ ἐν μέρει τὴν μὲν καταφατικὴν ἀντιστρέφειν ἀνάγκη
κατὰ μέρος (εἰ γὰρ ἡδονή τις ἀγαθόν, καὶ ἀγαθόν τι ἔσται
ἡδονή), τὴν δὲ στερητικὴν οὐκ ἀναγκαῖον" (οὐ γὰρ εἰ ἄνθρωπος
μὴ ὑπάρχει τινὶ ζῴῳ, καὶ ζῷον οὐχ ὑπάρχει τινὶ ἀνθρώπῳ).
Πρῶτον μὲν οὖν ἔστω στερητικὴ καθόλον ἡ A B πρότασις.
15 εἰ οὖν μηδενὶ τῷ Bro A ὑπάρχει, οὐδὲ τῷ A οὐδενὶ ὑπάρξει
τὸ B εἰ γάρ τινι, οἷον τῷ Γ,, οὐκ ἀληθὲς ἔσται τὸ μηδενὶ τῷ
* [4 , ‘ A ^ ME; H A M M
B τὸ A ὑπάρχειν: τὸ yàp Γ τῶν B τί ἐστιν. εἰ δὲ παντὶ τὸ
A τῷ B, καὶ τὸ B τινὶ τῷ A ὑπάρξει: εἰ γὰρ μηδενί, οὐδὲ
τὸ Α οὐδενὶ τῷ Β ὑπάρξει: ἀλλ᾽ ὑπέκειτο παντὶ ὑπάρχειν.
20 ὁμοίως δὲ καὶ εἰ κατὰ μέρος ἐστὶν ἡ πρότασις. εἰ γὰρ τὸ A
* ^ M Ν ^ ^ 2 , L4 , > ‘
τινὶ TQ DB, καὶ τὸ B τινὶ τῷ A ἀνάγκη ὑπάρχειν: εἰ yap
μηδενί, οὐδὲ τὸ A οὐδενὴ τῷ B. εἰ δέ γε τὸ A τυὶ
b20 τὸ] τῷ C 21 συμβαίνειν om. ΓΠ τῷ δὲ AC 27 érepov - ἐν
BC 28 θάτερον θατέρου ΓΠ 29 κατηγορεῖσθαι om. ΓΠ τοῦ
ὑποκειμένου BCdII: τῶν τοῦ ὑποκειμένου A: om. Al 25312 οὐ γὰρ εἰ
BC'd, fecit A: εἰ yàp C 15 τῷ CII Al: τῶν ABC*d τῷ mnAl*: τῶν
ABCd 16 7a? B*mII: τῶν ABCd 18 τῷ] τῶν A? τῶναΓΠ
ὑπάρξει ΓΠ : ὑπάρχει ABCA 19 τῷ ABCd Al* : τῶν APS 21 τῷ
bis fm Al: τῶν A BCd a ὑπάρχει C 22 τῷ fim Al: τῶν ABCd
8:1 ὑπάρξει fim
I. 24°20 — 3. 25915
^ A € , > > , 4 A M ~ A f
TQ B μὴ ὑπάρχει, οὐκ ἀνάγκη καὶ τὸ B τινὶ τῷ A μὴ !
"P > E 1 2 as * 1 * !
ὑπάρχειν, olov εἰ τὸ μὲν B ἐστὶ ζῷον, τὸ δὲ A ἄνθρωπος"!
» x A ᾽ x , ^ M M > , .
ἄνθρωπος μὲν yàp od παντὶ ζῴῳ, ζῷον δὲ παντὶ ἀνθρώπῳ Ὡς
ὑπάρχει.
3 Τὸν αὐτὸν δὲ τρόπον ἕξει καὶ ἐπὶ τῶν ἀναγκαίων προ-
r4 [4 Ἂς A = ^ , » , ^
τάσεων. ἡ μὲν yàp καθόλου στερητικὴ καθόλου ἀντιστρέφει, τῶν
δὲ καταφατικῶν ἑκατέρα κατὰ μέρος. εἰ μὲν γὰρ ἀνάγκη
A] ~ ' ἡ , > , ‘ M ^
τὸ A τῷ B μηδενὶ ὑπάρχειν, ἀνάγκη καὶ τὸ B τῷ A μη- 3.
^ [4 Jr , MJ M > P * * ~ ' ᾽
devi ὑπάρχειν: εἰ γὰρ τινὶ ἐνδέχεται, καὶ τὸ A τῷ B τινὶ ἐν-
, L4 > ν᾿ , , , ^ S * ^ [4 ,
δέχοιτο dv. εἰ δὲ ἐξ ἀνάγκης τὸ A παντὶ ἢ τινὶ τῷ B ὑπάρ-
χει, καὶ τὸ B τινὲ τῷ A ἀνάγκη ὑπάρχειν: εἰ γὰρ μὴ
> Lg 2» > n ^ Si ^ > > , € , M 3
ἀνάγκη, οὐδ᾽ ἂν τὸ Α τινὶ τῷ Β ἐξ ἀνάγκης ὑπάρχοι. τὸ ὃ
ἐν μέρει στερητικὸν οὐκ ἀντιστρέφει, διὰ τὴν αὐτὴν αἰτίαν δι᾿ ἣν as
καὶ πρότερον ἔφαμεν.
πὶ δὲ τῶν ἐνδεχομένων, ἐπειδὴ πολλαχῶς λέγεται
τὸ ἐνδέχεσθαι (καὶ γὰρ τὸ ἀναγκαῖον καὶ τὸ μὴ ἀναγκαῖον
καὶ τὸ δυνατὸν ἐνδέχεσθαι λέγομεν), ἐν μὲν τοῖς καταφατικοῖς
« , μι AY A > 4 > L4 > ^ ^
ὁμοίως ἕξει κατὰ τὴν ἀντιστροφὴν ἐν ἅπασιν. εἰ yàp τὸ A 4o
παντὶ ἢ τινὶ TQ DB ἐνδέχεται, καὶ τὸ B. τινὶ τῷ A ἐνδέχοιτο 25b
» , A , »095 bal AJ > M - L4 ^
dv: el yap μηδενί, οὐδ᾽ av τὸ A οὐδενὶ τῷ B- δέδεικται yàp
^ , *, 4 ^ 3 ^ ΕΣ Li , > ?
τοῦτο πρότερον. ev δὲ rois ἀποφατικοῖς οὐχ ὡσαύτως, ἀλλ
ὅσα μὲν ἐνδέχεσθαι λέγεται 7j τῷ ἐξ ἀνάγκης ὑπάρχειν ἢ τῷ
μὴ ἐξ ἀνάγκης μὴ ὑπάρχειν, ὁμοίως, οἷον εἴ τις φαίη τὸν
» * , Ἂς - ^ M x i1 €
ἄνθρωπον ἐνδέχεσθαι μὴ εἶναι ἵππον ἢ τὸ λευκὸν μηδενὶ ἱμα-
wn
τίῳ ὑπάρχειν (τούτων yap τὸ μὲν ἐξ ἀνάγκης οὐχ ὑπάρχει,
τὸ δὲ οὐκ ἀνάγκη ὑπάρχειν, καὶ ὁμοίως ἀντιστρέφει ἡ πρό-
Taos: εἰ γὰρ ἐνδέχεται μηδενὶ ἀνθρώπῳ ἵππον, καὶ ἀνθρω-
mov ἐγχωρεῖ μηδενὶ ἵππῳ" καὶ εἰ τὸ λευκὸν ἐγχωρεῖ μηδενὶ
ἱματίῳ, καὶ τὸ ἱμάτιον ἐγχωρεῖ μηδενὶ λευκῷ" εἰ γάρ τινι
-
o
ἀνάγκη, kai τὸ λευκὸν ἱματίῳ Twi ἔσται ἐξ ἀνάγκης- τοῦτο
γὰρ δέδεικται πρότερον), ὁμοίως δὲ καὶ ἐπὶ τῆς ἐν μέρει ἀπο-
φατικῆς" ὅσα δὲ τῷ ὡς ἐπὶ τὸ πολὺ καὶ τῷ πεφυκέναι λέγεται
ἐνδέχεσθαι, καθ᾽ ὃν τρόπον διορίζομεν τὸ ἐνδεχόμενον, οὐχ
223 τῶνβ ΒΟΑΓΠ τῶνα ΠΡ 29-34 εἰ... ὑπάρχοι codd. ΓΠΑ͂ΙΡ:
secl. Becker 3o τῶ B ACI kai BPc: om. ACd τῶνα APC
31, 32 τῷ) τῶν A*CT'H 33 τῷ ABd Al: τῶν ACT μὴ ἀνάγκη) ἐν-
δέχεται μηδενί PvP 34 ràv B. A*CT'II ὑπάρχῃ fecit A 39 καὶ τὸ
δυνατὸν codd. ΓΠΑ͂ΙΡ : secl. Becker br τῶν B ACI τῷ ABAAl:
τῶν CI'II 2-3 εἰ... πρότερον codd. PTAl: sec]. Becker 2 τῶν B
CTI 4 ἀνάγκης- μὴ AMPPCATAD — s ui om. ABICAAIP — 7
οὐχ om. ΓΠ 8 ὑπάρχει Γ: μὴ ὑπάρχειν CP 14 τὸ Cd? Al: om. ABd
-
5
ANAAYTIKQN TIPOTEPQN A
ὁμοίως ἕξει ἐν ταῖς στερητικαῖς ἀντιστροφαῖς, ἀλλ᾽ ἡ μὲν Ka-
θόλου στερητικὴ πρότασις οὐκ ἀντιστρέφει, ἡ δὲ ἐν μέρει ἀντι-
στρέφει. τοῦτο 86 ἔσται φανερὸν ὅταν περὶ τοῦ ἐνδεχομένου
λέγωμεν. νῦν δὲ τοσοῦτον ἡμῖν ἔστω πρὸς τοῖς εἰρημένοις δῆ-
LÀ M >? , * - * M t ,
20 λον, ὅτι τὸ ἐνδέχεσθαι μηδενὶ ἢ Twi μὴ ὑπάρχειν καταφατι-
25
30
35
40
265
Io
4 ~ ~
κὸν ἔχει τὸ σχῆμα (τὸ yap ἐνδέχεται τῷ ἔστιν ὁμοίως τάτ-
* A i μ ~
τεται, τὸ δὲ ἔστιν, ols ἂν προσκατηγορῆται, κατάφασιν dei
a \ , e
ποιεῖ καὶ πάντως, otov τὸ ἔστιν οὐκ ἀγαθόν ἢ ἔστιν od λευκόν ἢ
e ~ M ^ ^ -^
ἁπλῶς τὸ ἔστιν od τοῦτο: δειχθήσεται δὲ Kat τοῦτο διὰ τῶν émo-
L4 M δὲ ^ ? ^ 4 , L4 ^ L4
μένων), κατὰ δὲ τὰς ἀντιστροφὰς ὁμοίως ἕξουσι ταῖς ἄλλαις.
A ,
Διωρισμένων δὲ τούτων λέγωμεν ἤδη διὰ τίνων Kal πότε
καὶ πῶς γίνεται πᾶς συλλογισμός: ὕστερον δὲ λεκτέον περὶ
> , , b 4 ~ , n A
ἀποδείξεως. πρότερον δὲ περὶ συλλογισμοῦ λεκτέον ἢ περὶ
ἀποδείξεως διὰ τὸ καθόλου μᾶλλον εἶναι τὸν συλλογισμόν"
€ A ‘ 3 55 , Lj M δὲ
ἡ μὲν γὰρ ἀπόδειξις συλλογισμός τις, ὃ συλλογισμὸς δὲ
οὐ πᾶς ἀπόδειξις.
Ὅ > Ld ^ L4 LÀ * > ὅλ, σ M
rav οὖν ὅροι τρεῖς οὕτως ἔχωσι πρὸς ἀλλήλους ὥστε TOV
ἔσχατον ἐν ὅλῳ εἶναι τῷ μέσῳ καὶ τὸν μέσον ἐν ὅλῳ τῷ πρώτῳ
ἢ εἶναι ἢ μὴ εἶναι, ἀνάγκη τῶν ἄκρων εἶναι συλλογισμὸν
τέλειον. καλῶ δὲ μέσον μὲν ὃ καὶ αὐτὸ ἐν ἄλλῳ καὶ ἄλλο
, 5 3 ᾿ a A ^ , , , » * M 9 ,
ἐν τούτῳ ἐστίν, ὃ καὶ τῇ θέσει γίνεται μέσον: ἄκρα δὲ τὸ αὐτό
τε ἐν ἄλλῳ ὃν καὶ ἐν ᾧ ἄλλο ἐστίν. εἰ γὰρ τὸ Α κατὰ παν-
A ~ 4 * A X. ~ > , ^ A
τὸς τοῦ B καὶ τὸ B κατὰ παντὸς τοῦ I’, ἀνάγκη τὸ A κατὰ
- ^ LÀ ~
παντὸς τοῦ I” κατηγορεῖσθαι: πρότερον yap εἴρηται πῶς τὸ
κατὰ παντὸς λέγομεν. ὁμοίως δὲ καὶ εἰ τὸ μὲν A κατὰ μη-
δενὸς τοῦ B, τὸ δὲ B κατὰ παντὸς τοῦ I, ὅτι τὸ A οὐδενὶ τῷ
Γ ὑπάρξει. εἰ δὲ τὸ μὲν πρῶτον mavri τῷ μέσῳ ἀκολουθεῖ,
τὸ δὲ μέσον μηδενὶ τῷ ἐσχάτῳ ὑπάρχει, οὐκ ἔσται συλλογι-
σμὸς τῶν ἄκρων' οὐδὲν γὰρ ἀναγκαῖον συμβαίνει τῷ ταῦτα
εἶναι: καὶ γὰρ παντὶ καὶ μηδενὶ ἐνδέχεται τὸ πρῶτον τῷ
ἐσχάτῳ ὑπάρχειν, ὥστε οὔτε τὸ κατὰ μέρος οὔτε τὸ καθόλου γί-
a Ν M K
νεται ἀναγκαῖον: μηδενὸς δὲ ὄντος ἀναγκαίου διὰ τούτων οὐκ
^ M ^
ἔσται συλλογισμός. ὅροι τοῦ παντὶ ὑπάρχειν ζῷον-ἄνθρωπος--
L4 ~ * ^ L4 if 29? L4 , ^
ἵππος, τοῦ μηδενὶ ζῷον-ἀνθρωπος-λίθος. οὐδ᾽ ὅταν μήτε τὸ
~ ^ ^ ,
πρῶτον τῷ μέσῳ μήτε TO μέσον TH ἐσχάτῳ μηδενὶ ὑπάρχῃ,
οὐδ᾽ οὕτως ἔσται συλλογισμός. ὅροι τοῦ ὑπάρχειν ἐπιστήμη--
bi? στερητικὴ om. ΓΠ 19-25 vüv . . . ἄλλαις codd. DILAIP : secl.
Becker 26 λέγωμεν d* Al: λέγομεν ABCd 30 rís-- ἐστι C 38
τὸ] xai τὸ ΓΠ 2682 ἀκολουθεῖ Al: ὑπάρχει codd. Io ὑπάρχει B
3. 25516 — 4. 2654
, ὦν ,ὔ ~ x L4 , , , ,
γραμμήπτἰατρική, τοῦ μὴ ὑπάρχειν ἐπιστήμη-γραμμή-τμο-
L4 ~ ~ ~
vds. καθόλου μὲν οὖν ὄντων τῶν ὅρων, δῆλον ἐν τούτῳ τῷ σχή-
ματι πότε ἔσται καὶ πότε οὐκ ἔσται συλλογισμός, καὶ ὅτι ὄν-
Tos τε συλλογισμοῦ τοὺς ὅρους ἀναγκαῖον ἔχειν ὡς εἴπομεν, 15
ἄν θ᾽ οὕτως ἔχωσιν, ὅτι ἔσται συλλογισμός.
, >» € A , ^ Ld Lj > * , M M -΄
Εἰ δ᾽ ὃ μὲν καθόλου τῶν ὅρων 6 δ᾽ ἐν μέρει πρὸς τὸν ἕτερον,
ὅταν μὲν τὸ καθόλου τεθῇ πρὸς τὸ μεῖζον ἄκρον ἣ κατηγορικὸν ἢ
στερητικόν, τὸ δὲ ἐν μέρει πρὸς τὸ ἔλαττον κατηγορικόν, ἀνάγ-
Kn συλλογισμὸν εἶναι τέλειον, ὅταν δὲ πρὸς τὸ ἔλαττον ἢ 20
" " μ᾿ L4 Ld 3 z À , ὃ M ^
καὶ ἄλλως πως ἔχωσιν οἱ ὅροι, ἀδύνατον. λέγω δὲ μεῖζον
M Ld » ^ 4 » ’ ,ὔ L4 δὲ M t ‘ M ,
μὲν ἄκρον ἐν ᾧ τὸ μέσον ἐστίν, ἔλαττον δὲ τὸ ὑπὸ τὸ μέσον
» ¢ , ^ ^ 3. ^ ~ ^ * M ~ I
ὄν. ὑπαρχέτω yap τὸ μὲν A παντὶ τῷ B, τὸ δὲ B τινὶ τῷ T.
οὐκοῦν εἰ ἔστι παντὸς κατηγορεῖσθαι τὸ ἐν ἀρχῇ λεχθέν, ἀνάγκη
M M ^ L4 , * > ^ b A ^
τὸ A rui τῷ I ὑπάρχειν. καὶ εἰ τὸ μὲν A μηδενὶ τῷ B a;
Li , 4 * M ^ > d ^ M ^ b
ὑπάρχει, τὸ δὲ B τινὶ τῷ I, ἀνάγκη τὸ A τινὶ τῷ Γ μὴ
ὑπάρχειν: ὥρισται γὰρ καὶ τὸ κατὰ μηδενὸς πῶς λέγομεν"
σ L4 * , L4 , * M , > ,
ὦστε ἔσται συλλογισμὸς τέλειος. ὁμοίως δὲ καὶ εἰ ἀδιόριστον
LÀ ^ ‘ L4 « * *, A μὴ
εἴη τὸ B Γ᾽, κατηγορικὸν ὄν: ὁ γὰρ αὐτὸς ἔσται συλλογι-
σμὸς ἀδιορίστου τε καὶ ἐν μέρει ληφθέντος. 30
! Ea δὲ M LA
‘av δὲ πρὸς TO EAGT- 30
L4 4 , an M -^ , > L4
rov ἄκρον τὸ καθόλου τεθῇ 7) κατηγορικὸν ἢ στερητικόν, οὐκ ἔσται
συλλογισμός, οὔτε καταφατικοῦ οὔτε ἀποφατικοῦ τοῦ ἀδιορί-
n * , Ld > x * M ~ t a
crov ἢ κατὰ μέρος ὄντος, οἷον εἰ τὸ μὲν A τινὶ τῷ B ὑπάρ-
bal * € , ^ * ^ ~ € , Ld ~
χει ἢ μὴ ὑπάρχει, τὸ δὲ B παντὶ τῷ Γ᾽ ὑπάρχει" ὅροι τοῦ
[4 ) > 6 , L4 i ~ b « ὔ » 6 , μὴ
ὑπάρχειν ἀγαθόν--ἕξις- φρόνησις, τοῦ μὴ ὑπάρχειν ἀγαθόν--ἔξις-- 35
ἀμαθία. πάλιν εἰ τὸ μὲν B μηδενὶ τῷ Γ, τὸ δὲ A τινὶ τῷ B 1
ὑπάρχει ἢ μὴ ὑπάρχει ἢ μὴ παντὶ ὑπάρχει, οὐδ᾽ οὕτως ἔσται
συλλογισμός. ὅροι λευκόν--ππος--κύκνος, λευκόν--[ππος--κό-
« *, * * M , 4 3 ,
pag. οἱ αὐτοὶ δὲ καὶ εἰ τὸ A B ἀδιόριστον. 30
> *95 v M ^ M
Οὐδ᾽ ὅταν τὸ μὲν πρὸς 39
~ , w 0 5X , "^ M] -^ [4 b
TQ μείζονι ἄκρῳ καθόλου γένηται 7) κατηγορικὸν ἢ στερητικόν, 26
τὸ δὲ πρὸς τῷ ἐλάττονι στερητικὸν κατὰ μέρος, οὐκ ἔσται συλ-
λογισμός [ἀδιορίστου τε καὶ ἐν μέρει ληφθέντος], οἷον εἰ τὸ μὲν
Α * ^ B € , ^ δὲ Β M ^ I , ^ > ^
παντὶ τῷ B ὑπάρχει, τὸ δὲ B τινὲ τῷ D μή, 7) εἰ μὴ
413 οὖν om. C 23 y+a.B.y B 24 €ort+ κατὰ d : 4- παντὸς κατὰ C
29 6v om. CIT 31 ?! om. C 32 τοῦ f : οὔτε ABCdT' II 33
5 Ad Al: rod C, fecit Β: otre PITT = trav B A?r 36 7 om. FIT 37
3! om. C 38 dport τοῦ μὲν ὑπάρχειν CIT Aevxóy?] τοῦ δὲ μὴ ὑπάρχειν
λευκόν CIT 39 ἀδιόριστον- εἴ ΟΓΠ b2-3 οὐκ. ληφθέντος BC,
fecit A: ἀδιορίστου... ληφθέντος om. d! et fort. ALP 43 εὖ ὑπάρχει FCT
ANAAYTIKQN IIPOTEPON A
ςπαντὶ ὑπάρχει: ᾧ yap av τινι μὴ ὑπάρχῃ τὸ μέσον, τούτῳ
* ~
καὶ παντὶ Kal οὐδενὶ ἀκολουθήσει τὸ πρῶτον. ὑποκείσθωσαν
yap οἱ ὅροι ζῷον-ἀνθρωπος-λευκόν- εἶτα καὶ ὧν μὴ κατη-
^ ^ € » » , , ‘ ^
yopetrat λευκῶν 6 ἄνθρωπος, εἰλήφθω κύκνος καὶ xwóv:
οὐκοῦν τὸ ζῷον τοῦ μὲν παντὸς κατηγορεῖται, τοῦ δὲ οὐδενός, ὥστε
», » , , ^ * X. ^ t
10 οὐκ ἔσται συλλογισμός. πάλιν τὸ μὲν A μηδενὶ τῷ B ὑπαρ-
H A * A ~ ^ € Li M c 3 LÀ
xéro, τὸ δὲ B rui τῷ I μὴ ὑπαρχέτω" καὶ οἱ ὅροι ἔστωσαν
» » , "n T D
ἄψυχον--ἄνθρωπος--λευκόν: εἶτα εἰλήφθωσαν, ὧν μὴ κατη-
^ ^ * LÀ "
γορεῖται λευκῶν ὁ ἄνθρωπος, κύκνος καὶ χιών' τὸ γὰρ ἄψυ-
xov τοῦ μὲν παντὸς κατηγορεῖται, τοῦ δὲ οὐδενός. ἔτι ἐπεὶ ἀδιό-
* ^ ~ I ^ B * L4 , > 0 , δέ M
i5 puo Tov. τὸ Twi τῷ Γ τὸ B μὴ ὑπάρχειν, ἀληθεύεται δέ, καὶ
εἰ μηδενὶ ὑπάρχει καὶ εἰ μὴ παντί, ὅτι Twi οὐχ ὑπάρχει,
ληφθέντων δὲ τοιούτων ὅρων ὥστε μηδενὶ ὑπάρχειν οὐ γίνεται
συλλογισμός (τοῦτο γὰρ εἴρηται πρότερον), φανερὸν οὖν ὅτι
τῷ οὕτως ἔχειν τοὺς ὅρους οὐκ ἔσται συλλογισμός: ἦν γὰρ ἂν
M 3 , € ? x , \ , A ,
2o Kal ἐπὶ τούτων. ὁμοίως δὲ δειχθήσεται kai εἰ τὸ καθόλου
ax τεθείη στερητικόν.
21 Οὐδὲ ἐὰν ἄμφω τὰ διαστήματα κατὰ μέ-
ρος ἢ κατηγορικῶς ἢ στερητικῶς, ἢ τὸ μὲν κατηγορικῶς τὸ δὲ
στερητικῶς λέγηται, ἢ τὸ μὲν ἀδιόριστον τὸ δὲ διωρισμένον, ἢ
» 3 , , L4 t *, ~ - M 4
ἄμφω ἀδιόριστα, οὐκ ἔσται συλλογισμὸς οὐδαμῶς. ὅροι δὲ κοινοὶ
as πάντων ζῷον-λευκόν--ἶππος, ζῷον -λευκόν-λίθος.
~ 4 >
Φανερὸν οὖν ἐκ τῶν εἰρημένων ws ἐὰν ἦ συλλογισμὸς ev
τούτῳ τῷ οχήματι κατὰ μέρος, ὅτι ἀνάγκη τοὺς ὅρους οὕτως
Ν t » » M , , 3 ~ , ^
ἔχειν ὡς εἴπομεν: ἄλλως yàp ἐχόντων οὐδαμῶς γίνεται. δῆ-
᾿ M " , |j > > ~ X P , >
λον δὲ kai ὅτι πάντες οἱ ἐν αὐτῷ συλλογισμοὶ τέλειοί εἰσι"
, ᾿ ^ , ^ ὃ ^ ~ > > ~ X θέ ν 97
3o (πάντες γὰρ ἐπιτελοῦνται διὰ τῶν ἐξ ἀρχῆς ληφθέντων), καὶ ὅτι
πάντα τὰ προβλήματα δείκνυται διὰ τούτου τοῦ σχήματος"
καὶ γὰρ τὸ παντὶ καὶ τὸ μηδενὶ καὶ τὸ τινὶ καὶ τὸ μή τινι
ὑπάρχειν. καλῶ δὲ τὸ τοιοῦτον σχῆμα πρῶτον.
~ ~ ^ ,
Ὅταν δὲ τὸ αὐτὸ τῷ μὲν παντὶ τῷ δὲ μηδενὶ ὑπάρ-
-^ , ἣν ^ M ^
as Xp, ἢ ἑκατέρῳ παντὶ ἢ μηδενί, TO μὲν σχῆμα τὸ τοιοῦτον
^ > ~ s ,
καλῶ δεύτερον, μέσον δὲ ἐν αὐτῷ λέγω τὸ κατηγορούμενον
? Po^ » * » T , ^ ^ * Ld ‘
ἀμφοῖν, ἄκρα δὲ καθ᾽ ὧν λέγεται τοῦτο, μεῖζον δὲ ἄκρον τὸ
πρὸς τῷ μέσῳ κείμενον: ἔλαττον δὲ τὸ πορρωτέρω τοῦ μέσου.
τίθεται δὲ τὸ μέσον ἔξω μὲν τῶν ἄκρων, πρῶτον δὲ τῇ θέσει.
by of om. C κατηγορῆται A 19 τῷ . . . ὅρους] οὕτως ἐχόντων
τῶν ὅδωωυ C τῷ] τὸ ἃ 20 καὶ εἰ CAL: κἂν ABd 21 τεθῇα οὐδέ
tye AC uépos4- 3 C 32 r0? om. ABd nui... μή fecit B
34 ὑπάρχῃ om. IIT 37 8&8] μὲν FIT 38 ἔλαττον... μέσου om. B!
b a
4. 26°5 — 5. 2734
τέλειος μὲν οὖν οὐκ ἔσται συλλογισμὸς οὐδαμῶς ἐν τούτῳ τῷ σχή- 27"
ματι, δυνατὸς δ᾽ ἔσται καὶ καθόλου καὶ μὴ καθόλου τῶν ὅρων
x αθόλ - 7 x L4 3 ld 4 ,
ὄντων. καθόλου μὲν οὖν ὄντων ἔσται συλλογισμὸς ὅταν τὸ μέ-
σον τῷ μὲν παντὶ τῷ δὲ μηδενὶ ὑπάρχῃ, ἂν πρὸς ὁποτερῳοῦν
ἢ τὸ στερητικόν: ἄλλως δ᾽ οὐδαμῶς. κατηγορείσθω γὰρ τὸ M 5
~ A » ~ A r- , > M 4 > , *
τοῦ μὲν N μηδενός, τοῦ δὲ & παντός. ἐπεὶ οὖν ἀντιστρέφει τὸ
στερητικόν, οὐδενὶ τῷ Μ ὑπάρξει τὸ N- τὸ δέ γε Μ παντὶ τῷ
A^ € , e A > M ~ γα ^ ^ / /
& ὑπέκειτο: ὥστε τὸ Ν οὐδενὶ τῷ Ξ τοῦτο yàp δέδεικται mpó-
τερον. πάλιν εἰ τὸ M τῷ μὲν Ν παντὶ τῷ δὲ X μηδενί,
A 5; m ^ Aa m
οὐδὲ τὸ E τῷ Ν οὐδενὶ ὑπάρξει (εἰ yap τὸ M οὐδενὶ τῷ E, οὐδὲ 1o
^ ^ ^ M
τὸ E οὐδενὶ τῷ Μ' τὸ δέ ye M παντὶ τῷ Ν ὑπῆρχεν" τὸ ἄρα
— > M ^ € , ,^ ^ , A ^
& οὐδενὶ TQ Ν ὑπάρξει: γεγένηται yap πάλιν τὸ πρῶτον
^ , M MEI , A , , M * , M ~
σχῆμα)" ἐπεὶ δὲ ἀντιστρέφει τὸ στερητικόν, οὐδὲ τὸ N οὐδενὶ τῷ
m € , - , Ww L4 , A , w $ 2,
& ὑπάρξει, ὥστ᾽ ἔσται 0 αὐτὸς συλλογισμός. ἔστι δὲ δεικνύναι
ταῦτα καὶ εἰς τὸ ἀδύνατον ἄγοντας. ὅτι μὲν οὖν γίνεται συλ- τς
4 L4 , , ^ Ld , > ᾽ > la 3
λογισμὸς οὕτως ἐχόντων τῶν ὅρων, φανερόν, ἀλλ᾽ οὐ τέλειος" οὐ
* , » ~ , , ~ 3 4 M > w » ^ A
yàp μόνον ἐκ τῶν ἐξ ἀρχῆς ἀλλὰ καὶ ἐξ oes ἐπιτελεῖται TO
ἀναγκαῖον. ἐὰν δὲ τὸ M παντὸς τοῦ Ν kai τοῦ & κατηγορῆται,
οὐκ ἔσται συλλογισμός. ὅροι τοῦ ὑπάρχειν οὐσία--ζῷον-ἄνθρωπος,
τοῦ μὴ ὑπάρχειν οὐσία--ζ ῷον-ἀριθμός- μέσον οὐσία. οὐδ᾽ ὅταν ao
μήτε τοῦ Ν μήτε τοῦ & μηδενὸς κατηγορῆται τὸ M. ὅροι τοῦ
ὑπάρχειν γραμμή --ζῷον-ἄνθρωπος, τοῦ μὴ ὑπάρχειν γραμμή--
ζῷον-λίθος. φανερὸν οὖν ὅτι ἄν fj συλλ 86A Ὁ
f s. φανερὸν οὖν ὅτι dv ἦ συλλογισμὸς καθόλου τῶν
ὅρων ὄντων, ἀνάγκη τοὺς ὅρους ἔχειν ws ἐν ἀρχῇ εἴπομεν'
ἄλλως γὰρ ἐχόντων οὐ γίνεται τὸ ἀναγκαῖον. 25
» ^ X A ΑἹ ov , A , e *
Ἐὰν δὲ πρὸς τὸν ἕτερον jj καθόλου τὸ μέσον, ὅταν μὲν
πρὸς τὸν μείζω γένηται καθόλου ἢ κατηγορικῶς 7) στερητικῶς,
πρὸς δὲ τὸν ἐλάττω κατὰ μέρος καὶ ἀντικειμένως τῷ καθόλου
(λέγω δὲ τὸ ἀντικειμένως, εἰ μὲν τὸ καθόλου στερητικόν, τὸ
ἐν μέρει καταφατικόν" εἰ δὲ κατηγορικὸν τὸ καθόλου, τὸ ἐν 30
μέρει στερητικόν), ἀνάγκη γίνεσθαι συλλογισμὸν στερητικὸν
M δ > A: M M ~ A N ὃ ' ^ δὲ ny '
κατὰ μέρος. εἰ yàp TO τῷ μὲν Ν μηδενὶ τῷ δὲ M τινὶ
^ M
ὑπάρχει, ἀνάγκη τὸ N τινὲ τῷ & μὴ ὑπάρχειν. ἐπεὶ yap
M ^ ^
ἀντιστρέφει τὸ στερητικόν, οὐδενὶ τῷ M ὑπάρξει τὸ Ν' τὸ 8é ye M
2733 οὖν om. C ὄντων- τῶν ὅρων CI 4 οὐδενὶ C xày ΓΠ
8 πρότερον-Ἐ εἰ γὰρ τὸ μ οὐδενὶ τῷ £ (v C) οὐδὲ τὸ £ & C) οὐδενὶ τῷ μ (cf. *10-
11) ÁAYBIC loro gta v BCdritAl: τῷ É τὸν 43: τὸν τῷ E imu: τὸ
£B €... I1 M! om. Bd Tm... 1I τῷ fecit A II τὸ dpa]
dore τὸ CI1: ὥστε dpa r6 Γ 15 ἀπάγοντας Cd II
ANAAYTIKQN IIPOTEPON A
= =
L4 , x ^ [4 , a * M ^ > L4 ,
35 ὑπέκειτο τινὶ τῷ E ὑπάρχειν: ὥστε τὸ Ν τινὶ τῷ Ξ ody ὑπάρ-
ξει" γίνεται γὰρ συλλογισμὸς διὰ τοῦ πρώτου σχήματος. πά-
3 ~ 4 X A ~ ^ quee M M t ,
Aw εἰ TQ μὲν Ν παντὶ τὸ M, τῷ δὲ X τινὶ μὴ ὑπάρχει,
3 , 4 ‘ ^ = M Li , , A x € ,
ἀνάγκη τὸ Ν τινὶ τῷ E μὴ ὑπάρχειν: εἰ yàp παντὶ ὑπάρ-
^ * 4 4 M ^ 3 , M
χει, κατηγορεῖται δὲ καὶ τὸ M παντὸς τοῦ N, ἀνάγκη τὸ M
27^ παντὶ τῷ E ὑπάρχειν: ὑπέκειτο δὲ τινὶ μὴ ὑπάρχειν. καὶ εἰ
Ml ^ A 4 € , ^ * — ^ , »
τὸ M τῷ μὲν Ν παντὶ ὑπάρχει τῷ δὲ EF μὴ παντί, ἔσται
λλ δ᾿ Ld 7 * ^ Id M N > ὃ ὃ᾽ - » ,
συλλογισμὸς ὅτι od παντὶ TQ Ξ τὸ N- ἀπόδειξις δ᾽ ἡ αὐτή.
ἐὰν δὲ τοῦ μὲν & παντὸς τοῦ δὲ Ν μὴ παντὸς κατηγορῆται,
, w , -* ~ , , la ^ *
5 οὐκ ἔσται συλλογισμός. ὅροι ζῷον-οὐσία--κόραξ, ζῷον--λευκόν--
, 95 & ^ bi - , ~ X la ΄ ^
κόραξ. οὐδ᾽ ὅταν τοῦ μὲν Ξ μηδενός, τοῦ δὲ Ν τινός. ὅροι τοῦ
ὑπάρχειν ζῷον-οὐσία-μονάς, τοῦ μὴ ὑπάρχειν ζῷον-οὐσία--
ἐπιστήμη.
Ὅ. A 7 » , T * 06A ~ M [4
ταν μὲν οὖν ἀντικείμενον ἦ TO καθόλου TH κατὰ μέρος,
LÀ p: ν A ,?O * μὲ , a *
ro εἴρηται πότ᾽ ἔσται kai πότ᾽ οὐκ ἔσται συλλογισμός: ὅταν δὲ
7 T
ὁμοιοσχήμονες ὦσιν αἱ προτάσεις, otov ἀμφότεραι στερητικαὶ
ἢ καταφατικαί, οὐδαμῶς ἔσται συλλογισμός. ἔστωσαν γὰρ
πρῶτον στερητικαί, καὶ τὸ καθόλου κείσθω πρὸς τὸ μεῖζον
» A ~ * * ^ * d LY * [4
ἄκρον, οἷον τὸ M τῷ μὲν N μηδενὶ τῷ δὲ E τινὶ μὴ ὑπαρ-
, , Li 4 M * M hi ^ -π M € ,
15 χέτω: ἐνδέχεται δὴ καὶ παντὶ καὶ μηδενὶ τῷ Ξ τὸ N ὑπάρ-
xew. ὅροι τοῦ μὲν μὴ ὑπάρχειν μέλαν--χιών--ζἨῷον- τοῦ δὲ παντὶ
coe , » ^ > * ^m As SY e ὦ
ὑπάρχειν οὐκ ἔστι λαβεῖν, εἰ τὸ M τῷ Ξ τινὶ μὲν ὑπάρχει
τινὶ δὲ μή. εἰ γὰρ παντὶ τῷ Ξ τὸ Ν, τὸ δὲ M μηδενὶ τῷ N,
kl , x ^ Lnd [4 , > , ¢ , * € ,
τὸ M οὐδενὶ τῷ E ὑπάρξει" ἀλλ᾽ ὑπέκειτο τινὶ ὑπάρχειν.
eu A T *, > ^ ~ L4 > X a > ,
20 οὕτω μὲν οὖν οὐκ ἐγχωρεῖ λαβεῖν ὅρους, ἐκ δὲ τοῦ ἀδιορίστου δει-
kTéov- ἐπεὶ γὰρ ἀληθεύεται τὸ τινὲ μὴ ὑπάρχειν τὸ M τῷ
m. * > * € » 4 M Li , Uu ἣν
Ξ καὶ εἰ μηδενὶ ὑπάρχει, μηδενὶ δὲ ὑπάρχοντος οὐκ ἦν συλ-
λογισμός, φανερὸν ὅτι οὐδὲ νῦν ἔσται. πάλιν ἔστωσαν κατηγορι-
, ' y H , e ΄ καὶ 3 ^A D
καί, kai τὸ καθόλου κείσθω ὁμοίως, otov τὸ M τῷ uev N
M ^ 4 op ^ [4 , , , M ki ^ Led τ
25 παντὶ τῷ δὲ E τινὶ ὑπαρχέτω. ἐνδέχεται δὴ τὸ Ν τῷ & καὶ
“- * ,
παντὶ καὶ μηδενὶ ὑπάρχειν. ὅροι τοῦ μηδενὶ ὑπάρχειν λευκόν--
JF 7 ~ x A > L4 ^ M ^ » v *,
kükvos-A(Bos* τοῦ δὲ παντὶ οὐκ ἔσται λαβεῖν διὰ THY αὐτὴν al-
, Ld , > > » LIN , , > 4 ^
Tíav ἥνπερ πρότερον, ἀλλ᾽ ἐκ τοῦ ἀδιορίστου δεικτέον. εἰ δὲ τὸ
/, A à om L4 > , § ‘ ^ x p
καθόλου πρὸς τὸ ἔλαττον ἄκρον ἐστί, kat τὸ M τῷ μὲν & μη-
'
30 δενὲ τῷ δὲ Ν τινὶ μὴ ὑπάρχει, ἐνδέχεται τὸ N τῷ & καὶ
335 ὑπόκειται ΑἸΒΟΓΠ τῷξ BcAl: τῶν ΑΓ ὑπάρχει C 37 ὑπάρ-
xn 41Β 38 ὑπάρξει ΟΓΠ bg παντὸς--ττὸμ ΓΠ κατηγορῆται- τὸ
pd 1 ro04-5e.C 14 τὸ δὲ A 17 AaBety+ ὅρους CIT 18 uj4-
ὑπάρχει CIT οὐδενὶ C 19 ὑπάρχει C Twi-F μὴ CUT 20 ἀορί-
στου d! 27 τὸς
5. 27935 — 6. 28225
A ^ * e , μὲ “- [4 , , ^
παντὶ καὶ μηδενὶ ὑπάρχειν. ὅροι τοῦ ὑπάρχειν λευκόν--ζῷον--
, ^ A € ld y 5, , 2 A
κόραξ, τοῦ μὴ ὑπάρχειν Aevkóv-A(Bos-kópa£. εἰ δὲ κατηγορι-
4 € - ^
καὶ ai προτάσεις, ὅροι τοῦ μὴ ὑπάρχειν λευκόν--ζῷον--χιών,
τοῦ ὑπάρχειν λευκόν--ζῷον--κύκνος. φανερὸν οὖν, ὅταν ὁμοιοσχή-
Li
poves ὦσιν ai προτάσεις καὶ ἡ μὲν καθόλου ἡ δ᾽ ἐν μέρει, ὅτι
9 ~ z , > > 0.» > ^ ¢ , L4 ,
οὐδαμῶς γίνεται συλλογισμός. ἀλλ᾽ οὐδ᾽ εἰ τινὶ ἑκατέρῳ ὑπάρ-
-^ 4 € , ^ ^ b
χει ἢ μὴ ὑπάρχει, T] τῷ μὲν τῷ δὲ μή, ἢ μηδετέρῳ παντί,
-* > , iia A ^ , , ~ v
ἢ ἀδιορίστως. ὅροι δὲ κοινοὶ πάντων λευκόν--ζῷον--ἄνθρωπος,
,
λευκόν--ζῷον- ἄψυχον.
Φ, ‘ T > ^ > LÀ Ld 7 e L4 *
avepóv οὖν ἐκ τῶν εἰρημένων ὅτι ἐάν Te οὕτως ἔχωσιν ot
ὅροι πρὸς ἀλλήλους ὡς ἐλέχθη, γίνεται συλλογισμὸς ἐξ
ἀνάγκης, ἄν τ᾽ ἢ συλλογισμός, ἀνάγκη τοὺς ὅρους οὕτως ἔχειν.
^ M ^ ~
δῆλον δὲ καὶ ὅτι πάντες ἀτελεῖς εἰσὶν ot ἐν τούτῳ TH σχήματι
συλλογισμοί (πάντες γὰρ ἐπιτελοῦνται προσλαμβανομένων
~ hal * ^
τινῶν, ἃ ἢ ἐνυπάρχει Tots ὅροις ἐξ ἀνάγκης ἢ τίθενται ws
[4 l4 Ly L4 ^ ^ > , , * a ,
ὑποθέσεις, otov Grav διὰ τοῦ ἀδυνάτου δεικνύωμεν), καὶ ὅτι οὐ
γίνεται καταφατικὸς συλλογισμὸς διὰ τούτου τοῦ σχήματος,
ἀλλὰ πάντες στερητικοί, καὶ οἱ καθόλου καὶ οἵ κατὰ μέρος.
"Ea δὲ ~ , ^ * * M A 4 ‘ L4 , ~
av δὲ τῷ αὐτῷ τὸ μὲν παντὶ τὸ δὲ μηδενὶ ὑπάρχῇ,
ἢ ἄμφω παντὶ ἣ μηδενί, τό μὲν σχῆμα τὸ τοιοῦτον καλῶ
,ὔ , ? > $3. ~ 2, i» T ow M ΄
τρίτον, μέσον δ᾽ ἐν αὐτῷ λέγω καθ᾽ οὗ ἄμφω τὰ κατηγορού-
μενα, ἄκρα δὲ τὰ κατηγορούμενα, μεῖζον δ᾽ ἄκρον τὸ πορρώ-
τερον τοῦ μέσου, ἔλαττον δὲ τὸ ἐγγύτερον. τίθεται δὲ τὸ μέσον
Ν͵ 4 ~ L4 L4 A -^ L4 , * 4 , ,
ἔξω μὲν τῶν ἄκρων, ἔσχατον δὲ τῇ θέσει. τέλειος μὲν οὖν οὐ γί-
νεται συλλογισμὸς οὐδ᾽ ἐν τούτῳ τῷ σχήματι, δυνατὸς δ᾽ ἔσται
καὶ καθόλου καὶ μὴ καθόλου τῶν ὅρων ὄντων πρὸς τὸ μέσον.
Καθόλου
A T » L4 a * ki 4 M ^ t , L4
μὲν οὖν ὄντων, ὅταν καὶ τὸ II kai τὸ P παντὶ τῷ L ὑπάρχῃ, ὅτι
M ~ * | 4 4 >, > , , * ^ > ,
Twi TQ P τὸ II ὑπάρξει ἐξ ἀνάγκης" ἐπεὶ yàp ἀντιστρέφει
M , € 4 € ^ M ^ P LA ? > X ^ * Pn
τὸ κατηγορικόν, ὑπάρξει τὸ Σ' τινὶ τῷ P, ὥστ᾽ ἐπεὶ τῷ μὲν
παντὶ τὸ II, τῷ δὲ P τινὶ τὸ Z2, ἀνάγκη τὸ IT τινὲ τῷ P ὑπάρ-
χειν- γίνεται γὰρ συλλογισμὸς διὰ τοῦ πρώτου σχήματος. ἔστι
4 ‘ ὃ ^ ^ 10 * d M ^5 0é. 0 ^ ^ > ὃ
δὲ καὶ διὰ τοῦ ἀδυνάτου καὶ τῷ ἐκθέσθαι ποιεῖν τὴν ἀπόδειξιν
εἰ γὰρ ἄμφω παντὶ τῷ L' ὑπάρχει, ἂν ληφθῇ τι τῶν L olov
τὸ Ν, τούτῳ καὶ τὸ IT καὶ τὸ P ὑπάρξει, ὥστε τινὶ τῷ P τὸ Π
bs2 εἰ δὲ] ἐπειδὴ d 33-4 χιών... ζῷον om. C! 34 τοῦ- δὲ
CH ὅτι ἐὰν C : ὅτι dv d 37 ἢ μὴ ὑπάρχει om. B! μηδ᾽ ἑτέρῳ
C 2844 ὅτι kai Cd 9 ἀλλ᾽ ἅπαντες C 10 ὅταν d 18 οὖν
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283
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15
17
17
20
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ANAAYTIKQN IIPOTEPQN A
ὑπάρξει. καὶ ἂν τὸ μὲν P παντὶ τῷ Σ, τὸ δὲ II μηδενὶ
€ L4 v a -" * M ^ > t F
ὑπάρχῃ, ἔσται συλλογισμὸς ὅτι τὸ IT τινὶ τῷ P οὐχ ὑπάρ-
£e. ἐξ ἀνάγκης: 6 γὰρ αὐτὸς τρόπος τῆς ἀποδείξεως ἀντι-
στραφείσης τῆς P Σ προτάσεως. δειχθείη δ᾽ ἂν καὶ διὰ τοῦ
> , , * * ^ , LA M i] X; 4
3o ἀδυνάτου, καθάπερ ἐπὶ τῶν πρότερον. ἐὰν δὲ τὸ μὲν P μηδενὶ
τὸ δὲ IT παντὶ ind Ὁ Σ, οὐκ € συλλι is. 6
pxn τῷ Σ, οὐκ ἔσται συλλογισμός. ὅροι
~ ~ ~ , ^
ToU ὑπάρχειν ζῷον--ἶππος- -ἄνθρωπος, τοῦ μὴ ὑπάρχειν ζῷον--
ἄψυχον-ἄνθρωπος. οὐδ᾽ ὅταν ἄμφω κατὰ μηδενὸς τοῦ X λέ-
γηται, οὐκ ἔσται συλλογισμός. ὅροι τοῦ ὑπάρχειν ζῷον--ἶππος--
-^ , LÀ
35 ἅψυχον, τοῦ μὴ ὑπάρχειν ἄνθρωπος--ἵππος- -ἄψυχον: μέσον
ἄψυχον. φανερὸν οὖν καὶ ἐν τούτῳ τῷ σχήματι πότ᾽ ἔσται καὶ
πότ᾽ οὐκ ἔσται συλλογισμὸς καθόλου τῶν ὅρων ὄντων. ὅταν μὲν
γὰρ ἀμφότεροι οἱ ὅροι ὦσι κατηγορικοί, ἔσται συλλογισμὸς
ὅτι τινὶ ὑπάρχει τὸ ἄκρον τῷ ἄκρῳ, ὅταν δὲ στερητικοί, οὐκ
&b w Ld δ᾽ ia * ^ A L4 δὲ , 7A A
28> ἔσται. ὅταν δ᾽ ὁ μὲν ἦὖ στερητικὸς 0 δὲ καταφατικός, ἐὰν μὲν
6 μείζων γένηται στερητικὸς ἅτερος δὲ καταφατικός, ἔσται
4 Ld 4 > e L4 M w ~ » oA
συλλογισμὸς ὅτι τινὶ οὐχ ὑπάρχει TO ἄκρον τῷ ἄκρῳ, ἐὰν
δ᾽ ἀνάπαλιν, οὐκ ἔσται.
5 Ἐὰν δ᾽ ὁ μὲν fj καθόλου πρὸς τὸ μέσον ὁ δ᾽ ἐν μέρει,
~ A » > - > 5, ,
κατηγορικῶν μὲν ὄντων ἀμφοῖν ἀνάγκη γίνεσθαι συλλογι-
σμόν, av ὁποτεροσοῦν ἢ καθόλου τῶν ὅρων. εἰ γὰρ τὸ μὲν P
παντὶ TQ Σ τὸ δὲ II τινί, ἀνάγκη τὸ IT τινὶ τῷ P ὑπάρ-
, * ^ 3 * * A € , ^
χειν. ἐπεὶ yàp ἀντιστρέφει τὸ καταφατικόν, ὑπάρξει τὸ Σ
a ~ L4 3 > 4 4 * Ν ~ A] * ^ ~
10 τινὶ TH II, ὥστ᾽ ἐπεὶ τὸ μὲν P παντὶ τῷ Σ, τὸ δὲ Σ τινὶ τῷ
II, καὶ τὸ P τινὶ τῷ II ὑπάρξει: ὥστε τὸ II τινὶ τῷ P. πά-
» + 4 * -^ 4 b M [4 ra > ,
Aw el τὸ μὲν P τινὶ τῷ Σ τὸ δὲ II παντὶ ὑπάρχει, ἀνάγκη
ὁ II τινὶ τῷ P ὑπάρχειν: 6 γὰρ αὐτὸς τρόπος τῆς ἀποδεί-
τ τινὶ τᾷ PX yàp αὐτὸς τρόπος τῆς ἀποδεί
LÀ » > ^ b A ^9 , * ^ ,
ξεως. ἔστι δ᾽ ἀποδεῖξαι καὶ διὰ τοῦ ἀδυνάτου καὶ τῇ ἐκθέσει,
15 καθάπερ ἐπὶ τῶν πρότερον.
> 4 > € A ^ οἷ e ^
15 Ἐὰν δ᾽ 6 μὲν fj κατηγορικὸς ὁ δὲ
, , , ες , L7 D ε νὰ 7 ,
στερητικός, καθόλου δὲ 6 κατηγορικός, ὅταν μὲν ὁ ἐλάττων jj
κατηγορικός, ἔσται συλλογισμός. εἰ γὰρ τὸ P παντὶ τῷ Σ,
x δὲ II ‘ A [4 , , , ^ II ' ~ * L4 "d
τὸ δὲ II τινὶ μὴ ὑπάρχει, ἀνάγκη τὸ [1 τινὶ τῷ P μὴ ὑπάρ-
, , M ^
xew. εἰ yàp παντί, καὶ τὸ P παντὶ τῷ Σ, kai τὸ II παντὶ
326 ὑπάρχει Ad 28 τρόπος -ἰ- ἔσται C: -ἰ ἐστί II 30 τῶν] τοῦ
cro μηδενὶ 4- T0 oC : -- rà o II 34 ἔστι d 35-6 rot... ἄψυχον
om. d* - 37 μὲν om. Ct 38 τεθῶσι CIT bi fom. ΓΠ 8
σ- ὑπάρχει Cri II ὦστε-: καὶ ΒΌΓΠΑϊς 15 ἐπὶ) καὶ ἐπὶ CIT
πρότερον BAIS: προτέρων ACd 17 ρ- μὲ ΓΠ o E ὑπάρχει C 18
ὑπάρχει] ὑπάρχη B!
6. 28°26 — 29*10
TQ Σ ὑπάρξει: ἀλλ᾽ οὐχ ὑπῆρχεν. δείκνυται δὲ καὶ ἄνευ τῆς 20
, με oN EN ὡς ^ Y 4 es
ἀπαγωγῆς, ἐὰν ληφθῇ τι τῶν Σ ᾧ τὸ Π μὴ ὑπάρχει.
ὅταν δ᾽ ὁ μείζων ἢ κατηγορικός, οὐκ ἔσται συλλογισμός, οἷον
> ^ A * ^ a b a ^ x t , Ld
εἰ τὸ μὲν II παντὶ τῷ Σ, τὸ δὲ P τινὶ τῷ Σ μὴ ὑπάρχει. ὅροι
~ ^ e , Μ LA ^ ^ * *
ToU παντὶ ὑπάρχειν ἔμψυχον--ἀνθρωπος--ζῷον. τοῦ δὲ μηδενὶ
> L4 ^ μὲ , M + [4 , ^ ‘ M A
οὐκ ἔστι λαβεῖν ὅρους, εἰ τινὶ μὲν ὑπάρχει TH Σ τὸ P, τινὶ δὲ 25
, 3 * M x II ~ [4 ,ὔ 4 a Á -
μή" εἰ yàp παντὶ τὸ II τῷ XY ὑπάρχει, τὸ δὲ P τινὶ τῷ Σ,
M \ S ^ ut y cif x + eos
καὶ τὸ IT τινὶ τῷ P ὑπάρξει: ὑπέκειτο δὲ μηδενὶ ὑπάρχειν.
ἀλλ᾽ ὥσπερ ἐν τοῖς πρότερον ληπτέον" ἀδιορίστου γὰρ ὄντος τοῦ
M M [4 4 M M 8 A. € Ca ax θὲ , ^ * X.
τινὶ μὴ ὑπάρχειν καὶ τὸ μηδενὶ ὑπάρχον ἀληθὲς εἰπεῖν τινὶ μὴ
ὑπάρχειν" μηδενὶ δὲ ὑπάρχοντος οὐκ ἦν συλλογισμός. φανερὸν 30
5,8 , LJ / 3^5 ae M , ^
οὖν ὅτι οὐκ ἔσται συλλογισμός. ἐὰν δ᾽ ὁ στερητικὸς 1) καθόλου τῶν
ὅρων, ὅταν μὲν ὁ μείζων ἢ στερητικὸς ὁ δὲ ἐλάττων κατηγορι-
Kos, ἔσται συλλογισμός. εἰ γὰρ τὸ IT μηδενὶ τῷ Σ, τὸ δὲ P
τινὶ ὑπάρχει TH Σ, τὸ II τινὶ τῷ P οὐχ ὑπάρξει" πάλιν γὰρ
ἔσται τὸ πρῶτον σχῆμα τῆς P Σ προτάσεως ἀντιστραφείσης. 35
ὅταν δὲ ὁ ἐλάττων 7 στερητικός, οὐκ ἔσται συλλογισμός. ὅροι
τοῦ ὑπάρχειν ζῷον-ἀνθρωπος-ἄγριον, τοῦ μὴ ὑπάρχειν ζῷον--
, a L4 , 2 > ^ MJ QO? tw 3 ,
ἐπιστήμη--ἄγριον" μέσον ἐν ἀμφοῖν τὸ ἄγριον. οὐδ᾽ ὅταν ἀμφό-
4 ~ 7 > € * id « > > H oe
Tepot στερητικοὶ τεθῶσιν, ἣ δ᾽ 6 μὲν καθόλου ὁ δ᾽ ἐν μέρει. ὅροι
Ld e > , > , a * , ~ , , a
ὅταν ὁ ἐλάττων ἦ καθόλου πρὸς TO μέσον, ζῷον-ἐπιστήμη-- 29
ἄγριον, ζῷον--ἄνθρωπος- ἄγριον: ὅταν δ᾽ ὁ μείζων, τοῦ μὲν
μὴ ὑπάρχειν xópa£—yuov-Àevkóv. τοῦ δ᾽ ὑπάρχειν οὐκ ἔστι
λαβεῖν, εἰ τὸ P τινὶ μὲν ὑπάρχει τῷ Σ,, τινὶ δὲ μὴ ὑπάρχει.
εἰ γὰρ τὸ IT παντὶ τῷ P, τὸ δὲ P τινὶ τῷ Zi, καὶ τὸ II cui τῷ 5
A ὑπέκειτο δὲ μηδενί. ἀλλ᾽ ἐκ τοῦ ἀδιορίστου δεικτέον. 6
Οὐδ᾽ ἂν 6
€ , e. ~ Li t , n M 4 , ^ LJ M € ,
ἑκάτερος τινὶ τῷ μέσῳ ὑπάρχῃ ἢ μὴ ὑπάρχῃ, 7 Ó μὲν ὑπάρ-
« * A € , "ἡ ε X ^ ¢ M ^ , a > LH
xn 9 δὲ μὴ ὑπάρχῃ, ἢ ὁ μὲν τινὶ ὁ δὲ μὴ παντί, 7) ἀδιορίστως,
οὐκ ἔσται συλλογισμὸς οὐδαμῶς. ὅροι δὲ κοινοὶ πάντων ζῷον--
ἄνθρωπος- λευκόν, ζῷον--ἀψυχον--λευκόν. 10
bo ὑπῆρχε-Ἐ παντί C 22 κατηγορικός -ἰ ὁ δ᾽ ἐλάττων pepixds στερητικός
AB 23 ὑπάρχῃ Al: om. d 28 ἀορίστου A 29 ὑπάρχον]
ὑπάρχειν A? 30 μηδενὶ. . . συλλογισμός om. IIT ὑπάρχοντι Ct
οὐκ ἣν συλλογισμός om. C 31 οὖν om. 484 32 ὁ δὲ ἕτερος
κατηγορικός d? : ὁ δὲ ἐλάττων fj καταφατικός I1: om, 44 38 ἐν om.
CII 39 ὅροι -- τοῦ μὴ ὑπάρχειν (ὉΠ 29*1 ἐπιστήμη] ἄνθρωπος
fecit B 2 ζῷον] τοῦ ὑπάρχειν ζῷον C: τοῦ δὲ ὑπάρχειν ζῷον IIT
ἄνθρωπος] ἐπιστήμη fecit B μείζων-" $ καθόλου CH: --ἦἶΤΠΓ᾽ 6 σ-
ὑπάρξει CI'II ἀορίστου A 7 μὴ ὑπάρχει C 3...8 μὴ ὑπάρχῃ
Ad Al: om. BCII
ANAAYTIKQN IIPOTEPQN A
@ ^ ^ * ᾽ 4, ~ ΄ > wv x ‘oy
avepóv οὖν Kal ἐν τούτῳ τῷ σχήματι πότ᾽ ἔσται καὶ πότ
οὐκ ἔσται συλλογισμός, καὶ ὅτι ἐχόντων τε τῶν ὅρων ὡς
3X / , a X > , L4 > 4
ἐλέχθη γίνεται συλλογισμὸς ἐξ ἀνάγκης, ἄν τ᾽ ἡ συλλογι-
σμός, ἀνάγκη τοὺς ὅρους οὕτως ἔχειν. φανερὸν δὲ καὶ ὅτι πάν-
15 τες ἀτελεῖς εἰσὶν oi ἐν τούτῳ τῷ σχήματι συλλογισμοί (πάν-
τες γὰρ τελειοῦνται προσλαμβανομένων τινῶν) καὶ ὅτι συλλο-
γίσασθαι τὸ καθόλου διὰ τούτου τοῦ σχήματος οὐκ ἔσται, οὔτε
4
στερητικὸν οὔτε καταφατικόν.
^ b ᾿ ΄σ , - ^ la 4 ^ ,
Δῆλον δὲ Kai ὅτι ἐν ἅπασι τοῖς σχήμασιν, ὅταν μὴ yc
2ο νῆται συλλογισμός, κατηγορικῶν μὲν ἢ στερητικῶν ἀμῴφοτέ-
L4 ^ ^ ^
ρων ὄντων τῶν ὅρων οὐδὲν ὅλως γίνεται ἀναγκαῖον, κατηγορικοῦ
δὲ καὶ στερητικοῦ, καθόλου ληφθέντος τοῦ στερητικοῦ ἀεὶ γίνεται
συλλογισμὸς τοῦ ἐλάττονος ἄκρου πρὸς τὸ μεῖζον, οἷον εἰ τὸ
μὲν A παντὶ τῷ B 7) τινί, τὸ δὲ B μηδενὶ τῷ Γ΄ ἀντιστρεφο-
25 μένων γὰρ τῶν προτάσεων ἀνάγκη τὸ Γ᾽ τινὶ τῷ A μὴ ὑπάρ-
xew. ὁμοίως δὲ κἀπὶ τῶν ἑτέρων σχημάτων: ἀεὶ γὰρ γίνεται
* ~ Lo - , ^ x 1 ow ^ > ,
διὰ τῆς ἀντιστροφῆς συλλογισμός. δῆλον δὲ καὶ ὅτι τὸ ἀδιό-
ριστον ἀντὶ τοῦ κατηγορικοῦ τοῦ ἐν μέρει τιθέμενον τὸν αὐτὸν
ποιήσει συλλογισμὸν ἐν ἅπασι τοῖς σχήμασιν.
‘ Xx * 4 , Ld > - M
39 Φανερὸν δὲ καὶ ὅτι πάντες oi ἀτελεῖς συλλογισμοὶ Te-
λειοῦνται διὰ τοῦ πρώτου σχήματος. ἢ γὰρ δεικτικῶς ἢ διὰ τοῦ
ἀδυνάτου περαίνονται πάντες: ἀμφοτέρως δὲ γίνεται τὸ πρῶτον
σχῆμα, δεικτικῶς μὲν τελειουμένων, ὅτι διὰ τῆς ἀντιστροφῆς
ἐπεραίνοντο πάντες, ἡ δ᾽ ἀντιστροφὴ τὸ πρῶτον ἐποίει σχῆμα,
ὃ A de a? , 8 , Ld 0 , ~ ^ €
35 διὰ δὲ τοῦ ἀδυνάτου δεικνυμένων, ὅτι τεθέντος τοῦ ψεύδους ὁ συλ-
͵ ^ ^
λογισμὸς γίνεται διὰ τοῦ πρώτου σχήματος, otov ἐν τῷ τελευ-
, , ’ A * M M ~ t , Ld a
ταίῳ σχήματι, εἰ τὸ A καὶ τὸ B παντὶ τῷ I ὑπάρχει, ὅτι τὸ
M ~ Li , > ^ , 4 M M ^
A τινὶ τῷ B ὑπάρχει: εἰ yap μηδενί, τὸ δὲ B παντὶ τῷ T,
οὐδενὶ τῷ Γ τὸ A: ἀλλ᾽ ἦν παντί. ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων.
2 b "E δὲ x > ~ , A ‘A »
29 cT. δὲ καὶ ἀναγαγεῖν πάντας τοὺς συλλογισμοὺς εἰς
τοὺς ἐν τῷ πρώτῳ σχήματι καθόλου συλλογισμούς. οἱ μὲν
γὰρ ἐν τῷ δευτέρῳ φανερὸν ὅτι δι’ ἐκείνων τελειοῦνται, πλὴν
Li , cf ^ ^
οὐχ ὁμοίως πάντες, ἀλλ᾽ οἱ μὲν καθόλου τοῦ στερητικοῦ ἀντι-
5 στραφέντος, τῶν δ᾽ ἐν μέρει ἑκάτερος διὰ τῆς εἰς τὸ ἀδύνα-
~ Li ^ ^
TOv ἀπαγωγῆς. οἱ δ᾽ ἐν τῷ πρώτῳ, of κατὰ μέρος, ἐπιτελοῦν-
312 τε om. d 16-17 τὸ καθόλου συλλογίσασθαι CI'II 17 ἔστιν ΟΠ
οὐδὲ Α 19 ὅτι καὶ Ο : καὶ ἃ γένηται ἃ 21 τῶν ὅρων] ἐπὶ μέρους τῶν
ὅρων II, fecit 41: καὶ ἐπὶ μέρους τῶν ὅρων C: τῶν ὅρων 3) ἐπὶ μέρους Γ
27 ὅτι καὶ Cd 29 ποιεῖ C 30 ὅτι καὶ C 45 δὲ om. BL’ ψευδοῦς
A Bd 36-8 ἐν... B! fecit A?
6. 29711 — 8. 3052
A * , € ~ w EY A ^ ^ , ,
ται μὲν καὶ δι᾿ αὑτῶν, ἔστι δὲ καὶ διὰ τοῦ δευτέρου σχήματος
, , 297 > , * , ' A * ^
δεικνύναι eis ἀδύνατον ἀπάγοντας, olov εἰ τὸ A παντὶ τῷ B,
^ ‘ ^ ^
τὸ δὲ B τινὶ τῷ Γ, ὅτι τὸ A τινὶ τῷ Γ΄ εἰ yàp μηδενί, τῷ
δὲ B παντί, οὐδενὶ τῷ I' τὸ B ὑπάρξει" τοῦτο γὰρ ἴσμεν διὰ
? *
τοῦ δευτέρου σχήματος. ὁμοίως δὲ καὶ ἐπὶ τοῦ στερητικοῦ ἔσται
ἡ ἀπόδειξις. εἰ γὰρ τὸ Α μηδενὶ τῷ Β, τὸ δὲ Β τινὶ τῷ Γ
[4 , ‘ ‘ ^ » t , > ^ , ^ A
ὑπάρχει, τὸ A τινὶ τῷ Γ' οὐχ ὑπάρξει: εἰ yap παντί, τῷ δὲ
‘ ^ M , ^
B μηδενὶ ὑπάρχει, οὐδενὶ τῷ I' τὸ B ὑπάρξει" τοῦτο δ᾽ ἦν τὸ
^ [2 , > b] H ' , ^ ,
μέσον σχῆμα. wor ἐπεὶ οἱ μὲν ἐν TH μέσῳ σχήματι συλ-
> AY , ^
λογισμοὶ πάντες ἀνάγονται εἰς τοὺς ev TH πρώτῳ καθόλου
συλλογισμούς, οἱ δὲ κατὰ μέρος ἐν τῷ πρώτῳ εἰς τοὺς ἐν
τῷ μέσῳ, φανερὸν ὅτι καὶ οἱ κατὰ μέρος ἀναχθήσονται εἰς
τοὺς ἐν τῷ πρώτῳ σχήματι καθόλου συλλογισμούς. οἱ δ᾽
ἐν τῷ τρίτῳ καθόλου μὲν ὄντων τῶν ὅρων εὐθὺς ἐπιτελοῦνται
δι’ ἐκεζων τῶν συλλογισμῶν, ὅταν δ᾽ ἐν μέρει ληφθῶσι, διὰ
τῶν ἐν μέρει συλλογισμῶν τῶν ἐν τῷ πρώτῳ σχήματι: οὗτοι
δὲ ἀνήχθησαν εἰς ἐκείνους, ὥστε καὶ oi ἐν τῷ τρίτῳ σχήματι,
οἱ κατὰ μέρος. φανερὸν οὖν ὅτι πάντες ἀναχθήσονται εἰς τοὺς
ἐν τῷ πρώτῳ σχήματι καθόλου συλλογισμούς.
Οἱ μὲν οὖν τῶν συλλογισμῶν ὑπάρχειν ἢ μὴ ὑπάρχειν
-^ |j ~ -^
δεικνύντες εἴρηται πῶς ἔχουσι, καὶ καθ᾽ ἑαυτοὺς of ἐκ τοῦ αὐτοῦ
΄ Ὶ ^ 2 L4 t€ ^ t ,
σχήματος kai πρὸς ἀλλήλους οἱ ἐκ τῶν ἑτέρων.
2 * , L4 H Ἄν € , Ἂς , , , € ,
B ᾿Επεὶ δ᾽ érepóv ἐστιν ὑπάρχειν τε καὶ ἐξ ἀνάγκης ὑπάρ-
^ , , € , ^ ‘ L4 , , ,
xev καὶ ἐνδέχεσθαι ὑπάρχειν (πολλὰ yap ὑπάρχει μέν, o)
, > 2 A E3 , » 7 > > , MO? € , L4
μέντοι ἐξ dváykgs: τὰ δ᾽ οὔτ᾽ ἐξ ἀνάγκης οὔθ᾽ ὑπάρχει ὅλως,
, a , Li A ^ 4 M * € ,
ἐνδέχεται δ᾽ ὑπάρχειν), δῆλον ὅτι καὶ συλλογισμὸς ἑκάστου
τούτων ἕτερος ἔσται, καὶ οὐχ ὁμοίως ἐχόντων τῶν ὅρων, ἀλλ᾽
Lj A , , L4 € , , € , [4 > , ,
ὁ μὲν ἐξ ἀναγκαίων, ὁ δ᾽ ἐξ ὑπαρχόντων, ὁ δ᾽ ἐξ ἐνδεχο-
μένων.
^ Eni A T ~ > , 86 L4 , μ᾿ M
i μὲν οὖν τῶν ἀναγκαίων σχεδὸν ὁμοίως ἔχει xai
ἐπὶ τῶν ὑπαρχόντων: ὡσαύτως γὰρ τιθεμένων τῶν ὅρων ἔν
^ [4 , M ^ > | uf (4 , ^ εἴ t ,
τε τῷ ὑπάρχειν καὶ τῷ ἐξ ἀνάγκης ὑπάρχειν ἢ μὴ ὑπάρ-
Μ " / , ~
xew ἔσται τε Kal οὐκ ἔσται συλλογισμός, πλὴν διοίσει τῷ
^ ^ A », > , € , -^ M ,
προσκεῖσθαι τοῖς ὅροις τὸ ἐξ ἀνάγκης ὑπάρχειν ἢ μὴ ὑπάρ-
χειν. τό τε γὰρ στερητικὸν ὡσαύτως ἀντιστρέφει, καὶ τὸ ἐν
20 τινὶ τῷ F20m.d! — y ὑπάρξει CIT: - ὑπάρχει Γ 17 πρώτῳ]
aB 20 τρίτῳ] y B 22 πρώτῳ] ἃ B ox1juart-t- ἀνάγονται etg
τοὺς καθόλου C 23 τρίτῳ] y B 24 οἱ om. B 25 πρώτῳ] ἃ Β
28 ἀλλήλους B*Cd* AIP : ἄλλους A Bd ἑτέρων dU'IIP* : - σχημάτων ABC:
+ ἢ τῷ μέσῳ 1] τῷ ἀνάγεσθαι εἰς τὸ πρῶτον ut vid. Al 3051 προκεῖσθαι ACI
Io
15
20
25
30
35
3o*
5
IO
1$
20
25
3o
35
ANAAYTIKQN IIPOTEPON A
Ld ^ ‘ M N. Ld , > , , M
ὅλῳ εἶναι kai τὸ κατὰ παντὸς ὁμοίως ἀποδώσομεν. ἐν μὲν
4 a E \ > \ " 4 \ ^ >
οὖν τοῖς ἄλλοις τὸν αὐτὸν τρόπον δειχθήσεται διὰ τῆς ἀντι-
στροφῆς τὸ συμπέρασμα ἀναγκαῖον, ὥσπερ ἐπὶ τοῦ ὑπάρχειν"
ἐν δὲ τῷ μέσῳ σχήματι, ὅταν ἢ τὸ καθόλου καταφατικὸν
τὸ δ᾽ ἐν μέρει στερητικόν, καὶ πάλιν ἐν τῷ τρίτῳ, ὅταν τὸ
μὲν καθόλου κατηγορικὸν τὸ δ᾽ ἐν μέρει στερητικόν, οὐχ ὁμοίως
ν € oo ΣᾺ 313? 5,7 , [MD a 5 tr;
ἔσται ἡ ἀπόδειξις, ἀλλ᾽ ἀνάγκη ἐκθεμένους ᾧ τινὶ ἑκάτερον
μὴ ὑπάρχει, κατὰ τούτου ποιεῖν τὸν συλλογισμόν" ἔσται γὰρ
^ ? ~ >
ἀναγκαῖος ἐπὶ τούτων- εἰ δὲ κατὰ τοῦ ἐκτεθέντος ἐστὶν dvay-
καῖος, καὶ κατ᾽ ἐκείνου τινός" τὸ γὰρ ἐκτεθὲν ὅπερ ἐκεῖνό τί
ἐστιν. γίνεται δὲ τῶν συλλογισμῶν ἑκάτερος ἐν τῷ οἰκείῳ
σχήματι.
’ , M ^ Fo , >
Συμβαίνει δέ ποτε καὶ τῆς ἑτέρας προτάσεως avay-
καίας οὔσης ἀναγκαῖον γίνεσθαι τὸν συλλογισμόν, πλὴν οὐχ
ὁποτέρας ἔτυχεν, ἀλλὰ τῆς πρὸς τὸ μεῖζον ἄκρον, οἷον εἰ τὸ
* Lal B , > 7 Ww t / n 4 L4 4
μὲν A τῷ B ἐξ ἀνάγκης εἴληπται ὑπάρχον ἢ μὴ ὑπάρχον,
M Ἂς - e , , eu s ? i ^
τὸ δὲ B τῷ I ὑπάρχον μόνον- οὕτως yap εἰλημμένων τῶν
, 2 3 » ^ ~ « , ^ > £ +
προτάσεων ἐξ ἀνάγκης τὸ A τῷ I ὑπάρξει ἢ οὐχ ὑπάρξει.
ἐπεὶ γὰρ παντὶ τῷ Β ἐξ ἀνάγκης ὑπάρχει ἢ οὐχ ὑπάρχει
τὸ A, τὸ δὲ Γ τι τῶν B ἐστί, φανερὸν ὅτι καὶ τῷ Γ᾽ ἐξ ἀνάγ-
μὴ , , > *. i x * Ww 3
«ys ἔσται θάτερον τούτων. εἰ δὲ τὸ μὲν A B μὴ ἔστιν ἀναγ-
καῖον, τὸ δὲ BI ἀναγκαῖον, οὐκ ἔσται τὸ συμπέρασμα ἀναγ-
καῖον. εἰ γὰρ ἔστι, συμβήσεται τὸ A τινὶ τῷ DB ὑπάρχειν
ἐξ ἀνάγκης διά τε τοῦ πρώτου καὶ διὰ τοῦ τρίτου σχήματος.
τοῦτο δὲ ψεῦδος- ἐνδέχεται γὰρ τοιοῦτον εἶναι τὸ Β ᾧ ἐγχω-
- ^ ‘ € 4 L4 M 3 ^ Ld ^ bd
pet τὸ A μηδενὶ ὑπάρχειν. ἔτι kal ἐκ τῶν ὅρων φανερὸν ὅτι
οὐκ ἔσται τὸ συμπέρασμα ἀναγκαῖον, οἷον εἰ τὸ μὲν Α εἴη κί-
νησις, τὸ δὲ B ζῷον, ἐφ᾽ d δὲ τὸ I ἄνθρωπος: ζῷον μὲν
^ € »w* Ü 3 > 7 2 P ^ δὲ & ^ ? ?
yàp ὁ ἄνθρωπος ἐξ ἀνάγκης ἐστί, κινεῖται δὲ τὸ ζῷον οὐκ ἐξ
ἀνάγκης, οὐδ᾽ ὁ ἄνθρωπος. ὁμοίως δὲ καὶ εἰ στερητικὸν εἴη
A € ^ i NEA: > P, ba x ~ 2 ,
τὸ A B- ἡ yap αὐτὴ ἀπόδειξις. ἐπὶ δὲ τῶν ἐν μέρει συλ-
^ , ^ M > ‘
λογισμῶν, εἰ μὲν τὸ καθόλου ἐστὶν ἀναγκαῖον, kai τὸ συμ-
L4
πέρασμα ἔσται ἀναγκαῖον, εἰ δὲ τὸ κατὰ μέρος, οὐκ ἀναγ-
καῖον, οὔτε στερητικῆς οὔτε κατηγορικῆς οὔσης τῆς καθόλου προ-
ἃς τὸ] ὅτι TOC 6 τὸ per C 7 ὅταν ἧς 10 ὑπάρχῃ Ald
τοῦτο B*C : τούτων I 11 ἀναγκαίως Ct τό τὸν om. C 20 ἣ
οὐχ ὑπάρξει om. d 21 γὰρ: τὸ o CI 22T0aom.CI' τῷ ABCP:
τὸ Bid 24 ἔστι ἀ τὸ om. C 25 ἔσται C 27 yàp] δὲ Al
30 ró* om. d! 35 οὐκ] οὔκουν d 36 -rucjs ... τῆς et 38-P1 -τι τῷ B...
συλλογισμός fecit A
8. 3073 — 10. 30°30
, Li * ~ ‘ , > -^ M d '
τάσεως. ἔστω δὴ πρῶτον τὸ καθόλου ἀναγκαῖον, Kal τὸ μὲν
Α παντὶ τῷ Β ὑπαρχέτω ἐξ ἀνά τὸ δὲ Β τινὶ τῷ Γ
t PX ὙΚΉς, Ω
[4 ig , > , X M M ^ £ , ,
ὑπαρχέτω μόνον: ἀνάγκη δὴ τὸ A tui τῷ Γ ὑπάρχειν ἐξ
> , 4 ^ * A x B > , -^ b M
ἀνάγκης" τὸ yap I ὑπὸ τὸ ἐστί, τῷ δὲ B παντὶ 49
€ ^ », > , ¢ , δὲ : » M LJ € b
ὑπῆρχεν ἐξ ἀνάγκης, ὁμοίως δὲ καὶ εἰ στερητικὸς εἴη 6 συλ- 30
λογισμός: ἡ γὰρ αὐτὴ ἔσται ἀπόδειξις. εἰ δὲ τὸ κατὰ μέ-
ρος ἐστὶν ἀναγκαῖον, οὐκ ἔσται τὸ συμπέρασμα ἀναγκαῖον
Or ^ > L4 , , 95 > ^ ,
(οὐδὲν yàp ἀδύνατον συμπίπτει), καθάπερ οὐδ᾽ ἐν τοῖς καθό-
λου συλλογισμοῖς. ὁμοίως δὲ κἀπὶ τῶν στερητικῶν. ὅροι κί- 5
νησις--ζῷον-λευκόν.
3 ^ b ^ , ^ , M t ^ ,
10 "Emi δὲ τοῦ δευτέρου σχήματος, εἰ μὲν ἡ στερητικὴ mpó-
τασίς ἐστιν ἀναγκαία, καὶ τὸ συμπέρασμα ἔσται ᾿ἀναγκαῖον,
εἰ δ᾽ ἡ κατηγορική, οὐκ ἀναγκαῖον. ἔστω γὰρ πρῶτον ἡ στε-
ρητικὴ ἀναγκαία, καὶ τὸ Α τῷ μὲν Β μηδενὶ ἐνδεχέσθω, τῷ το
δὲ Γ᾿ ὑπαρχέτω μόνον. ἐπεὶ οὖν ἀντιστρέφει τὸ στερητικόν, οὐδὲ
τὸ B τῷ A οὐδενὶ ἐνδέχεται. τὸ δὲ A παντὶ τῷ Γ᾽ ὑπάρχει,
ὥστ᾽ οὐδενὶ τῷ Γ τὸ B ἐνδέχεται: τὸ yap Γ ὑπὸ τὸ A ἐστίν.
ὡσαύτως δὲ καὶ εἰ πρὸς τῷ Γ᾽ τεθείη τὸ στερητικόν" εἰ γὰρ τὸ
A μηδενὶ τῷ Γ ἐνδέχεται, οὐδὲ τὸ Γ οὐδενὶ τῷ A ἐγχωρεῖ: 15
τὸ δὲ A παντὶ τῷ B ὑπάρχει, ὥστ᾽ οὐδενὶ τῷ B τὸ Γ ἐνδέχε-
ται" γίνεται γὰρ τὸ πρῶτον σχῆμα πάλιν. οὐκ ἄρα οὐδὲ τὸ B
^ > L M © Po
τῷ Γ᾽: ἀντιστρέφει yàp ὁμοίως. 18
* ᾿ € * ,
Εἰ δὲ ἡ κατηγορικὴ mpóra.- 18
σίς ἐστιν ἀναγκαία, οὐκ ἔσται τὸ συμπέρασμα ἀναγκαῖον.
« , * 4 * ~ ed > , -^ A
ὑπαρχέτω yap τὸ A παντὶ τῷ B ἐξ ἀνάγκης, τῷ δὲ Γ μη- 20
δενὶ ὑπαρχέτω μόνον. ἀντιστραφέντος οὖν τοῦ στερητικοῦ τὸ πρῶ-
TOV γίνεται σχῆμα’ δέδεικται δ᾽ ἐν τῷ πρώτῳ ὅτι μὴ ἀναγ-
καίας οὔσης τῆς πρὸς τὸ μεῖζον στερητικῆς οὐδὲ τὸ συμπέρασμα
LÀ > ^ LÀ , *?Q»? 9?» * , LÀ > > , LJ »
ἔσται ἀναγκαῖον, ὥστ᾽ οὐδ᾽ ἐπὶ τούτων ἔσται ἐξ ἀνάγκης. ἔτι ὃ
εἰ τὸ συμπέρασμά ἐστιν ἀναγκαῖον, συμβαίνει τὸ Γ τινὶ τῷ 25
4 € , , > , » ^ ^ ~ M
A μὴ ὑπάρχειν ἐξ ἀνάγκης. εἰ yàp τὸ B τῷ Γ᾽ μηδενὶ
€ , > > , γῶν M ^ > M € 4 2
ὑπάρχει ἐξ ἀνάγκης, οὐδὲ τὸ Γ τῷ B οὐδενὶ ὑπάρξει ἐξ
3. e M » * ^ > ΄ € , LÀ M
ἀνάγκης. τὸ δέ ye B τινὶ τῷ A ἀνάγκη ὑπάρχειν, εἴπερ καὶ
M M ^ , > "4 L4 ^ σ ^ > ,
τὸ A παντὶ τῷ B ἐξ ἀνάγκης ὑπῆρχεν. ὥστε τὸ I ἀνάγκη
τινὶ τῷ A μὴ ὑπάρχειν. ἀλλ᾽ οὐδὲν κωλύει τὸ A τοιοῦτον λη- 30
239 δὲ d 40 δέ- ye A? mavri--ró a ACdr — bi ἐξ ἀνάγκης ὑπῆρχεν
413: ὑπῆρχεν ἐξ ἀνάγκης toad δὲ] γὰρ A? 14 κἂν εἰ Aldina τεθείη
AD P: τεθῇ codd. 16 τῷξ P : τῶν codd. 17 dpa-- 5e C 23
τῷ μείζονι C 27 μηδενὶ d 28 ye om. B 30 τινὶ
om. d!
4985 I
35
40
31»
1o
15
20
25
ANAAYTIKQN HPOTEPQN A
φθῆναι ᾧ παντὶ τὸ Γ ἐνδέχεται ὑπάρχειν. ἔτι κἂν ὅρους ἐκ-
θέμενον εἴη δεῖξαι ὅτι τὸ συμπέρασμα οὐκ ἔστιν ἀναγκαῖον
« ~ , A P4 ΕΔ » a w a ~
ἁπλῶς, ἀλλὰ τούτων ὄντων ἀναγκαῖον. olov ἔστω τὸ A ζῷον,
^ * Li A 4 , M Lj P a € ,
τὸ δὲ B ἄνθρωπος, τὸ δὲ Γ λευκόν, καὶ αἱ προτάσεις ὁμοίως
» ^ > , ^ ^ - ^ ~ . 4
εἰλήφθωσαν: ἐνδέχεται yap τὸ ζῷον μηδενὶ λευκῷ Ündpyew.
οὐχ ὑπάρξει δὴ οὐδ᾽ ὁ ἄνθρωπος οὐδενὶ λευκῷ, ἀλλ᾽ οὐκ ἐξ
ἀνάγκης" ἐνδέχεται γὰρ ἄνθρωπον γενέσθαι λευκόν, οὐ μέντοι
~ ‘. ~ ,
ἕως dv ζῷον μηδενὶ λευκῷ ὑπάρχῃ. ὥστε τούτων μὲν ὄν-
των ἀναγκαῖον ἔσται τὸ συμπέρασμα, ἁπλῶς δ᾽ οὐκ ἀναγ-
καῖον.
‘Opoiws δ᾽ ἔξει καὶ ἐπὶ τῶν ἐν μέρει συλλογισμῶν.
μὲ ^ ^ € k » la > M >
ὅταν μὲν yap ἡ στερητικὴ πρότασις καθόλου τ᾽ j Kal dvay-
nd ^ X , μὲ 5 ^ a ^ L4
καία, καὶ τὸ συμπέρασμα ἔσται ἀναγκαῖον: ὅταν δὲ ἡ kar-
ηγορικὴ καθόλου, ἡ δὲ στερητικὴ κατὰ μέρος, οὐκ ἔσται τὸ
συμπέρασμει ἀναγκαῖον. ἔστω δὴ πρῶτον ἡ στερητικὴ καθ-
L4 ^ , , A x ~ 4 A. » ,
ὅλου Te kai ἀναγκαία, kal τὸ A τῷ μὲν B μηδενὶ ἐνδεχέ-
L4 4 ~ ^ M [4 , , M T , ,
σθω ὑπάρχειν, τῷ δὲ Γ τινὲ ὑπαρχέτω. ἐπεὶ οὖν ἀντιστρέφει
M -* , A 3 ^ > * ? , » an € 4
τὸ στερητικόν, οὐδὲ τὸ B τῷ A οὐδενὶ ἐνδέχοιτ᾽ av ὑπάρχειν"
^ , ^ ~ L4 , wv > , » d A ~
τὸ δέ ye A τινὶ τῷ Γ ὑπάρχει, ὥστ᾽ ἐξ ἀνάγκης τινὶ τῷ D
a) e , a F4 » € * , Y
οὐχ ὑπάρξει τὸ B. πάλιν ἔστω ἡ κατηγορικὴ καθόλου τε kai
ἀναγκαία, καὶ κείσθω πρὸς 'τῷ DB τὸ κατηγορικόν. εἰ δὴ τὸ
A a ^ B ἐξ > , [4 7 - δὲ I * M [4 é =
παντὶ TQ B ἐξ ἀνάγκης ὑπάρχει, τῷ δὲ Γ τινὶ μὴ ὑπάρ
e€ , ^ ~ > >
χει, ὅτι μὲν ody ὑπάρξει τὸ B τινὶ τῷ I’, φανερόν, ἀλλ᾽ οὐκ
> > , € A , * σ LÀ ^ M > ,
ἐξ ἀνάγκης: οἱ yap αὐτοὶ ὅροι ἔσονται πρὸς τὴν ἀπόδειξιν
LJ ἣν. ἢ ^ , ~ > > ΟΣ » ^4
οἵπερ ἐπὶ τῶν καθόλου συλλογισμῶν. ἀλλ᾽ οὐδ᾽ εἰ TO στερητι-
κὸν ἀναγκαῖόν ἐστιν ἐν μέρει ληφθέν, οὐκ ἔσται τὸ συμπέρασμα
ἀναγκαῖον: διὰ γὰρ τῶν αὐτῶν ὅρων ἡ ἀπόδειξις.
» A m^ , , , ^ L4 ~
Ev δὲ τῷ τελευταίῳ σχήματι καθόλου μὲν ὄντων τῶν
ὅρων πρὸς τὸ μέσον καὶ κατηγορικῶν ἀμφοτέρων τῶν προ-
τάσεων, ἐὰν ὁποτερονοῦν ἦ ἀναγκαῖον, καὶ τὸ συμπέρασμα
ἔσται ἀναγκαῖον. ἐὰν δὲ τὸ μὲν jj στερητικὸν τὸ δὲ κατηγορι-
^ ^
κόν, ὅταν μὲν τὸ στερητικὸν ἀναγκαῖον 7, kai τὸ συμπέρα-
σμα ἔσται ἀναγκαῖον, ὅταν δὲ τὸ κατηγορικόν, οὐκ ἔσται ἀναγ-
καῖον. ἔστωσαν γὰρ ἀμφότεραι κατηγορικαὶ πρῶτον αἱ προ-
iT ~ 3
τάσεις, καὶ τὸ A καὶ τὸ B παντὶ τῷ Γ᾽ ὑπαρχέτω, ἀναγ-
bar τῷ γ΄.41814" 33 ἀναγκαίων B! 35 λευκῷ Cd Al* : λευκὸν AB
3132 τ᾿ om. B! οτῷ imDP:rày ABCd ὑπάρξει 4 τῷ PP: τῶν codd.
13 τινὲ om. I 17 ἀπόδειξις} ἑνὸς μόνον μεταλαμβανομένου Aly?
20 ὁποτεροσοῦν (-ἰ ἦ n?) ἀναγκαῖος n 21 κατηγορικὸν τὸ δὲ στερη-
Tcov ἩΓ
XX
IO. 30°31-11. 31°16
xaiov δ᾽ ἔστω τὸ À Γ. ἐπεὶ οὖν τὸ B παντὶ τῷ Γ ὑπάρχει,
^ A 4 ~ 5 4
καὶ "τὸ Γ τινὶ τῷ B ὑπάρξει διὰ τὸ ἀντιστρέφειν τὸ καθόλου
^ MJ , LÀ , b * ^ ^ > > , € ,
τῷ κατὰ μέρος, ὥστ᾽ εἰ παντὶ τῷ Γ τὸ A ἐξ ἀνάγκης ὑπάρ-
^ , ^ ^
χει καὶ τὸ D τῷ B τινί, kai τῷ B τινὶ ἀναγκαῖον ὑπάρχειν
^ M ^ [4 * 4 , , , a. ^ ^ ^
τὸ Á* τὸ yàp B ὑπὸ τὸ Γ ἐστίν. γίγνεται otv τὸ πρῶτον σχῆμα. 30
Lg J b , a » 4 > ^ > ^ >
ὁμοίως δὲ δειχθήσεται καὶ εἰ τὸ BI ἐστὶν ἀναγκαῖον" ἀντι-
A A ~ ^
στρέφει yap τὸ Γ τῷ A τινί, dor εἰ παντὶ τῷ Γ τὸ B ἐξ
a e , ^ ^ A ur , , 2 ,
ἀνάγκης ὑπάρχει, καὶ TH A τινὶ ὑπάρξει ἐξ ἀνάγκης. 33
4
Ilá- 33
L4 4 ki ^
Aw ἔστω τὸ μὲν A I στερητικόν, τὸ δὲ B I’ καταφατικόν,
> ^ ' A] , >» ^ s > , ‘ ^ M
ἀναγκαῖον δὲ τὸ στερητικόν. ἐπεὶ οὖν ἀντιστρέφει τινὶ τῷ Bro Γ, 35
τὸ δὲ Α οὐδενὶ τῷ Γ ἐξ ἀνάγκης, οὐδὲ τῷ Β τινὶ ὑπάρξει ἐξ ἀνάγ-
M A M € A] ^ > , > M ^ * 3
κης τὸ A: τὸ yàp B ὑπὸ τὸ Γ ἐστίν. εἰ δὲ τὸ κατηγορικὸν avay-
καῖον, οὐκ ἔσται τὸ συμπέρασμα ἀναγκαῖον. ἔστω γὰρ τὸ ΒΓ
κατηγορικὸν καὶ ἀναγκαῖον, τὸ δὲ A Γ στερητικὸν καὶ μὴ ἀναγ-
^ , * T 3 , A , L4 , * 4
καῖον. ἐπεὶ οὖν ἀντιστρέφει TO καταφατικόν, ὑπάρξει kal τὸ 4o
A ~ > 2 , e > » A * ^ ^ ^
I τινὶ τῷ B ἐξ ἀνάγκης, ὥστ᾽ εἰ τὸ μὲν A μηδενὶ τῷ Γ τὸ
.
δὲ Γ τινὶ τῷ B, τὸ A τινὶ τῷ B οὐχ ὑπάρξει: ἀλλ᾽ οὐκ ἐξ 31>
ἀνάγκης" δέδεικται γὰρ ἐν τῷ πρώτῳ σχήματι ὅτι τῆς στε-
ρητικῆς προτάσεως μὴ ἀναγκαίας οὔσης οὐδὲ τὸ συμπέρασμα
^ ^ wv
ἔσται ἀναγκαῖον. ἔτι Kav διὰ τῶν ὅρων εἴη φανερόν. ἔστω yàp
^ * > , X , NARI κα - * 4 LU *
τὸ μὲν A ἀγαθόν, τὸ δ᾽ ἐφ᾽ à B ζῷον, τὸ δὲ Γ ἵππος. τὸς
x ^ 3 θ A , ὃ H o mJ Li , a δὲ ^
μὲν οὖν ἀγαθὸν ἐνδέχεται μηδενὶ ἵππῳ ὑπάρχειν, τὸ δὲ ζῷον
, , ^ € 4 > 3 3 > ἣν af *
ἀνάγκη παντὶ ὑπάρχειν: ἀλλ᾽ οὐκ ἀνάγκη ζῷόν τι μὴ elvai
3 7: LJ > Li ^ > , "^ > A ^
ἀγαθόν, εἴπερ ἐνδέχεται πᾶν εἶναι ἀγαθόν. ἢ εἰ μὴ τοῦτο δυ-
, > a A , td bl ‘A LÀ L4 , ΄
νατόν, ἀλλὰ τὸ ἐγρηγορέναι ἢ τὸ καθεύδειν ὅρον θετέον: ἅπαν
γὰρ ζῷον δεκτικὸν τούτων. 10
> * T € Ld L4 M 4 , > , LÀ
Ei μὲν οὖν of ὅροι καθόλου πρὸς τὸ μέσον εἰσίν, εἴρηται
πότε ἔσται τὸ συμπέρασμα ἀναγκαῖον" εἰ δ᾽ 6 μὲν καθόλου
ὃ δ᾽ ἐν μέρει, κατηγορικῶν μὲν ὄντων ἀμφοτέρων, ὅταν τὸ
καθόλου γένηται ἀναγκαῖον, καὶ τὸ συμπέρασμα ἔσται ἀναγ-
a © >
καῖον. ἀπόδειξις δ᾽ ἡ αὐτὴ ἣ Kal πρότερον: ἀντιστρέφει yàp 15
, > M " ~
Kai TO ἐν μέρει κατηγορικόν. εἰ οὖν ἀνάγκη τὸ B παντὶ τῷ
226 ὑπάρχει om. nT 27 τῷ καθόλου τὸ Cn 29 xai? , . . 30 A]
ἀναγκαῖον καὶ τὸ a τινὶ τῷ D ὑπάρχειν nT 30 σχῆμα om. d 31
πάλιν ὁμοίως nt 32 τῷ] καὶ τῷ ACldn: καὶ τῷ B καὶ τῷ D 33 τὸ
Βι: τῶν Γ 46 οὐδὲ] dare οὐδὲ π 36-7 τὸ a ἐξ ἀνάγκης ἩΓ 38
οὐκ ἔστι d 41 τὸ om. d! τῷ ΒΓΑ͂ΙΡ: τῶν ACdn br τῷ bis
I'AIP : τῶν codd. 5 ἐφ᾽ dom. nl 6 ἵππῳ om. d' ὃ ἢ εἰ]
εἰ δὲ n 9 r9? nP*^: om. 4 BCd 11 οὗ om, A
ANAAYTIKQN IIPOTEPON A
Γ ὑπάρχειν, τὸ δὲ A ὑπὸ τὸ Γ ἐστίν, ἀνάγκη τὸ B τινὶ τῷ
A ὑπάρχειν. εἰ δὲ τὸ Β τῷ A τινί, καὶ τὸ A τῷ Β τινὶ
Ul rd > ^ > ¥ , ec , 4 b > A
ὑπάρχειν ἀναγκαῖον" ἀντιστρέφει γάρ. ὁμοίως δὲ kai εἰ τὸ A
r3 LÀ > ^ ’ wv ἈΝ. * L4 A A > Ld , \
20 I" εἴη ἀναγκαῖον καθόλου àv: τὸ yàp B ὑπὸ τὸ I ἐστίν. εἰ δὲ
τὸ ἐν μέρει ἐστὶν ἀναγκαῖον, οὐκ ἔσται τὸ συμπέρασμα ἀναγ-
- L4 ^ A J l4 M > ^ A 3
καῖον. ἔστω yap τὸ Β Γ ἐν μέρει te καὶ ἀναγκαῖον, τὸ δὲ A
παντὶ τῷ I ὑπαρχέτω, μὴ μέντοι ἐξ ἀνάγκης. ἀντιστρα-
φέντος οὖν τοῦ B I' τὸ πρῶτον γίγνεται σχῆμα, καὶ ἡ μὲν κα-
25 θόλου πρότασις οὐκ ἀναγκαία, ἡ δ᾽ ἐν μέρει ἀναγκαία. ὅτε
δ᾽ οὕτως ἔχοιεν αἱ προτάσεις, οὐκ ἦν τὸ συμπέρασμα ἀναγ-
^ L4 > 70» ? x 4 Ww 4 ^ > ~ LÀ ra
kaiov, ὥστ᾽ οὐδ᾽ ἐπὶ τούτων. ἔτι δὲ Kal ἐκ τῶν ὅρων φανερόν.
ἔστω γὰρ τὸ μὲν A ἐγρήγορσις, τὸ δὲ B δίπουν, ἐφ᾽ ᾧ δὲ τὸ I
^ a a 5 * ^ 3 7 c+ E] H ^
ζῷον. τὸ μὲν οὖν B τινὶ τῷ I ἀνάγκη ὑπάρχειν, τὸ δὲ A τῷ
3 » 4 x ~ > > ~ , M > ,
3o Γ ἐνδέχεται, καὶ τὸ A τῷ B οὐκ ἀναγκαῖον: οὐ yàp ἀνάγκη
δίπουν τι καθεύδειν 7 ἐγρηγορέναι. ὁμοίως δὲ καὶ διὰ τῶν
ΕΣ ^ L4 ta ^ » εἶ μ᾿ 3 , *
αὐτῶν ὅρων δειχθήσεται καὶ εἰ τὸ A Γ εἴη ἐν μέρει τε καὶ
33 ἀναγκαῖον.
> > Lj A a € Y * ~ Ld
33 Et δ᾽ ὁ μὲν κατηγορικὸς ὁ δὲ στερητικὸς τῶν ὅρων,
ὅταν μὲν fj τὸ καθόλου στερητικόν τε καὶ ἀναγκαῖον, καὶ τὸ
35 συμπέρασμα ἔσται ἀναγκαῖον: εἰ γὰρ τὸ A τῷ Γ᾽ μηδενὶ ἐν-
Z M b ᾿ ~ e , A a ^ 3 ,ὔ
δέχεται, τὸ δὲ B τινὶ τῷ Γ ὑπάρχει, τὸ A τινὶ τῷ B ἀνάγκη
μὴ ὑπάρχειν. ὅταν δὲ τὸ καταφατικὸν ἀναγκαῖον τεθῇ, ἢ
καθόλου ὃν ἢ ἐν μέρει, ἢ τὸ στερητικὸν κατὰ μέρος, οὐκ ἔσται
τὸ συμπέρασμα ἀναγκαῖον. τὰ μὲν γὰρ ἄλλα ταὐτὰ ἃ καὶ
4o ἐπὶ τῶν πρότερον ἐροῦμεν, ὅροι δ᾽ ὅταν μὲν 7j καθόλου τὸ κα-
τηγορικὸν ἀναγκαῖον, ἐγρήγορσις--ζῷον--ἄνθρωπος, μέσον dv-
323 θρωπος, ὅταν δ᾽ ἐν μέρει τὸ κατηγορικὸν ἀναγκαῖον, ἐγρήγορ-
σις--ζῷον-λευκόν: ζῷον μὲν γὰρ ἀνάγκη τινὲ λευκῷ ὑπάρ-
^ > , ^4
xew, ἐγρήγορσις δ᾽ ἐνδέχεται μηδενί, καὶ οὐκ ἀνάγκη τινὶ
ζῴῳ μὴ ὑπάρχειν ἐγρήγορσιν. ὅταν δὲ τὸ στερητικὸν ἐν μέ-
5 pet ὃν ἀναγκαῖον 7, δίπουν--κινούμενον--ζῷον, μέσον ζῷον.
Φανερὸν οὖν ὅτι τοῦ μὲν ὑπάρχειν οὐκ ἔστι συλλογισμός,
ἐὰν μὴ ἀμφότεραι ὦσιν αἱ προτάσεις ἐν τῷ ὑπάρχειν, τοῦ
LI > ^ >
δ᾽ ἀναγκαίου ἔστι kal τῆς ἑτέρας μόνον ἀναγκαίας οὔσης. ἐν
big xai εἰ AC Al: εἰ καὶ Bdn 29 a-r παντὶ di 31 τι μὴ ni Alc
ἢ ἐγρηγορέναι om. n 36B...D]y...Bnir 39 dom. ἡ
40 προτέρων Cdn: ἑτέρων d? καθόλου τὸ nI' : τὸ καθόλου A BCd 41
néaov 4-86 C 3245 ὃν om. d μέσον ζῷον CL: ζῷον μέσον ΒΖ, coni.
Al: δίπουν μέσον AdnAl et ut vid. B: δίπουν μέσον ζῷον d?: μέσον δίπαυν
Pye
12
II. 31*17-13. 323
» , , * ~ 4 ~ w ~
ἀμφοτέροις δέ, καὶ καταφατικῶν καὶ στερητικῶν ὄντων τῶν
^ 5 * ^
συλλογισμῶν, ἀνάγκη τὴν ἑτέραν πρότασιν ὁμοίαν εἶναι τῷ 10
»
συμπεράσματι. λέγω δὲ τὸ ὁμοίαν, εἰ μὲν ὑπάρχον, ὑπάρ-᾿
3 5 3 ^ -^ ^
xovcav, εἰ δ᾽ ἀναγκαῖον, ἀναγκαίαν. ὥστε kai τοῦτο δῆλον,
> ^
ὅτι οὐκ ἔσται τὸ συμπέρασμα οὔτ᾽ ἀναγκαῖον οὔθ᾽ ὑπάρχον εἶναι
,
μὴ ληφθείσης ἀναγκαίας ἢ ὑπαρχούσης προτάσεως.
T7 ^ 3 ~
Περὶ μὲν οὖν τοῦ ἀναγκαίου, πῶς γίγνεται καὶ τίνα διαφο- 15
^ LÀ * 5 © 4 LÀ ^ [3 ^ M *.
13 pàv ἔχει πρὸς τὸ ὑπάρχον, εἴρηται σχεδὸν ἱκανῶς- περὶ δὲ
^ *, , A ~ , ~
τοῦ ἐνδεχομένου peta ταῦτα λέγωμεν πότε kal πῶς koi διὰ
, L4 , 4 > > 4 M 4 » ,
τίνων ἔσται συλλογισμός. λέγω δ᾽ ἐνδέχεσθαι Kai τὸ ἐνδεχό-
A > ,
μενον, o μὴ ὄντος ἀναγκαίου, τεθέντος δ᾽ ὑπάρχειν, οὐδὲν ἔσται
διὰ τοῦτ᾽ ἀδύνατον: τὸ γὰρ ἀναγκαῖον ὁμωνύμως ἐνδέχεσθαι 20
^5 ^
λέγομεν. [ὅτι δὲ τοῦτ᾽ ἔστι τὸ ἐνδεχόμενον, φανερὸν ἔκ τε τῶν
ἀποφάσεων καὶ τῶν καταφάσεων τῶν ἀντικειμένων: τὸ γὰρ
οὐκ ἐνδέχεται ὑπάρχειν καὶ ἀδύνατον ὑπάρχειν καὶ ἀνάγκη
* £ = Μ 5 , > hd > ~ > , "
μὴ ὑπάρχειν ἤτοι ταὐτά ἐστιν ἢ ἀκολουθεῖ ἀλλήλοις, ὥστε
καὶ τὰ ἀντικείμενα, τὸ ἐνδέχεται ὑπάρχειν καὶ οὐκ 25
>
ἀδύνατον ὑπάρχειν καὶ οὐκ ἀνάγκη μὴ ὑπάρχειν, ἤτοι
» hk: » μι > ~ , L4 A M * €
ταὐτὰ ἔσται ἢ ἀκολουθοῦντα ἀλλήλοις: κατὰ παντὸς yàp ἡ
φάσις ἢ ἡ ἀπόφασις. ἔσται ἄρα τὸ ἐνδεχόμενον οὐκ
^ à * - >
ἀναγκαῖον καὶ TO μὴ ἀναγκαῖον ἐνδεχόμενον.) cvpflaive
δὲ πάσας τὰς κατὰ τὸ ἐνδέχεσθαι προτάσεις ἀντιστρέφειν 30
Ἂν , a i > M A ^ + ^
ἀλλήλαις. λέγω δὲ οὐ tas καταφατικὰς ταῖς ἀποφατικαῖς,
᾿ ^
ἀλλ᾽ ὅσαι καταφατικὸν ἔχουσι τὸ σχῆμα κατὰ THY ἀντίθεσιν,
τ * > P4 € 4, ^ » ΕΣ x L4 , 4
olov τὸ ἐνδέχεσθαι ὑπάρχειν τῷ ἐνδέχεσθαι μὴ ὑπάρχειν, καὶ
τὸ παντὶ ἐνδέχεσθ Ὁ ἐνδέχεσθ. δενὶ καὶ μὴ i, καὶ
χεσθαι τῷ ἐνδέχεσθαι μηδενὶ καὶ μὴ παντί, καὶ
M τ ^ A , 4 > * M , M H M ^ LA
TO τινὶ τῷ μὴ τινί. τὸν αὐτὸν δὲ τρόπον kai ἐπὶ τῶν ἄλλων. 35
ἐπεὶ γὰρ τὸ ἐνδεχόμενον οὐκ ἔστιν ἀναγκαῖον, τὸ δὲ μὴ ἀναγ-
^ ^ * >
Katov ἐγχωρεῖ μὴ ὑπάρχειν, φανερὸν ὅτι, εἰ ἐνδέχεται τὸ
- > M
A τῷ B ὑπάρχειν, ἐνδέχεται καὶ μὴ ὑπάρχειν: koi εἰ
παντὶ ἐνδέχεται ὑπάρχειν, καὶ παντὶ ἐνδέχεται μὴ ὑπάρ-
* * > * ^ » * , e ^ "ἢ
χειν. ὁμοίως δὲ κἀπὶ τῶν ἐν μέρει καταφάσεων: ἡ γὰρ αὐτὴ 4o
M > € ^ , M
ἀπόδειξις. εἰσὶ δ᾽ αἱ τοιαῦται προτάσεις κατηγορικαὶ καὶ 32>
~ 4“ « *
οὐ στερητικαί: TO yap ἐνδέχεσθαι τῷ εἶναι ὁμοίως τάττεται,
,
καθάπερ ἐλέχθη πρότερον.
217 λέγομεν Ad 20 ἀναγκαῖον -Ἰ- ὃν i 21-9 ὅτι... ἐνδεχόμενον codd.
I'AUP : secl. Becker 22 καὶ τῶν καταφάσεων om. n 23-4 kai? . ..
ὑπάρχειν om. nil 25 ἀντικείμενα Γ΄: -ἰ τούτοις A BCd 25 et 26 καὶ Ἐ τὸ C
20 ἤτοι) 5 4 277]2 πτὴ ἡ AP 28 κατάφασις (ἃ ἀπόφασις Ἐ ἐστιν 4:
T ἔσται DP τῷ] τὸ Αὶ 34 καὶ -- τῷ n 4o δὲ om. BC
33 74
ANAAYTIKON IIPOTEPQN A
, A ’ ‘3 , e A 2 P)
Διωρισμένων δὲ τούτων πάλιν λέγωμεν ὅτι τὸ ἐνδέχε-
A , , , v * x € 9.5. *
saÜav. κατὰ δύο λέγεται τρόπους, ἕνα μὲν TO ὡς ἐπὶ TO
A , * , A > ^ x ^
πολὺ γίνεσθαι καὶ διαλείπειν τὸ ἀναγκαῖον, οἷον τὸ πολιοῦ-
σθαι ἄνθρωπον ἢ τὸ αὐξάνεσθαι ἢ φθίνειν, 7 ὅλως τὸ πεφυ-
κὸς ὑπάρχειν (τοῦτο γὰρ οὐ συνεχὲς μὲν ἔχει τὸ ἀναγκαῖον
M A x * X 4 L4 » ^ > , -^ >
διὰ τὸ μὴ dei εἶναι ἄνθρωπον, ὄντος μέντοι ἀνθρώπου ἢ ἐξ
> , * t $2. ^ x9K * LÀ x * 3 ἢ ^ M
ro ἀνάγκης ἢ ὡς ἐπὶ τὸ πολύ ἐστιν), ἄλλον δὲ τὸ ἀόριστον, ὃ Kal
“ ‘ x e ΄ f * , ^ ^
οὕτως καὶ μὴ οὕτως δυνατόν, olov τὸ βαδίζειν ζῷον 1
, , , ^ μὲ x > ‘ , »
βαδίζοντος γενέσθαι σεισμόν, ἢ ὅλως τὸ ἀπὸ τύχης ywó-
γῶν A ^ L4 , ^ > , 3 L4
μενον" οὐδὲν yàp μᾶλλον οὕτως πέφυκεν 7) ἐναντίως. ἀντιστρέ-
X ^ >
φει μὲν οὖν’ [καὶ] κατὰ Tas ἀντικειμένας προτάσεις ἑκάτερον
Lal » L4 + M x > J- , > A x '
15 τῶν ἐνδεχομένων, od μὴν τὸν αὐτόν ye τρόπον, ἀλλὰ τὸ μὲν
4 ~ * , > , t TA Ὁ εὖ > ,
πεφυκὸς εἶναι τῷ μὴ ἐξ ἀνάγκης ὑπάρχειν (οὕτω yap ἐνδέ-
εἶ ~ »» * ? 5» ~ ^ ~
χεται μὴ πολισῦσθαι dvOpwrov), τὸ δ᾽ ἀόριστον τῷ μηδὲν μᾶλ-
λον οὕτως ἢ ἐκείνως. ἐπιστήμη δὲ καὶ συλλογισμὸς ἀποδεικτι-
κὸς τῶν μὲν ἀορίστων οὐκ ἔστι διὰ τὸ ἄτακτον εἶναι τὸ μέσον,
~ A , », * a Lj , * € ,
20 τῶν δὲ πεφυκότων ἔστι, καὶ σχεδὸν οἱ λόγοι καὶ αἱ σκέψεις
5 E B ^
γίνονται περὶ τῶν οὕτως ἐνδεχομένων- ἐκείνων δ᾽ ἐγχωρεῖ μὲν
, , * * » L4 ~
γενέσθαι συλλογισμόν, od μὴν εἴωθέ ye ζητεῖσθαι.
Ταῦτα μὲν οὖν διορισθήσεται μᾶλλον ἐν τοῖς ἑπομένοις-"
νῦν δὲ λέγωμεν πότε καὶ πῶς καὶ τίς ἔσται συλλογισμὸς ἐκ τῶν
, Ld ἂν Σ ^ * X. 3 Li , ~
25 ἐνδεχομένων προτάσεων. ἐπεὶ δὲ τὸ ἐνδέχεσθαι τόδε τῷδε
Ψ' , ^ LÀ * ^ nn P1 T € , , Lol T
ὑπάρχειν διχῶς ἔστιν ékAaDeiv- ἢ yàp ᾧ ὑπάρχει τόδε ἢ ᾧ
3 , $ t € , x 5 > φ a A H
ἐνδέχεται αὐτὸ ὑπάρχειν--τὸ yap, καθ᾽ οὗ τὸ B, τὸ A év-
, , , 5 ^ , T7 , ‘
δέχεσθαι τούτων σημαίνει θάτερον, ἢ καθ᾽ οὗ λέγεται τὸ B
ἢ καθ᾽ οὗ ἐνδέχεται λέγεσθαι: τὸ δέ, καθ᾽ οὗ τὸ B, τὸ A
3o ἐνδέχεσθαι ἢ παντὶ τῷ B τὸ A ἐγχωρεῖν οὐδὲν διαφέρει--
4 Ld ^ hd , * ~ 4 > ,
φανερὸν ὅτι διχῶς ἂν λέγοιτο τὸ A τῷ B παντὶ ἐνδέχεσθαι
eo: ἣν > , > T H Η͂ , ,
ὑπάρχειν. πρῶτον οὖν εἴπωμεν, εἰ καθ᾽ οὗ τὸ I τὸ B ἐνδέ-
A > ἊΝ ‘ x , L4 ‘ ^
χεται, καὶ καθ᾽ οὗ τὸ B τὸ A, τίς ἔσται Kai motos συλλο-
ywpós: οὕτω γὰρ at προτάσεις ἀμφότεραι λαμβάνονται
ἣν 4 3 , LÀ A > - ^ e€ , i
35 κατὰ τὸ ἐνδέχεοθαι, ὅταν δὲ καθ᾽ ob τὸ B ὑπάρχει τὸ A
2 , e ‘ e 5, τ >? , , LA 2 > LÀ
ἐνδέχηται, ἡ μὲν ὑπάρχουσα ἡ δ᾽ ἐνδεχομένη. ὥστ᾽ ἀπὸ
^ > , , ^
τῶν ὁμοιοσχημόνων ἀρκτέον, καθάπερ Kai ἐν rots ἄλλοις.
b4-22 Διωρισμένων... ζητεῖσθαι codd, FAlP : susp. Becker 4 λέγομεν
A B3Cd 5TH ὡς ἢ 7 αὔξεσθαι n 9 elvac4- τὸν C Io ἄλλο
A 11 #+70 484 I4 xai codd. Al: om. Pacius et ut vid. P
‘ar ἐκείνως Bd? 23 obvom. C 24 λέγωμεν BdnT': λέγομεν AC kai
πῶς BI':0om. ACda 25-32 ἐπεὶ... ὑπάρχειν codd. AIP : secl. Becker
38 τῷ Br? 34-7 οὕτω . . . ἄλλοις codd. IP : secl. Becker 35
ὑπάρχῃ B 37 ὁμοιοσχήμων Al xai om. «D
b a
I3. 324-14. 33°30
Ὅταν οὖν τὸ A παντὶ τῷ B ἐνδέχηται kai τὸ B παντὶ
TQ D, συλλογισμὸς ἔσται τέλειος ὅτι τὸ A παντὶ τῷ Γ᾽ ἐν-
δέχεται ὑπάρχειν. τοῦτο δὲ φανερὸν ἐκ τοῦ ὁρισμοῦ" τὸ γὰρ 40
1 , ‘ L4 4 " 3 , « , ‘A " a
ἐνδέχεσθαι παντὶ ὑπάρχειν οὕτως ἐλέγομεν. ὁμοίως δὲ xai 33
εἰ τὸ μὲν A ἐνδέχεται μηδενὶ τῷ B, τὸ δὲ B παντὶ τῷ T,
ὅτι τὸ A ἐνδέχεται μηδενὶ τῷ I^ τὸ γὰρ καθ᾽ οὗ τὸ B ἐνδέ-
^ * » , ^95 ^ * 3 ,
χεται, τὸ Α μὴ ἐνδέχεσθαι, τοῦτ᾽ ἦν τὸ μηδὲν ἀπολείπειν
τῶν ὑπὸ τὸ B ἐνδεχομένων. ὅταν δὲ τὸ A παντὶ τῷ B ἐν- 5
δέχηται, τὸ δὲ B ἐνδέχηται μηδενὶ τῷ I, διὰ μὲν τῶν εἰ-
λημμένων προτάσεων οὐδεὶς γίνεται συλλογισμός, ἀντιστρα-
, * ^ ^4 ^ > ,^ LA € * s.
φείσης δὲ τῆς BI κατὰ τὸ ἐνδέχεσθαι γίνεται ὁ αὐτὸς
σ , , ‘ ^ > , ^ M ^ [4 4
ὅσπερ πρότερον. ἐπεὶ yap ἐνδέχεται τὸ Β μηδενὶ τῷ Γ᾽ ὑπάρ-
χειν, ἐνδέχεται καὶ παντὶ ὑπάρχειν: τοῦτο δ᾽ εἴρηται πρότε- το
ρον. ὥστ᾽ εἰ τὸ μὲν B παντὶ τῷ I, τὸ δ᾽ A παντὶ τῷ B,
, e , ‘ 4 ,^ L4 , b ‘ i *
πάλιν ὁ αὐτὸς γίνεται συλλογισμός. ὁμοίως δὲ kai εἰ πρὸς
3 , ^ Ld € > , 4, ^ ~ H ,
ἀμφοτέρας τὰς προτάσεις ἡ ἀπόφασις τεθείη μετὰ τοῦ ἐνδέ-
χεσθαι. λέγω δ᾽ οἷον εἰ τὸ A ἐνδέχεται μηδενὶ τῷ B καὶ
^ M ^ ^ * Ἂς ~ , , ,
τὸ B μηδενὶ τῷ I^ διὰ μὲν yàp τῶν εἰλημμένων προτάσεων 15
ΕἸ M , , > , * , © ,
οὐδεὶς γίνεται συλλογισμός, ἀντιστρεφομένων δὲ πάλιν 6 ad-
τὸς ἔσται ὅσπερ καὶ πρότερον. φανερὸν οὖν ὅτι τῆς ἀποφάσεως
, Ἂς x » Ld hal * > , M
τιθεμένης πρὸς τὸ ἔλαττον ἄκρον ἢ πρὸς ἀμφοτέρας τὰς
a ^ , , M a , a > 3
προτάσεις ἢ οὐ γίνεται συλλογισμὸς ἢ yiverar μὲν ἀλλ
οὐ τέλειος: ἐκ γὰρ τῆς ἀντιστροφῆς περαίνεται τὸ ἀναγκαῖον. 20
> ^ > € 4 , - La v > » , ~
Ἐὰν δ᾽ ἡ μὲν καθόλου τῶν προτάσεων ἡ δ᾽ ἐν μέρει ληφθῇ,
πρὸς μὲν τὸ μεῖζον ἄκρον κειμένης τῆς καθόλου συλλογισμὸς
ἔσται [τέλειος]. εἰ γὰρ τὸ Α παντὶ τῷ Β ἐνδέχεται, τὸ δὲ Β
τινὶ τῷ Γ, τὸ Α τινὶ τῷ Γ ἐνδέχεται. τοῦτο δὲ φανερὸν ἐκ τοῦ
ὁρισμοῦ τοῦ ἐνδέχεσθαι. πάλιν εἰ τὸ A ἐνδέχεται μηδενὶ τῷ B, 25
^ Ri * ^ > , L4 ,ὔ , , H > ,
τὸ δὲ B τινὶ τῷ I ἐνδέχεται ὑπάρχειν, ἀνάγκη τὸ A ἐνδέχε-
, - ad e , » ta > L4 *, , LA] b
obai τινι τῶν Γ μὴ ὑπάρχειν. ἀπόδειξις δ᾽ ἡ αὐτή. ἐὰν δὲ στε-
4 ~ [4 » , , t b à ,
ρητικὴ ληφθῇ ἡ ἐν μέρει πρότασις, ἡ δὲ καθόλου καταφατική,
~ x , e , » 4 b M ^ ? ,
τῇ δὲ θέσει ὁμοίως ἔχωσιν (olov τὸ μὲν A παντὶ τῷ B evde-
‘ ‘A ‘ ^ I > ! A ᾿ , MJ *
χεται, τὸ δὲ B τινὶ τῷ I ἐνδέχεται μὴ ὑπάρχειν), διὰ μὲν 30
3341 λέγομεν n Alc 4 μὴ om. nT' et ut vid. Al 9 ὦσπερ Adn:
ὅσπερ xai C : ὥσπερ xai C? ἐπεὶ... 10 πρότερον om. πὸ 11 ἐπεὶ Β
14 εἴ 15 τῷ DP: τῶν codd. 17 ὅσπερ ΒΓ: ὥσπερπ: ὡς ACd xai om.
B 20 mepaiverat A?nT : γίνεται A BCd 23 τέλειος susp, Becker,
om. ut vid. AIP 25 ἐνδέχεσθαι dT Al: ἐνδέχεσθαι a. B. y. ABCn?:
ἐνδέχεσθαι B. n : ἐνδέχεσθαι παντί B* : κατὰ παντὸς ἐνδέχεσθαι (343 26 τῷ
Crt: τῶν ABd 29 ἔχουσιν γι ofov]+et coni. Waitz ἐνδέχηται
Waitz 30 ἐνδέχηται n
ANAAYTIKQN IIPOTEPON A
~ i] , , *, , * 5,
τῶν εἰλημμένων προτάσεων οὐ γίνεται φανερὸς συλλογισμός,
ἀντιστραφείσης δὲ τῆς ἐν μέρει καὶ τεθέντος τοῦ Β τινὶ τῷ Γ
ἐνδέχεσθαι ὑπάρχειν τὸ αὐτὸ ἔσται συμπέρασμα ὃ καὶ πρό-
34 τερον, καθάπερ ἐν τοῖς ἐξ ἀρχῆς.
> M , t * X ^
34 Ἐὰν δ᾽ ἡ πρὸς τὸ μεῖζον
35 ἄκρον ἐν μέρει ληφθῇ, ἡ δὲ πρὸς τὸ ἔλαττον καθόλου, ἐάν
» 2 , A ^ LA 3 27
T ἀμφότεραι καταφατικαὶ τεθῶσιν ἐάν re στερητικαὶ ἐάν τε
M = , LR » > té > , - ^ ,
μὴ ὁμοιοσχήμονες, ἐάν τ’ ἀμφότεραι ἀδιόριστοι 7) κατὰ ué-
, ~ Li , Uu x ^ , ‘
pos, οὐδαμῶς ἔσται ovdAoyiopds: οὐδὲν yap κωλύει τὸ B
€ L4 ^ * X; ^ > > © 7 * x
Urepreivew τοῦ A καὶ μὴ κατηγορεῖσθαι ἐπ᾽ ἴσων: ᾧ δ᾽ ὑπερ-
A ~ , ^ Y M L4
4o τείνει TO B τοῦ A, εἰλήφθω τὸ I> τούτῳ yàp οὔτε παντὶ
b LÀ M Ww M » L4 » 4, * * , ΝΜ
33° οὔτε μηδενὶ οὔτε τινὶ οὔτε μή τινι ἐνδέχεται τὸ A ὑπάρχειν, εἴ-
περ ἀντιστρέφουσιν αἱ κατὰ τὸ ἐνδέχεσθαι προτάσεις καὶ τὸ
x , ~
B πλείοσιν ἐνδέχεται 7j τὸ A ὑπάρχειν. ἔτι δὲ Kal ἐκ τῶν
ὅρων φανερόν: οὕτω γὰρ ἐχουσῶν τῶν προτάσεων τὸ πρῶτον
5T ἐσχάτῳ καὶ οὐδενὶ ἐνδέχεται καὶ παντὶ ὑπάρχειν ἀναγ-
Katov. ὅροι δὲ κοινοὶ πάντων τοῦ μὲν ὑπάρχειν ἐξ ἀνάγκης
^ Ls L4 ^ * x , , ^ td
ζῷον-λευκόν-ἄνθρωπος, τοῦ δὲ μὴ ἐνδέχεσθαι ζῷον-λευκόν--
ἱμάτιον. φανερὸν οὖν τοῦτον τὸν τρόπον ἐχόντων τῶν ὅρων ὅτι
οὐδεὶς γίνεται συλλογισμός. ἣ γὰρ τοῦ ὑπάρχειν ἢ τοῦ ἐξ
~ ~ M ^
10 ἀνάγκης ἢ τοῦ ἐνδέχεσθαι πᾶς ἐστὶ συλλογισμός. τοῦ μὲν
οὖν ὑπάρχειν καὶ τοῦ ἀναγκαίου φανερὸν ὅτι οὐκ ἔστιν" ὁ μὲν
γὰρ καταφατικὸς ἀναιρεῖται τῷ στερητικῷ, ὁ δὲ στερητικὸς
~ ^ ^ > ~
τῷ καταφατικῷ. λείπεται δὴ τοῦ ἐνδέχεσθαι εἶναι: τοῦτο δ᾽
~ ‘
ἀδύνατον: δέδειιςται yap ὅτι οὕτως ἐχόντων τῶν ὅρων καὶ
i5 παντὶ τῷ ἐσχάτῳ τὸ πρῶτον ἀνάγκη καὶ οὐδενὶ ἐνδέχεται
coy LOB ᾽ > " ^ or ‘ i
ὑπάρχειν. ὥστ᾽ οὐκ av etn τοῦ ἐνδέχεσθαι συλλογισμός. τὸ
γὰρ ἀναγκαῖον οὐκ ἦν ἐνδεχόμενον.
4 3 LÀ ta a « a ? ^ 3
Φανερὸν δὲ ὅτι καθόλου τῶν ὅρων ὄντων ἐν tats ἐνδε-
χομέναις προτάσεσιν ἀεὶ γίνεται συλλογισμὸς ἐν τῷ πρώ-
20 TQ σχήματι, καὶ κατηγορικῶν καὶ στερητικῶν ὄντων,
^ ^ $ ^
πλὴν κατηγορικῶν μὲν τέλειος, στερητικῶν δὲ ἀτελής. δεῖ
* M > , Li ^ > ^ > , ?
δὲ τὸ ἐνδέχεσθαι λαμβάνειν μὴ ἐν τοῖς ἀναγκαίοις, dA-
M ^ * > A , > ἢ ^ , M
Aad κατὰ τὸν εἰρημένον διορισμόν. ἐνίοτε δὲ λανθάνει τὸ
τοιοῦτον.
25 Ἐὰν δ᾽ ἡ μὲν ὑπάρχειν ἡ δ᾽ ἐνδέχεσθαι λαμβάνηται
^ ^ *
τῶν προτάσεων, ὅταν μὲν ἡ πρὸς TO μεῖζον ἄκρον ἐνδέχεσθαι
347 ὁμοιοσχήμονες CAP: ὁμοσχήμονες ABn 39 τοῦ C?P : τὸ ABCdn
40 τοῦ] 76% br4 τῶν ὅρων om. d! 18 ὄντων τῶν ópo di 21 uév4-
ὄντων nt” 22 μὴ- τὸ d
IS
‘
a a
I4. 33°31-15. 34°19
, L4 , > » , Lj M * ~
σημαίνῃ, τέλειοί τ᾽ ἔσονται πάντες οἱ συλλογισμοὶ Kal τοῦ
ἐνδέχεσθαι κατὰ τὸν εἰρημένον διορισμόν, ὅταν δ᾽ ἡ πρὸς τὸ
ἔλαττον, ἀτελεῖς τε πάντες, καὶ οἱ στερητικοὶ τῶν συλλογι-
ouv οὐ τοῦ κατὰ τὸν διορισμὸν ἐνδεχομένου, ἀλλὰ τοῦ μηδενὶ 30
ἢ μὴ παντὶ ἐξ ἀνάγκης ὑπάρχειν: εἰ γὰρ μηδενὶ ἢ μὴ
^ * > , + , , A 54 * xv
παντὶ ἐξ ἀνάγκης, ἐνδέχεσθαί φαμεν καὶ μηδενὶ καὶ μὴ
^ ς ’ * , * Ly lj ^ x M
παντὶ ὑπάρχειν. ἐνδεχέσθω yàp τὸ A παντὶ τῷ B, τὸ δὲ
a ^ , € P > 5 T € M M > ^ A
B παντὶ τῷ Γ κείσθω ὑπάρχειν. ἐπεὶ οὖν ὑπὸ τὸ B ἐστὶ τὸ
I, τῷ δὲ B παντὶ ἐνδέχεται τὸ A, φανερὸν ὅτι καὶ τῷ I 15
A ᾽ , , ^ Là , [4 , X
παντὶ ἐνδέχεται. γίνεται δὴ τέλειος συλλογισμός: ὁμοίως δὲ
καὶ στερητικῆς οὔσης τῆς A B προτάσεως, τῆς δὲ BI kara-
φατικῆς, καὶ τῆς μὲν ἐνδέχεσθαι τῆς δ᾽ ὑπάρχειν λαμβα-
, la LÀ x Ld x > ,ὔ a ~
νομένης, τέλειος ἔσται συλλογισμὸς ὅτι τὸ A ἐνδέχεται μηδενὶ τῷ
I' ὑπάρχειν. 40
LÀ 1 LS ^ € 7; 8 n 1 . 0» y a
Ort μὲν οὖν τοῦ ὑπάρχειν τιθεμένου πρὸς τὸ ἔλαττον ἄκρον 34
L4 , , , Ld » » 2 LÀ
τέλειοι γίγνονται συλλογισμοί, φανερόν: ὅτι δ᾽ ἐναντίως éxov-
Tos ἔσονται συλλογισμοί, διὰ τοῦ ἀδυνάτου δεικτέον. ἅμα
δ᾽ ἔσται δῆλον καὶ ὅτι ἀτελεῖς: ἡ γὰρ δεῖξις οὐκ ἐκ τῶν εἰ-
λημμένων προτάσεων. πρῶτον δὲ λεκτέον ὅτι εἰ τοῦ A ὄντος 5
ἀνάγκη τὸ Β εἶναι, καὶ δυνατοῦ ὄντος τοῦ A δυνατὸν ἔσται
4 X n > 4 »* * e , , 8 x Ὁ M
xai τὸ B ἐξ ἀνάγκης. ἔστω yàp οὕτως ἐχόντων τὸ μὲν ἐφ᾽ ᾧ τὸ
A δυνατόν, τὸ δ᾽ ἐφ᾽ à τὸ B ἀδύνατον. εἰ οὖν τὸ μὲν δυνα-
, Ὁ 4 , >? ww x 3 > £, eo > > va
τόν, ὅτε δυνατὸν εἶναι, γένοιτ᾽ dv, τὸ δ᾽ ἀδύνατον, ὅτ᾽ ἀδύ-
> bj , Ld > LÀ a 4 M X.
varov, οὐκ ἂν γένοιτο, ἅμα δ᾽ εἴη τὸ A δυνατὸν καὶ τὸ Bio
> 4, , , >? bal * , » LJ > & ,
ἀδύνατον, ἐνδέχοιτ᾽ ἂν τὸ A γενέσθαι ἄνευ τοῦ B, εἰ δὲ yevé-
σθαι, καὶ εἶναι: τὸ γὰρ γεγονός, ὅτε γέγονεν, ἔστιν. δεῖ δὲ
λαμβάνειν μὴ μόνον ἐν τῇ γενέσει τὸ ἀδύνατον καὶ δυνατόν,
» M 4 3 ^ > L4 4 , -^ € , L| [4
ἀλλὰ Kal ἐν τῷ ἀληθεύεσθαι καὶ ἐν τῷ ὑπάρχειν, καὶ óca-
~ LÀ , * , kJ L4 ^ e , LÀ
χῶς ἄλλως λέγεται τὸ δυνατόν: ἐν ἅπασι yàp ὁμοίως ἕξει. 15
LÀ à 0x ^ s.l ΕΣ [4 € , w ^ ^
ἔτι τὸ ὄντος τοῦ A τὸ B εἶναι, οὐχ ὡς ἑνός τινος ὄντος τοῦ A τὸ
v ^ € LE J * L4 > M > , fa « ,
B ἔσται δεῖ ὑπολαβεῖν: οὐ yàp ἔστιν οὐδὲν ἐξ ἀνάγκης ἑνός
ν ? * ^ εἶ , LÀ Li ,
twos ὄντος, ἀλλὰ δυοῖν éAaxíarow, olov ὅταν ai προτάσεις
5Ὰ 2
οὕτως ἔχωσιν ὡς ἐλέχθη κατὰ τὸν συλλογισμόν. εἰ γὰρ τὸ
b27 συμβαίνῃ ni 29 re om. C xal... συλλογισμῶν et 31-2 μηδενὶ
... παντὶ codd. I AIP : of συλλογισμοὶ xal et μὴ coni. Becker 34 παντὶ
om. n 36 δὲ) δὴ π 38 λαμβανομένης 42 ΒάξηΓ: λαμβανούσης
ACd 39 ἔσται BdnT': om. AC 3431 τοῦ om. n! ἄκρον on, »
2 ἔχοντες A} 4 ὅτι καὶ d: ὅτι Ct 7 καὶ dnI' : om. ABC éxóv-
των- τῶν ὅρων A? 9 ὅτι A ὅτ᾽ ἀδύνατον AB*Cd*n Al: ὅταν
δυνατόν Bd IO εἴη scripsi: εἰ codd. Al: om. P 14 xai! om. C
18 δυεῖν B. ἐλαχίστου B : ἐλάχιστον B?
ANAAYTIKQN IIPOTEPQON A
^ ^ ^ ~
20 I' xara τοῦ A, τὸ δὲ A κατὰ τοῦ Z, καὶ τὸ Γ κατὰ τοῦ Z
3 , M *,
ἐξ ἀνάγκης" kai εἰ δυνατὸν ἑκάτερον, καὶ τὸ συμπέρασμα
LÀ
δυνατόν. ὥσπερ οὖν et τις θείη τὸ μὲν A τὰς προτάσεις, TO δὲ
B τὸ συμπέρασμα, συμβαίνοι ἂν οὐ μόνον ἀναγκαίου τοῦ A
w ΄ ^ ‘ > - > ^ M ^ ,
ὄντος ἅμα kai τὸ B εἶναι ἀναγκαῖον, ἀλλὰ Kat δυνατοῦ δυνατόν.
Ὡς Τούτου δὲ δειχθέντος, φανερὸν ὅτι ψεύδους ὑποτεθέν-
M A > , * M ^ ^ M € ,
Tos Kai μὴ ἀδυνάτου Kal τὸ συμβαῖνον διὰ τὴν ὑπόθεσιν
^ μὴ Li
ψεῦδος ἔσται καὶ οὐκ ἀδύνατον. οἷον εἰ τὸ A ψεῦδος μέν ἐστι
^ , , P L4 * ^ M w M 4 L4
μὴ μέντοι ἀδύνατον, ὄντος δὲ τοῦ A τὸ B ἔστι, kai τὸ B ἔσται
^ ^ > , > , , M ^ Li Ld ,
ψεῦδος μὲν od μέντοι ἀδύνατον. ἐπεὶ yàp δέδεικται ὅτι εἰ
"^ L4 ^ ~ *
3o ToU A ὄντος τὸ B ἔστι, kai δυνατοῦ ὄντος τοῦ A ἔσται τὸ B 8v-
, € , A M ^ M ^ w
νατόν, ὑπόκειται δὲ τὸ A δυνατὸν εἶναι, καὶ τὸ B. ἔσται δυ-
varóv: εἰ γὰρ ἀδύνατον, ἅμα δυνατὸν ἔσται τὸ αὐτὸ καὶ
ἀδύνατον.
, x 4 e £f ^ * ^
Διωρισμένων δὴ τούτων ὑπαρχέτω τὸ A παντὶ τῷ B,
35 τὸ δὲ B παντὶ τῷ [᾿ ἐνδεχέσθω: ἀνάγκη οὖν τὸ A παντὶ τῷ
*, , e , ‘ * > P, * Ἂς ^
Γ᾽ ἐνδέχεσθαι ὑπάρχειν. μὴ yàp ἐνδεχέσθω, τὸ δὲ B παντὶ
- , € € , ^ M =! if > ,
τῷ l' κείσθω ws ὑπάρχον: τοῦτο δὲ ψεῦδος μέν, οὐ μέντοι
ἀδύνατον. εἰ οὖν τὸ μὲν A μὴ ἐνδέχεται παντὶ τῷ I’, τὸ δὲ B
a « ’ ~ x *, M -^ > , ,
παντὶ ὑπάρχει τῷ I, τὸ A οὐ παντὶ τῷ B ἐνδέχεται: γί-
M 4 A ~ , Lg > > L4 ,
4o νεται yàp συλλογισμὸς διὰ τοῦ τρίτου σχήματος. ἀλλ᾽ ὑπέ-
kevro παντὶ ἐνδέχεσθαι ὑπάρχειν. ἀνάγκη ἄρα τὸ A παντὶ
34b τῷ Γ᾽ ἐνδέχεσθαι- ψεύδους γὰρ τεθέντος καὶ οὐκ ἀδυνάτου τὸ
συμβαῖνόν ἐστιν ἀδύνατον. [ἐγχωρεῖ δὲ καὶ διὰ τοῦ πρώτου
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, M ^ ^ ^ Li , ^ b A X. ^
xew. εἰ yàp τὸ B παντὶ τῷ I ὑπάρχει, τὸ δὲ A παντὶ τῷ
5B ἐνδέχεται, κἂν τῷ Γ΄ παντὶ ἐνδέχοιτο τὸ A. ἀλλ᾽ ὑπέκειτο
μὴ παντὶ ἐγχωρεῖν.
^ a , M M [4 , M A ,
Δεῖ δὲ λαμβάνειν τὸ παντὶ ὑπάρχον μὴ κατὰ χρόνον
e f ~ ^ > ~ ~ , > ΕΣ € ^ MJ
ópícavras, olov viv ἢ ἐν τῶδε TH χρόνῳ, GAN ἁπλῶς" διὰ
τοιούτων γὰρ προτάσεων καὶ τοὺς συλλογισμοὺς ποιοῦμεν,
~ , ^ LÀ
10 ἐπεὶ κατά ye τὸ viv λαμβανομένης τῆς προτάσεως οὐκ ἔσται
M
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421 δυνατὸν. δ᾽ ABdn: an-- 85? 24 ἅμα om. ACd 28 -ros δὲ...
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nl 32-3 ef... ἀδύνατον om. πὶ 38 μὲν om. d παντὶ om.
ABCd Al 41 ἐνδέχεσθαι codd. D AIP : secl. Becker dpa om. d!
by ὑποτεθέντος γ1 2-6 ἐγχωρεῖ... ἐγχωρεῖν codd. ALP: secl. Becker
ς καὶ ABCnT ἐνδέχεται d: ἂν ἐνδέχοιτο ἢ 1 ὑπάρχειν n 8-11
&à .. . συλλογισμός codd. D: secl. Becker rr kai om. Cnt”
a a
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, > , * @ , > LÀ , iJ
κινούμενον ἐνδέχεται παντὶ ἵππῳ" ἀλλ᾽ ἄνθρωπον οὐδενὶ ἵππῳ
ἐνδέχεται. ἔτι ἔστω τὸ μὲν πρῶτον ζῷον, τὸ δὲ μέσον κινού-
μενον, τὸ δ᾽ ἔσχατον ἄνθρωπος. αἱ μὲν οὖν προτάσεις ὁμοίως
ἕξουσι, τὸ δὲ συμπέρασμα ἀναγκαῖον, οὐκ ἐνδεχόμενον: ἐξ
ΕΣ P4 * [4 LÀ ^ ' a d Ld x ,
ἀνάγκης yap ὁ ἄνθρωπος ζῷον. φανερὸν οὖν ὅτι τὸ καθόλου
ληπτέον ἁπλῶς, καὶ οὐ χρόνῳ διορίζοντας.
Πάλιν ἔστω στερητικὴ πρότασις καθόλου ἡ Α Β, καὶ
εἰλήφθω τὸ μὲν Α μηδενὶ τῷ Β ὑπάρχειν, τὸ δὲ Β παντὶ
> » »* Ed ~ , 7 , > , Y
ἐνδεχέσθω ὑπάρχειν τῷ Γ΄. τούτων οὖν τεθέντων ἀνάγκη τὸ A
Li , M ~ τ , x M > , ^
ἐνδέχεσθαι μηδενὶ τῷ I ὑπάρχειν. μὴ yàp ἐνδεχέσθω, τὸ
δὲ Β τῷ Γ κείσθω ὑπάρχον, καθάπερ πρότερον. ἀνάγκη δὴ
τὸ Α τινὶ τῷ Β ὑπάρχειν: γίνεται γὰρ συλλογισμὸς διὰ
τοῦ τρίτου σχήματος" τοῦτο δὲ ἀδύνατον. ὥστ᾽ ἐνδέχοιτ᾽ ἂν τὸ
Ἂν ^ [4 ΑἹ * » , ^ ^
A μηδενὶ τῷ I" ψεύδους yàp τεθέντος ἀδύνατον τὸ συμβαῖ-
νον. οὗτος οὖν ὁ συλλογισμὸς οὐκ ἔστι τοῦ κατὰ τὸν διορισμὸν
2 , > A —^ A > > , L4 , > L4
ἐνδεχομένου, ἀλλὰ τοῦ μηδενὶ ἐξ ἀνάγκης (αὕτη ydp ἐστιν ἡ
> , ~ , € , > ¢ M > > ,
ἀντίφασις τῆς γενομένης ὑποθέσεως: ἐτέθη yap ἐξ avay-
4 * ~ € , L4 * ^ ^ > ,
kns τὸ A τινὶ τῷ Γ ὑπάρχειν, ὁ δὲ διὰ τοῦ ἀδυνάτου συλλο-
γισμὸς τῆς ἀντικειμένης ἐστὶν φάσεως). ἔτι δὲ καὶ ἐκ τῶν
ὅρων φανερὸν ὅτι οὐκ ἔσται τὸ συμπέρασμα ἐνδεχόμενον. ἔστω
γὰρ τὸ μὲν A κόραξ, τὸ δ᾽ ἐφ᾽ ᾧ B διανοούμενον, ἐφ᾽
ᾧ δὲ Γ ἄνθρωπος. οὐδενὶ δὴ τῷ B τὸ A ὑπάρχει: οὐδὲν γὰρ
διανοούμενον κόραξ. τὸ δὲ B παντὶ ἐνδέχεται τῷ I> παντὶ ;
γὰρ ἀνθρώπῳ τὸ διανοεῖσθαι. ἀλλὰ τὸ A ἐξ ἀνάγκης οὐδενὶ
TQ I: οὐκ ἄρα τὸ συμπέρασμα ἐνδεχόμενον. ἀλλ᾽ οὐδ᾽ ἀναγ-
^ x A a M x ? ,
katov ἀεί. ἔστω yap τὸ μὲν A κινούμενον, τὸ δὲ B ἐπιστήμη,
τὸ δ᾽ éd? ᾧ Γ ἄνθρωπος. τὸ μὲν οὖν A οὐδενὶ τῷ B ὑπάρξει,
τὸ δὲ B παντὶ τῷ Γ᾽ ἐνδέχεται, καὶ οὐκ ἔσται τὸ συμπέρασμα
ἀναγκαῖον. οὐ γὰρ ἀνάγκη μηδένα κινεῖσθαι ἄνθρωπον, ἀλλ᾽
^ Ld * , ^0» ^ ^
οὐκ ἀνάγκη τινά. δῆλον οὖν ὅτι τὸ συμπέρασμά ἐστι τοῦ μηδενὶ
, hj L4 € , , X Li U Ld
ἐξ ἀνάγκης ὑπάρχειν. ληπτέον δὲ βέλτιον τοὺς ὅρους.
^ ^ ~ ^ ^ LÀ L4 ?, ,
'Eàv δὲ τὸ στερητικὸν τεθῇ πρὸς τὸ ἔλαττον ἄκρον ἐνδέ-
χεσθαι σημαῖνον, ἐξ αὐτῶν μὲν τῶν εἰλημμένων προτάσεων
Uis παντὶ τῷ n 14-17 ἔτι... ζῷον codd. FALM?: secl. Becker
18 ἁπλῶς] ἀορίστως C διορίζοντας C?n : διορίζοντι A Bd 19-3592 πάλιν
... ὅρους codd. I'ALP : secl. Becker 28 ἐστιν om. d! 29 ὑπετέθη n
31 φάσεως A*C?nT'P* : ἀντιφάσεως ABCA 33 μὲν ἡ ἐφ᾽ ὧν n: -ἰ ἐφ᾽ ᾧ
36 ἀνθρώπῳ" ἐνδέχεται n 40-1 xai . . . ἀναγκαῖον om. Al 35*1
ὅτι om. d
I5
20
40
35*
ANAAYTIKQN IIPOTEPQN A
*, ‘ w * 5 , * ^ a 4
ς οὐδεὶς ἔσται συλλογισμός, ἀντιστραφείσης δὲ THs κατὰ TO
ἐνδέχεσθαι προτάσεως ἔσται, καθάπερ ἐν τοῖς πρότερον. ὑπαρ-
χέτω γὰρ τὸ Α παντὶ τῷ Β, τὸ δὲ Β ἐνδεχέσθω μηδενὶ
τῷ Γ΄. οὕτω μὲν οὖν ἐχόντων τῶν ὅρων οὐδὲν ἔσται ἀναγκαῖον"
ἐὰν δ᾽ ἀντιστραφῇ τὸ B I' καὶ ληφθῇ τὸ B παντὶ τῷ Γ év-
10 δέχεσθαι, γίνεται συλλογισμὸς ὥσπερ πρότερον: ὁμοίως γὰρ
ἔχουσιν οἱ ὅροι τῇ θέσει. τὸν αὐτὸν δὲ τρόπον καὶ στερητικῶν
Y , jh ~ F 3. ^ ^ *
ὄντων ἀμφοτέρων τῶν διαστημάτων, ἐὰν τὸ μὲν A B μὴ
ὑπάρχειν, τὸ δὲ BI μηδενὶ ἐνδέχεσθαι ίνῃ" δι᾿ αὐτῶν
pxew, μη x σημαίνῃ
* h. ^ , , > ~ , M » ^ >
μὲν yap τῶν εἰλημμένων οὐδαμῶς γίνεται τὸ ἀναγκαῖον, ἀντι-
ts στραφείσης δὲ τῆς κατὰ τὸ ἐνδέχεσθαι προτάσεως ἔσται
συλλογισμός. εἰλήφθω γὰρ τὸ μὲν A μηδενὶ τῷ B ὑπάρ-
xew, τὸ δὲ B ἐνδέχεσθαι μηδενὶ τῷ I. διὰ μὲν οὖν τούτων
οὐδὲν ἀναγκαῖον: ἐὰν δὲ ληφθῇ τὸ B παντὶ τῷ I' ἐνδέχεσθαι,
ὅπερ ἐστὶν ἀληθές, ἡ δὲ A Β πρότασις ὁμοίως ἔχῃ, πάλιν
« » ‘ L4 , νυ b ^ τ Ld ~ x
20 0 αὐτὸς ἔσται συλλογισμός. ἐὰν δὲ μὴ ὑπάρχειν τεθῇ τὸ B
παντὶ τῷ l' καὶ μὴ ἐνδέχεσθαι μὴ ὑπάρχειν, οὐκ ἔσται συλ-
λογισμὸς οὐδαμῶς, οὔτε στερητικῆς οὔσης οὔτε καταφατικῆς τῆς
A B προτάσεως. ὅροι δὲ κοινοὶ τοῦ μὲν ἐξ ἀνάγκης ὑπάρχειν
λευκόν--ζῷον--χιών, τοῦ δὲ μὴ ἐνδέχεσθαι λευκόν--ζῷον--πίττα.
a5 Φανερὸν οὖν ὅτι καθόλου τῶν ὅρων ὄντων, καὶ τῆς μὲν
ὑπάρχειν τῆς δ᾽ ἐνδέχεσθαι λαμβανομένης τῶν προτάσεων,
-" € * a w L4 > , a ,
ὅταν ἡ πρὸς τὸ ἔλαττον ἄκρον ἐνδέχεσθαι λαμβάνηται mpó-
τασις, ἀεὶ γίνεται συλλογισμός, πλὴν ὁτὲ μὲν ἐξ αὐτῶν
« * 2 ? , ^ , , x rd Lj ,
ὁτὲ δ᾽ ἀντιστραφείσης τῆς προτάσεως. πότε δὲ τούτων ékdre-
30 pos καὶ διὰ τίν᾽ αἰτίαν, εἰρήκαμεν.
? MJ & * M ,
30 Ἐὰν δὲ τὸ μὲν καθόλου
A LI , , ^ ^ , Ld x A] ^
τὸ δ᾽ ἐν μέρει ληφθῇ τῶν διαστημάτων, ὅταν μὲν τὸ πρὸς
Y ^ M Y 05 * ? δ Ld wo ,
τὸ μεῖζον ἄκρον καθόλου τεθῇ καὶ ἐνδεχόμενον, εἴτ᾽ amo$a-
τικὸν εἴτε καταφατικόν, τὸ δ᾽ ἐν μέρει καταφατικὸν καὶ
€ , L4 * 4 , * ,
ὑπάρχον, ἔσται συλλογισμὸς τέλειος, καθάπερ καὶ καθόλου
35 τῶν ὅρων ὄντων. ἀπόδειξις δ᾽ ἡ αὐτὴ ἣ καὶ πρότερον. ὅταν
δὲ καθόλου μὲν 4 τὸ πρὸς τὸ μεῖζον ἄκρον, ὑπάρχον δὲ καὶ
μὴ ἐνδεχόμενον, θάτερον δ᾽ ἐν μέρει καὶ ἐνδεχόμενον, ἐάν τ᾽
> ' +7 M ^ > ^ 7s
ἀποφατικαὶ ἐάν τε καταφατικαὶ τεθῶσιν ἀμφότεραι, ἐάν
36-15 καθάπερ... ἔσται om. A ὃ τῷ 44Γ: τῶν BCn 9 ἐνδέχε-
σθαι om. nl Ale 13 ὑπάρχῃ ABCA σημαίνειν d : συμβαίνειν d? 14
οὐδαμῶς] οὐ I 16 συλλογισμός-Ἐ a. B. y. π ὑπάρχειν C 17
ἐνδεχέσθω nT 21 παντὶ om. 71 ui om. BC 27 λαμβάνῃ n
29 τῆς om. d
a b
15. 35°5-16. 35°31
τε ἡ μὲν ἀποφατικὴ ἡ δὲ καταφατική, πάντως ἔσται συλ-
λογισμὸς ἀτελής. πλὴν οἱ μὲν διὰ τοῦ ἀδυνάτου δειχθήσονται, 40
t ^ ' ὃ A ^ > ^ ^ ^2) δέ. , » b
of δὲ Kai διὰ τῆς ἀντιστροφῆς τῆς τοῦ ἐνδέχεσθαι, καθάπερ ἐν 35
^ , w ' A ^ a > ~ Hj
τοῖς πρότερον. ἔσται δὲ συλλογισμὸς διὰ τῆς ἀντιστροφῆς [Kat]
ὅταν ἡ μὲν καθόλου πρὸς τὸ μεῖζον ἄκρον τεθεῖσα σημαίνῃ
τὸ ὑπάρχειν [ἢ μὴ ὑπάρχειν], ἡ δ᾽ ἐν μέρει στερητικὴ οὖσα
τὸ ἐνδέχεσθαι λαμβάνῃ, οἷον εἰ τὸ μὲν A παντὶ τῷ B ὑπαρ- 5
ΩΣ ^ € , Al ὃ x B X. ~ D , δ P ^ € ,
xe ἢ μὴ ὑπάρχει, τὸ δὲ B τινὶ τῷ D ἐνδέχεται μὴ ὑπάρ-
xew: ἀντιστραφέντος γὰρ τοῦ B Γ κατὰ τὸ ἐνδέχεσθαι γίνεται
, Ld M ' ‘ Li y , € 4
συλλογισμός. ὅταν δὲ τὸ μὴ ὑπάρχειν λαμβάνῃ ἡ κατὰ
μέρος τεθεῖσα, οὐκ ἔσται συλλογισμός. ὅροι τοῦ μὲν ὑπάρχειν
λευκόν--ζῷον-χιών, τοῦ δὲ μὴ ὑπάρχειν λευκόν--ζῷον--πίττα" 10
διὰ γὰρ τοῦ ἀδιορίστου ληπτέον τὴν ἀπόδειξιν. ἐὰν δὲ τὸ καθόλου
τεθῇ πρὸς τὸ ἔλαττον ἄκρον, τὸ δ᾽ ἐν μέρει πρὸς τὸ μεῖζον,
ἐάν τε στερητικὸν ἐάν τε καταφατικόν, ἐάν τ᾽ ἐνδεχόμενον ἐάν
θ᾽ ὑπάρχον ὁποτερονοῦν, οὐδαμῶς ἔσται συλλογισμός. 14
Οὐδ᾽ 14
Ld > , ^ 3 , ~ e , ww? 3 ,
Grav ἐν μέρει ἢ ἀδιόριστοι τεθῶσιν ai προτάσεις, εἴτ᾽ ἐνδέχε- 15
σθαι λαμβάνουσαι εἴθ᾽ ὑπάρχειν εἴτ᾽ ἐναλλάξ, οὐδ᾽ οὕτως
LÀ , > , > e , a 4 > M - ,
ἔσται συλλογισμός. ἀπόδειξις δ᾽ ἡ αὐτὴ ἥπερ κἀπὶ τῶν πρότε-
ρον. ὅροι δὲ κοινοὶ τοῦ μὲν ὑπάρχειν ἐξ ἀνάγκης ζῷον-λευ-
, L4 ~ Xx Ἂς >? , ~ , e ,
κόν-ἄνθρωπος, τοῦ δὲ μὴ ἐνδέχεσθαι ζῷον-λευκόν--ἱμάτιον.
φανερὸν οὖν ὅτι τοῦ μὲν πρὸς τὸ μεῖζον ἄκρον καθόλου τεθέν- 20
LEA] LH , -^ * A] ‘ L4 > :
τος del γίνεται συλλογισμός, τοῦ δὲ πρὸς τὸ ἔλαττον οὐδέ-
ποτ᾽ οὐδενός.
16 Ὅταν δ᾽ ἡ μὲν ἐξ ἀνάγκης ὑπάρχειν ἡ δ᾽ ἐνδέχεσθαι
σημαίνῃ τῶν προτάσεων, ὁ μὲν συλλογισμὸς ἔσται τὸν αὐτὸν
τρόπον ἐχόντων τῶν ὅρων, καὶ τέλειος ὅταν πρὸς τῷ ἐλάτ- 25
τονι ἄκρῳ τεθῇ τὸ ἀναγκαῖον: τὸ δὲ συμπέρασμα κατηγο-
ρικῶν μὲν ὄντων τῶν ὅρων τοῦ ἐνδέχεσθαι καὶ οὐ τοῦ ὑπάρχειν
Ν b , M b , [4 LAJ » M x
ἔσται, καὶ καθόλου καὶ μὴ καθόλου τιθεμένων, ἐὰν δ᾽ 5j τὸ μὲν
καταφατικὸν τὸ δὲ στερητικόν, ὅταν μὲν ἦ τὸ καταφατικὸν
ἀναγκαῖον, τοῦ ἐνδέχεσθαι καὶ οὐ τῳῦ μὴ ὑπάρχειν, ὅταν δὲ 30
τὸ στερητικόν, καὶ τοῦ ἐνδέχεσθαι μὴ ὑπάρχειν καὶ τοῦ μὴ
br καὶ (43, coni. P: om. ABdn 2 καὶ om. Pacius 4 ὑπάρχον
ACd ἢ μὴ ὑπάρχον C : om. AdnI" 5 ὑπάρχειν 7 μὴ ὑπάρχειν C
10 ζῷον-λευκόν-πίττα d 11 dop(crov AdAl τὸ om. C 17 5
ABd Al* ἐπὶ n 23 ὑπάρχειν 3-7] μὴ ὑπάρχειν dnT 27 τῶν ὅρων
om, d 28 xai! om. d 30 864-5 C 31 erepnrikóv4-
ἀναγκαῖον C
ANAAYTIKON IIPOTEPON A
ὑπάρχειν, kai καθόλου kai μὴ καθόλου τῶν ὅρων ὄντων: τὸ
δ᾽ ἐνδέχεσθαι ἐν τῷ συμπεράσματι τὸν αὐτὸν τρόπον ληπτέον
ὅνπερ καὶ ἐν τοῖς πρότερον. τοῦ δ᾽ ἐξ ἀνάγκης μὴ ὑπάρχειν οὐκ
35 ἔσται συλλογισμός: ἕτερον γὰρ τὸ μὴ ἐξ ἀνάγκης ὑπάρχειν
* 4 3 > , \ € ,
kai τὸ ἐξ ἀνάγκης μὴ ὑπάρχειν.
- * T ^ 4 ~ "9 , , 4
Ὅτι μὲν οὖν καταφατικῶν ὄντων τῶν ὅρων od γίνεται τὸ
συμπέρασμα ἀναγκαῖον, φανερόν. ὑπαρχέτω γὰρ τὸ μὲν Α
M ~ , > , * * > , ^ ^
παντὶ τῷ B ἐξ ἀνάγκης, τὸ δὲ B ἐνδεχέσθω παντὶ τῷ T.
40 ἔσται δὴ συλλογισμὸς ἀτελὴς ὅτι ἐνδέχεται τὸ A παντὶ τῷ Γ
368 ὑπάρχειν. ὅτι δ᾽ ἀτελής, ἐκ τῆς ἀποδείξεως δῆλον: τὸν av-
I
I
M ^ , , σ > M ^ , ,
τὸν yàp τρόπον δειχθήσεται ὄνπερ κἀπὶ τῶν πρότερον. πάλιν
τὸ μὲν Α ἐνδεχέσθω παντὶ τῷ Β, τὸ δὲ Β παντὶ τῷ Γ ὑπαρ-
, 1 , , L4 i ^ Ld M A 4
xérw ἐξ ἀνάγκης. ἔσται δὴ συλλογισμὸς ὅτι TO παντὶ
~ , , e , td 3 % a L4 ' d M ,
ςτῷ I ἐνδέχεται ὑπάρχειν, ἀλλ᾽ οὐχ ὅτι ὑπάρχει, καὶ τέ-
λειος, GAN’ οὐκ ἀτελής: εὐθὺς γὰρ ἐπιτελεῖται διὰ τῶν ἐξ
ἀρχῆς προτάσεων.
» pr A « , € ,
1 Ei δὲ μὴ ὁμοιοσχήμονες αἱ προτάσεις,
ἔστω πρῶτον ἡ στερητικὴ ἀναγκαία, καὶ τὸ μὲν Α μηδενὶ
ἐνδεχέσθω τῷ B, τὸ δὲ B παντὲ τῷ Γ᾽ ἐνδεχέσθω.
ECT
, , A M * ^ . a L4 *
odvdykg δὴ τὸ A μηδενὶ τῷ I ὑπάρχειν. κείσθω yap
[4 5 ^ * ^ y ^ * t , M , LÀ
ὑπάρχειν ἢ παντὶ ἢ τινί τῷ δὲ B ὑπέκειτο μηδενὶ ἐνδέχε-
3 x ἫΝ » ts * , sor X ~ , M
σθαι. ἐπεὶ οὖν ἀντιστρέφει τὸ στερητικόν, οὐδὲ τὸ Β τῷ A οὐδενὶ
, , * 4 ~ nn X nn M ^ « f
ἐνδέχεται: τὸ δὲ A τῷ Γ᾽ ἢ παντὶ ἢ τινὶ κεῖται ὑπάρχειν"
σ , > * ^ , A - * ? 5, > ^ « ,
ὥστ᾽ οὐδενὶ ἢ οὐ παντὶ τῷ I τὸ B év8éyov àv ὑπάρχειν"
€ , 4 * , , ^ M > L4 * ^ , ΄
ὑπέκειτο δὲ παντὶ ἐξ ἀρχῆς. φανερὸν δ᾽ ὅτι καὶ τοῦ ἐνδέχε-
σθαι μὴ ὑπάρχειν γίγνεται συλλογισμός, εἴπερ καὶ τοῦ μὴ
Li , , L4 € X , 2 ,ὔ
ὑπάρχειν. πάλιν ἔστω ἡ καταφατικὴ πρότασις ἀναγκαία,
καὶ τὸ μὲν Α ἐνδεχέσθω μηδενὶ τῷ Β ὑπάρχειν, τὸ δὲ Β
M ~ e , > > , € b 7T M
παντὶ τῷ I ὑπαρχέτω ἐξ ἀνάγκης. ὁ μὲν οὖν συλλογισμὸς
tn
20 ἔσται τέλειος, ἀλλ᾽ ov τοῦ μὴ ὑπάρχειν ἀλλὰ τοῦ ἐνδέχεσθαι
A [4 , LÀ ^ 4 LÀ > , L4 > ^ ^
μὴ ὑπάρχειν: 7| τε yàp πρότασις οὕτως ἐλήφθη ἡ ἀπὸ τοῦ
^ ,
μείζονος ἄκρου, καὶ eis τὸ ἀδύνατον οὐκ ἔστιν ἀγαγεῖν" εἰ yap
€ , ^ ~ M e ^ ^ M M ^ %
ὑποτεθείη τὸ A τῷ Γ᾽ τινὶ ὑπάρχειν, κεῖται δὲ kai τῷ B év-
b34 καὶ 415: om. ABd 37 190m. C 38 τὸ μὲν A om. d! : μὲν
om. AB 40 ἔσται... ἀτελὴς orn. C: δὴ 0m. A. ór F8 n 3677
ὁμοσχήμονες Ant 9 ἐνδεχέσθω] ὑπαρχέτω d τῶν 42 — B'CnDIÁAl:
Β ἐξ ἀνάγκης ABA τι ὑπάρχον ἢ παντὶ ἢ τινί codd, D AIP: susp. Becker
12 τῷ] τὸ C1 13 ἢ παντὶ ἢ τινὶ codd. AIP: ἣ τινὶ 5j παντὶ D: susp. Becker
14 οὐδενὶ ἢ codd. ALP: susp. Becker οὐ om. n 16 ἐπείπερ n μὴ
om. d! 18 τῷ CnI Al: τῶν ABd 21 ἡ om. 5 22 dma-
γαγεῖν C 23 τινὶ AIY? : μηδενὶ codd. I Al xai+76 a B® 23-4
16. 35°32-36°16
, ^ * , or , ^ , 3 ,
δέχεσθαι μηδενὶ ὑπάρχειν, οὐδὲν συμβαίνει διὰ τούτων ἀδύ-
νατον. ἐὰν δὲ πρὸς τῷ ἐλάττονι ἄκρῳ τεθῇ τὸ στερητικόν, 25
ὅταν μὲν ἐνδέχεσθαι σημαίνῃ, συλλογισμὸς ἔσται διὰ τῆς
ἀντιστροφῆς, καθάπερ ἐν τοῖς πρότερον, ὅταν δὲ μὴ ἐνδέχε-
3 » $9»? € L4 A na , ^ bd ?
σθαι, οὐκ ἔσται. οὐδ᾽ ὅταν ἄμφω μὲν τεθῇ στερητικά, μὴ ἡ ὃ
ἐνδεχόμενον τὸ πρὸς τὸ ἔλαττον. ὅροι δ᾽ οἱ αὐτοί, τοῦ μὲν
ὑπάρχειν λευκόν--ζῷον-χιών, τοῦ δὲ μὴ ὑπάρχειν λευκόν-- 30
ζῷον--πίττα.
* , M A s L4 + 4 ^ > , ^
Tov αὐτὸν δὲ τρόπον ἕξει κἀπὶ τῶν ἐν μέρει συλλογισμῶν.
^ M
ὅταν μὲν yap ἢ τὸ στερητικὸν ἀναγκαῖον, καὶ TO συμπέρασμα ἔσται
~ ΑἹ € 4 » εἶ 4 M ^ > Li Lx ,
τοῦ μὴ ὑπάρχειν. olov εἰ τὸ μὲν A μηδενὶ τῷ B ἐνδέχεται ὑπάρ-
A δὲ Β M ~ ID > ὃ , - , > , A A M
xew, τὸ δὲ B rui τῷ Γ ἐνδέχεται ὑπάρχειν, ἀνάγκη τὸ A τινὶ 45
~ 3 € E *, M ^. € , ~ 4 M
TQ Γ μὴ ὑπάρχειν. εἰ yap παντὶ ὑπάρχει, τῷ δὲ B μηδενὶ
» , *, A Mi , * ~ 3 ’ « , LÀ > » *
ἐνδέχεται, οὐδὲ τὸ B οὐδενὶ τῷ A ἐνδέχεται ὑπάρχειν. ὥστ᾽ εἰ τὸ
A παντὶ τῷ Γ ὑπάρχει, οὐδενὶ τῷ Γ τὸ Β ἐνδέχεται. ἀλλ᾽ ὑπέ-
κειτό τινι ἐνδέχεσθαι. ὅταν δὲ τὸ ἐν μέρει καταφατικὸν ἀναγ-
καῖον ἦ, τὸ ἐν τῷ στερητικῷ συλλογισμῷ, οἷον τὸ B D, 7j τὸ ka- 40
θό τι» ~ ~ H ^ » wv ^7 , b
όλου τὸ ἐν τῷ κατηγορικῷ, olov τὸ A B, οὐκ ἔσται τοῦ ὑπάρχειν 36
, 3 , 3 € LEA ^ M » 3 ~ ,
συλλογισμός. ἀπόδειξις δ᾽ ἡ αὐτὴ ἣ καὶ ἐπὶ τῶν πρότερον.
23 δὲ a A , - ^ τ LÀ Y ^
ἐὰν δὲ τὸ μὲν καθόλου τεθῇ πρὸς τὸ ἔλαττον ἄκρον, ἢ Ka-
ταφατικὸν ἢ στερητικόν, ἐνδεχόμενον, τὸ δ᾽ ἐν μέρει ἀναγ-
^ A ~ * L4 E , » , e b
καῖον [πρὸς τῷ μείζονι ἄκρῳ], οὐκ ἔσται συλλογισμός (ὅροι δὲς
τοῦ μὲν ὑπάρχειν ἐξ ἀνάγκης ζῷον-λευκόν- ἄνθρωπος, τοῦ δὲ
A] > ,ὔ ~ le « , Ed > 3 ^ T^
μὴ ἐνδέχεσθαι ζῷον-λευκόν--ἱμάτιον) ὅταν δ᾽ ἀναγκαῖον ἢ
τὸ καθόλου, τὸ δ᾽ ἐν μέρει ἐνδεχόμενον, στερητικοῦ μὲν ὄντος
τοῦ καθόλου τοῦ μὲν ὑπάρχειν ὅροι ζῷον-λευκόν-κόραξ, τοῦ
δὲ μὴ ὑπάρχειν ζῷον-λευκόν-πίττα, καταφατικοῦ δὲ τοῦ τὸ
' * , ~ λ , , ^ δὲ A > δ Li cO.
μὲν ὑπάρχειν ζῷον-λευκόν-κύκνος, τοῦ δὲ μὴ ἐνδέχεσθαι
Ll , r d 29? Ld 2 , ~ © ,
ζῷον--λευκόν--χιών. οὐδ᾽ Grav ἀδιόριστοι ληφθῶσιν αἱ προτά-
- 3 ΄ A , o> L4 LÀ ,
σεις ἢ ἀμφότεραι κατὰ μέρος, οὐδ᾽ οὕτως ἔσται συλλογισμός.
ὅροι δὲ κοινοὶ τοῦ μὲν ὑπάρχειν ζῷον-λευκόν-ἄνθρωπος, τοῦ
δὲ μὴ ὑπάρχειν ζῷον-λευκόν- ἄψυχον. καὶ γὰρ τὸ ζῷον τις
τινὶ λευκῷ καὶ τὸ λευκὸν ἀψύχῳ τινὲ καὶ ἀναγκαῖον ὑπάρ-
μηδενὶ ἐνδέχεσθαι d 229 107] τῷ d 33 μὲν Cn: om. 4 Bd 34
τῷ I'ALP : τῶν codd. ἐνδέχεται] ἀνάγκη d ἃς τῷ CnTP : τῶν ABA
36 τῷ! FAL: τῶν codd. P δὲ om. A? 377 A om. d! 38 τῷ
AIP : τῶν codd. 39 ἐνδέχεσθαι-[-α. B. y. ἩΓ 4o-b1 re? . . . οἷον
om. A by τὸϊ dn: om. ABC Alc 2 καὶ om. C 3 τῷ ἐλάττονι
ἄκρῳ ACd 4 ἢ στερητικὸν ἣ ἐνδεχόμενον dP ς πρὸς... ἄκρῳ
ΒΟΆΓ: om, Ad 9 ὅροι om. C τό λευκῷ] λευκὸν ἡ
ANAAYTIKQN TIPOTEPQN A
4 » » , L4 ΄, 3 M ^» ὃ r4 6 ¢ ,
xew καὶ οὐκ ἐνδέχεται ὑπάρχειν. κἀπὶ τοῦ ἐνδέχεσθαι ὁμοίως,
ὥστε πρὸς ἅπαντα χρήσιμοι of ὅροι.
Φανερὸν οὖν ἐκ τῶν εἰρημένων ὅτι ὁμοίως ἐχόντων τῶν
20 ὅρων ἔν τε τῷ ὑπάρχειν καὶ ἐν τοῖς ἀναγκαίοις γίνεταΐ τε καὶ
οὐ γίνεται συλλογισμός, πλὴν κατὰ μὲν τὸ ὑπάρχειν τιθε-
μένης τῆς στερητικῆς προτάσεως τοῦ ἐνδέχεσθαι ἦν ὁ συλλογι-
σμός, κατὰ δὲ τὸ ἀναγκαῖον τῆς στερητικῆς καὶ τοῦ ἐνδέχεσθαι
M ^ ^ [4 , ^ , τσ ΄ > ^ €
καὶ τοῦ μὴ ὑπάρχειν. [δῆλον δὲ καὶ ὅτι πάντες ἀτελεῖς of συλ-
25 λογισμοὶ καὶ ὅτι τελειοῦνται διὰ τῶν προειρημένων σχημάτων.
Ἔν δὲ τῷ δευτέρῳ σχήματι ὅταν μὲν ἐνδέχεσθαι λαμ-
βάνωσιν ἀμφότεραι αἱ προτάσεις, οὐδεὶς ἔσται συλλογισμός,
οὔτε κατηγορικῶν οὔτε στερητικῶν τιθεμένων, οὔτε καθόλον οὔτε
κατὰ μέρος" ὅταν δὲ ἡ μὲν ὑπάρχειν ἡ δ᾽ ἐνδέχεσθαι σημαίνῃ,
3o τῆς μὲν καταφατικῆς ὑπάρχειν σημαινούσης οὐδέποτ᾽ ἔσται,
τῆς δὲ στερητικῆς τῆς καθόλου ἀεί. τὸν αὐτὸν δὲ τρόπον καὶ
- « A , > Ld € , > ΄ -* , ^
Grav ἡ μὲν ἐξ ἀνάγκης ἡ δ᾽ ἐνδέχεσθαι λαμβάνηται τῶν
προτάσεων. δεῖ δὲ καὶ ἐν τούτοις λαμβάνειν τὸ ἐν τοῖς συμ-
περάσμασιν ἐνδεχόμενον ὥσπερ ἐν τοῖς πρότερον.
Π, ^ T f Ld » > , * » ^ > ΄ 0
35 ρῶτον οὖν δεικτέον ὅτι οὐκ ἀντιστρέφει τὸ ἐν TH ἐνδέχεσθαι
, * 4 > , ‘ ~ 4 > , M
στερητικόν, otov εἰ τὸ A ἐνδέχεται μηδενὶ τῷ B, οὐκ ἀνάγκη καὶ
A 2 / M ^t L4 x ~ ki.» ,
τὸ B ἐνδέχεσθαι μηδενὶ τῷ A. κείσθω yap τοῦτο, kat ἐνδεχέσθω
M 4 ~ L4 ,ὔ Σ m~ -? τ» , € »
τὸ B μηδενὶ τῷ A ὑπάρχειν. οὐκοῦν ἐπεὶ ἀντιστρέφουσιν ai ἐν
“- » ig LÀ ^ > , M t 3 ,
τῷ ἐνδέχεσθαι καταφάσεις ταῖς ἀποφάσεσι, καὶ at ἐναντίαι
^ ε > , x x ^ > » M e ,
4o kai αἱ ἀντικείμεναι, τὸ δὲ B τῷ A ἐνδέχεται μηδενὶ ὑπάρ-
^ - * ^ * > H ^ e ,
373 xew, φανερὸν ὅτι καὶ παντὶ àv ἐνδέχοιτο τῷ A ὑπάρχειν.
“- * ^ > A » , ~ M > f ^
τοῦτο δὲ ψεῦδος- od ycp εἰ τόδε τῷδε παντὶ ἐνδέχεται, Kal
τόδε τῷδε ἀναγκαῖον: ὥστ᾽ οὐκ ἀντιστρέφει τὸ στερητικόν.
ἔτι δ᾽ οὐδὲν κωλύει τὸ μὲν Α τῷ Β ἐνδέχεσθαι μηδενί, τὸ δὲ
X ~ , 3 ΄ * [4 , ^ * M
s B τινὶ τῶν A ἐξ ἀνάγκης μὴ ὑπάρχειν, οἷον τὸ μὲν λευκὸν
παντὶ ἀνθρώπῳ ἐνδέχεται μὴ ὑπάρχειν (καὶ γὰρ ὑπάρχειν),
»w 0 LI 3 > θὲ , ^ € > , ' ^
ἄνθρωπον δ᾽ οὐκ ἀληθὲς εἰπεῖν ws ἐνδέχεται μηδενὶ λευκῷ"
πολλοῖς γὰρ ἐξ ἀνάγκης οὐχ ὑπάρχει, τὸ δ᾽ ἀναγκαῖον
b20 7e? om. » 21 τοῦ Οἱ 22 ὁ οἵη. π 24-5 δῆλον...
σχημάτων codd. ALP: secl. Maier 24 ὅτι kai C oi] εἰσὶν of C 26
δευτέρῳ] Bn λαμβάνωνται C*n* Al 31 τῆς om. C 33 mpord-
σεων -[- ὅσα yap ἐπὶ τοῦ ὑπάρχοντος xai ἐνδεχομένου εἴρηται ταῦτα καὶ ἐπὶ τούτων
ῥηθήσεται d 34 ἐν ABAAISPS: καὶ ἐν Cn 36 τῷ ACT: τῶν
4*BdnP καὶ οτὰ, ἃ 37 16 ABdnT': τῶν CP 38 ràvan 39-
40 καὶ... ἀντικείμεναι codd. FAP: susp. Becker 37?1 dv om. Ad:
post ἐνδέχοιτο B τῷ ΑἹ τὸ Bro a AB: καὶ B ro y T 3 ox 4- dv
Ada ἀντιστρέφοι 45 Bln 6 γὰρ ὑπάρχει C
16. 36°17-17. 3739
3 T J Fs
οὐκ ἦν ἐνδεχόμενον.
᾿Αλλὰ μὴν οὐδ᾽ ἐκ τοῦ ἀδυνάτου δειχθήσε-
> L4 L4 3 , > 4 ^ * > fa
ται ἀντιστρέφον, olov εἴ τις ἀξιώσειεν, ἐπεὶ ψεῦδος τὸ ἐνδέ-
χεσθαι τὸ Β τῷ Α μηδενὶ ὑπάρχειν, ἀληθὲς τὸ μὴ ἐνδέχε-
σθαι μηδενί (φάσις γὰρ καὶ ἀπόφασις), εἰ δὲ τοῦτ᾽, ἀληθὲς
> > , * ~ € , - A ἢ 4
ἐξ ἀνάγκης τινὶ TQ A ὑπάρχειν. ὥστε kai τὸ A τινὶ
~ ~ > > , > 4 * * 3 , ^
TQ B- τοῦτο δ᾽ ἀδύνατον. οὐ yap «i μὴ ἐνδέχεται μηδενὶ
τὸ Β τῷ A, ἀνάγκη τινὶ ὑπά ) γὰρ μὴ ἐνδέχεσθ
D A, γκὴ τινὶ ὑπάρχειν. τὸ yap μὴ ἐνδέχεσθαι
μηδενὶ διχῶς λέγεται, τὸ μὲν εἰ ἐξ ἀνάγκης τινὶ ὑπάρχει,
τὸ δ᾽ εἰ ἐξ ἀνάγκης τινὲ μὴ ὑπάρχει: τὸ γὰρ ἐξ ἀνάγκης
M ~ 4 [4 , 2 2 X > ^ « M > ,
τινὶ τῶν A μὴ ὑπάρχον οὐκ ἀληθὲς εἰπεῖν ὡς παντὶ ἐνδέχεται
μὴ ὑπάρχειν, ὥσπερ οὐδὲ τὸ τινὶ ὑπάρχον ἐξ ἀνάγκης ὅτι
^ ? f € LA > T 3 , , M » > 4
παντὶ ἐνδέχεται ὑπάρχειν. εἰ οὖν τις ἀξιοίη, ἐπεὶ οὐκ ἐνδέχε-
ται τὸ Γ τῷ 4 παντὶ ὑπάρχειν, ἐξ ἀνάγκης τινὶ μὴ ὑπάρχειν
> , ^ ^ , A ^ t , » ? ν
αὐτό, ψεῦδος ἂν λαμβάνοι: παντὶ γὰρ ὑπάρχει, ἀλλ᾽ ὅτι
* Wk , 5 , * s ^ =f , ^ 2 K
ἐνίοις ἐξ ἀνάγκης ὑπάρχει, διὰ τοῦτό φαμεν ov παντὶ evde-
χεσθαι. ὥστε τῷ ἐνδέχεσθαι παντὶ ὑπάρχειν τό 7° ἐξ ἀνάγ-
Kns τινὶ ὑπάρχειν ἀντίκειται καὶ τὸ ἐξ ἀνάγκης τινὶ μὴ ὑπάρ-
L4 , M 3 ~ ? , £s ^ T " *
xew. ὁμοίως δὲ καὶ τῷ ἐνδέχεσθαι μηδενί. δῆλον οὖν ὅτι πρὸς
τὸ οὕτως ἐνδεχόμενον καὶ μὴ ἐνδεχόμενον ὡς ἐν ἀρχῇ διωρί-
, * , > , * L4 ta > x A H > ,
σαμεν od τὸ ἐξ ἀνάγκης Twi ὑπάρχειν ἀλλὰ τὸ ἐξ ἀνάγκης
^ A 0€ , , Po Xx LA LENS! a
τινὶ μὴ ὑπάρχειν ληπτέον. τούτου δὲ ληφθέντος οὐδὲν συμβαίνει
ἀδύνατον, ὥστ᾽ οὐ γίνεται συλλογισμός. φανερὸν οὖν ἐκ τῶν εἰ-
ρημένων ὅτι οὐκ ἀντιστρέφει τὸ στερητικόν.
Τούτου δὲ δειχθέντος κείσθω τὸ Α τῷ μὲν Β ἐνδέχεσθαι
" ^ j D M Y 4. a 5 ^ , LJ
μηδενί, τῷ δὲ Γ παντί. διὰ μὲν οὖν τῆς ἀντιστροφῆς οὐκ ἔσται
συλλογισμός: εἴρηται γὰρ ὅτι οὐκ ἀντιστρέφει ἡ τοιαύτη πρό-
τασις. ἀλλ᾽ οὐδὲ διὰ τοῦ ἀδυνάτου- τεθέντος γὰρ τοῦ B «μὴ» παντὶ
τῷ Γ᾿ ἐνδέχεσθαι «μὴ» ὑπάρχειν οὐδὲν συμβαίνει ψεῦδος - ἐνδέ-
χοιτο. γὰρ ἂν τὸ A τῷ Γ᾽ καὶ παντὶ καὶ μηδενὶ ὑπάρχειν.
ὅλως δ᾽ εἰ ἔστι συλλογισμός, δῆλον ὅτι τοῦ ἐνδέχεσθαι ἂν
LÀ \ M , ~ [4 Wa , ^ L4 ,
εἴη διὰ τὸ μηδετέραν τῶν προτάσεων εἰλῆφθαι ἐν τῷ ὑπάρ-
812 κατάφασις yap C 13 ἐξὶ καὶ ἐξ B τῷ ΓΑ͂Ι: τῶν codd. P
ὑπάρχειν) τὸ B ὑπάρχειν A: ὑπάρξειν τὸ BC : ὑπάρχει τὸ Bn: ὑπάρχει D 14
τῷ mI Al: τῶν ABCdnP 15 τῶν a ἐξ ἀνάγκης τινὶ ὑπάρχει ( 16 εἰ
om. δὶ ὑπάρχει... .. 17 τινὶ om. A 16 ὑπάρχειν C1 17 ὑπάρχειν
Cl: ὑπάρχῃ n 22 ὑπάρχει- εἰ τύχοι n 23 ἐνίοις dnI P : ἐν ἐνίοις
Px) X X 3
ABC 25 ónápyew! om. d 26 τὸ C1 28 οὐ ACTA: οὐ
μόνον BdnP τινὶ - μὴ πὶ ἀλλὰ 441: -F καὶ BCdnP 35 μὴ adi.
Maier: om. codd. ΑἹΡ 36 μὴ coni. Al: om. codd. P οὐδενὶ n!
38 <i] ἐπεὶ πὶ
4985 K
9
9
To
ANAAYTIKQN TIPOTEPQN A
‘ T bal x ^ , 2 , , >
4o X€w, Kal οὗτος ἢ καταφατικὸς ἢ στερητικός" οὐδετέρως δ᾽ ἐγ-
b a ~ X * θέ ὃ 05 4 ~
37> χωρεῖ. καταφατικοῦ μὲν yap τεθέντος δειχθήσεται διὰ τῶν
ὅρων ὅτι οὐκ ἐνδέχεται ὑπάρχειν, στερητικοῦ δέ, ὅτι τὸ συμ-
πέρασμα οὐκ ἐνδεχόμενον ἀλλ᾽ ἀναγκαῖόν ἐστιν. ἔστω γὰρ τὸ
μὲν A λευκόν, τὸ δὲ B ἄνθρωπος, ef? ᾧ δὲ I ἵππος. τὸ
^ 4 , », , ^ ^ 3; ~ ^ A
«δὴ A, τὸ λευκόν, ἐνδέχεται TH μὲν παντὶ τῷ δὲ μηδενὶ
€ , > A ν᾿ ^ L4 [4 , > , LÀ M
ὑπάρχειν. ἀλλὰ τὸ B τῷ Γ οὔτε ὑπάρχειν ἐνδέχεται οὔτε μὴ
ὑπάρχειν. ὅτι μὲν οὖν ὑπάρχειν οὐκ ἐγχωρεῖ, φανερόν: οὐδεὶς
^ " » > > 39> ? ΄ ^ [4 rg
yap ἵππος ἄνθρωπος. ἀλλ᾽ οὐδ᾽ ἐνδέχεσθαι μὴ ὑπάρχειν"
ἀνάγκη γὰρ μηδένα ἵππον ἄνθρωπον εἶναι, τὸ δ᾽ ἀναγκαῖον
ro 00K ἦν ἐνδεχόμενον. οὐκ ἄρα γίνεται συλλογισμός. ὁμοίως
δὲ δειχθήσεται καὶ ἂν ἀνάπαλιν τεθῇ τὸ στερητικόν, κἂν ἀμ-
, M ^ hl , ‘ M
φότεραι καταφατικαὶ ληφθῶσιν ἢ στερητικαί (διὰ γὰρ
τῶν αὐτῶν ὅρων ἔσται ἡ ἀπόδειξις)" καὶ ὅταν ἡ μὲν καθόλου
t , * , - » , A , “a > , -^ €
ἡ δ᾽ ἐν μέρει, 7) ἀμφότεραι κατὰ μέρος ἢ ἀδιόριστοι, ἢ ὁσα-
~ L4 > , ^ M , >. 4
15 χῶς ἄλλως ἐνδέχεται μεταλαβεῖν τὰς προτάσεις: ἀεὶ yap
L4 A ~ > Lal Ld € > P M a " >
ἔσται διὰ τῶν αὐτῶν ὅρων ἡ ἀπόδειξις. φανερὸν οὖν ὅτι ἀμ-
φοτέρων τῶν προτάσεων κατὰ τὸ ἐνδέχεσθαι τιθεμένων οὐδεὶς
γίνεται συλλογισμός.
Εἰ δ᾽ ἡ μὲν ὑπάρχειν ἡ δ᾽ ἐνδέχεσθαι σημαίνει, τῆς
20 μὲν κατηγορικῆς ὑπάρχειν τεθείσης τῆς δὲ στερητικῆς ἐνδέ-
σθ ὑδέποτ᾽ é dA ós, oU θό Ὧν ὅ
χεσθαι οὐδέποτ᾽ ἔσται συλλογισμός, οὔτε καθόλου τῶν ὅρων
LORI , , , > ΄ 3 € , A M A
οὔτ᾽ ἐν μέρει λαμβανομένων (ἀπόδειξις δ᾽ ἡ αὐτὴ Kai διὰ
τῶν αὐτῶν ὅρων): ὅταν δ᾽ ἡ μὲν καταφατικὴ ἐνδέχεσθαι ἡ
δὲ στερητικὴ ὑπάρχειν, ἔσται συλλογισμός. εἰλήφθω γὰρ τὸ
^ M * e , ~ LY * » ,
2A τῷ μὲν B μηδενὶ ὑπάρχειν, τῷ δὲ D παντὶ ἐνδέχεσθαι.
> fs T -^ ~ M ^ > ^ 4 ,
ἀντιστραφέντος οὖν τοῦ στερητικοῦ τὸ B τῷ A οὐδενὶ ὑπάρξει"
τὸ δὲ A mavr τῷ l' ἐνεδέχετο: γίνεται δὴ συλλογισμὸς
L4 ᾽ , ^ ^ ^ M ^ ’ ,
ὅτι ἐνδέχεται τὸ Β μηδενὶ τῷ Γ διὰ τοῦ πρώτου σχήματος.
[4 , ‘ x , M ^ , ^ , >. > >
ὁμοίως δὲ καὶ εἰ πρὸς τῷ Γ τεθείη τὸ στερητικόν. ἐὰν δ᾽ ἀμ-
φότεραι μὲν ὦσι στερητικαί, σημαίνῃ δ᾽ ἡ μὲν μὴ ὑπάρχειν
€ ? > Li , LN * ^ » La
ἡ δ᾽ ἐνδέχεσθαι, δι’ αὐτῶν μὲν τῶν εἰλημμένων
οὐδὲν συμβαίνει ἀναγκαῖον, ἀντιστραφείσης δὲ τῆς κατὰ τὸ
ἐνδέχεσθαι προτάσεως γίγνεται συλλογισμος ὅτι τὸ Β τῷ
Γ ἐνδέχεται μηδενὶ ὑπάρχειν, καθάπερ ἐν τοῖς πρότερον"
o
3
b8 ἄνθρωπος ἵππος d. ἐνδέχεται ri 11 dvom. d καὶ A 13
ἐστὶν d 15 μεταβαλεῖν C : μεταβάλλειν Ad 16 ὅτι om. d 19
σημαίνοι C 20 τιθεμένης C 26 ἀντιστρέφοντος d ὑπάρχει A Bd
29 δὲ om. C 30 σημαίνει C μὴ om. Cr 31 evddxeo8ar+ μὴ
ὑπάρχειν B
18
17. 37°40-19. 38°27
v A , * ~ ~ LAT » $3 ,
ἔσται yap πάλιν τὸ πρῶτον σχῆμα. ἐὰν δ᾽ ἀμφότεραι Te- 35
θῶσι κατηγορικαΐ, οὐκ ἔσται συλλογισμός. ὅροι τοῦ μὲν ὑπάρ-
χειν ὑγίεια--ζῷον -ἄνθρωπος, τοῦ δὲ μὴ ὑπάρχειν ὑγίεια--
ἵππος- ἄνθρωπος.
a $, ^ * , φ > 4 ^ > 4,
Tov αὐτὸν δὲ τρόπον ἕξει κἀπὶ τῶν ἐν μέρει συλλογι-
σμῶν. ὅταν μὲν yap f] τὸ καταφατικὸν ὑπάρχον, εἴτε κα- 4o
θόλου εἴτ᾽ ἐν μέρει ληφθέν, οὐδεὶς ἔσται συλλογισμός (τοῦτο 385
δ᾽ ὁμοίως καὶ διὰ τῶν αὐτῶν ὅρων δείκνυται τοῖς πρότερον),
ὅταν δὲ τὸ στερητικόν, ἔσται διὰ τῆς ἀντιστροφῆς, καθάπερ
*, - , , Lal L4 ^ ^ ,
ἐν τοῖς πρότερον. πάλιν, ἐὰν ἄμφω μὲν τὰ διαστήματα στερη-
A ~ , ^ ^ M e , > », ~ M
τικὰ ληφθῇ, καθόλου δὲ TO μὴ ὑπάρχειν, ἐξ αὐτῶν μὲν
wm
τῶν προτάσεων οὐκ ἔσται τὸ ἀναγκαῖον, ἀντιστραφέντος δὲ τοῦ
> , , ᾽ ^ Ld wv ,
ἐνδέχεσθαι καθάπερ ἐν τοῖς πρότερον ἔσται συλλογισμός.
vA A € , A T^ A , > , ‘ ^ >
ἐὰν δὲ ὑπάρχον μὲν jj τὸ στερητικόν, ἐν μέρει δὲ ληφθῇ, οὐκ
ἔσται συλλογισμός, οὔτε καταφατικῆς οὔτε στερητικῆς οὔσης
^ Hi , £z 0.» 4 > , ^ 2 ,
τῆς ἑτέρας προτάσεως. οὐδ᾽ ὅταν ἀμφότεραι ληφθῶσιν ἀδιό- 10
ριστοι--ἢ καταφατικαὶ ἢ ἀποφατικαί--- κατὰ μέρος. ἀπό-
δειξις δ᾽ ἡ αὐτὴ καὶ διὰ τῶν αὐτῶν ὅρων.
ori} ρω
>
19 Ἐὰν δ᾽ ἡ μὲν ἐξ ἀνάγκης ἡ δ᾽ ἐνδέχεσθαι σημαίνῃ
τῶν προτάσεων, τῆς μὲν στερητικῆς ἀναγκαίας οὔσης ἔσται
συλλογισμός, οὐ μόνον ὅτι ἐνδέχεται μὴ ὑπάρχειν, ἀλλὰ τς
* a » L4 , ^ * - , L4 ,
καὶ ὅτι ody ὑπάρχει, THs δὲ καταφατικῆς οὐκ ἔσται. κείσθω
A A ^ * 3 3 , * e , ^ δὲ
γὰρ τὸ Α τῷ μὲν Β ἐξ ἀνάγκης μηδενὶ ὑπάρχειν, τῷ δὲ
Γ παντὶ ἐνδέχεσθαι. ἀντιστραφείσης οὖν τῆς στερητικῆς οὐδὲ
τὸ B rà A οὐδενὶ ὑπάρξει: τὸ δὲ A παντὶ τῷ Γ ἐνεδέχετο"
, δὲ , ^ ^ * , Li ^
γίνεται δὴ πάλιν διὰ τοῦ πρώτου σχήματος ὁ συλλογισμὸς 20
LÀ t ^ » , ^ L4 , LA ' ^
ὅτι τὸ B τῷ Γ᾽ ἐνδέχεται μηδενὶ ὑπάρχειν. ἅμα δὲ δῆλον
* +> € » ^ , H ^ FL , \ €
ὅτι οὐδ᾽ ὑπάρξει τὸ B οὐδενὶ τῷ D. κείσθω yap ὑπάρχειν"
, ~ > A ^ Ν, > a M] M € ,
οὐκοῦν εἰ τὸ A τῷ B μηδενὶ ἐνδέχεται, τὸ δὲ B ὑπάρχει
τινὶ τῷ Γ, τὸ A τῷ Γ᾽ τινὶ οὐκ ἐνδέχεται. ἀλλὰ παντὶ ὑπέ-
> ‘ * , ^ x , , ^ »
κειτο ἐνδέχεσθαι. τὸν αὐτὸν δὲ τρόπον δειχθήσεται Kai εἰ 25
πρὸς τῷ Γ τεθείη τὸ στερητικόν. 26
Πάλιν ἔστω τὸ κατηγορικὸν 26
> ^ , > , , 5. M ~ M ,
ἀναγκαῖον, θάτερον δ᾽ ἐνδεχόμενον, καὶ τὸ A τῷ μὲν B év-
b35 πάλιν om. d 3876 room. d 88d Fun A 10 ἑτέρας
om. d£ ἀπροσδιόριστοι d 11 ἢ émoóarixa( om. A? 13
σημαίνει n 17 1688 y d 19 ὑπάρχει n 20 óom.C
22 ὑπάρχει A Bd raul: τῶν ABCdn κείσθω... 23 ἐνδέχεσθαι codd.
AIP: susp. Becker 24 rà bis Al: ràv codd. P 26 τὸξ-Ἐ μὲν πὶ
27 δὲ-Ἐ στερητικὸν καὶ n
ANAAYTIKQN TIPOTEPQN A
δεχέσθω μηδενί, τῷ δὲ D' παντὶ ὑπαρχέτω ἐξ ἀνάγκης. ov-
τως οὖν ἐχόντων τῶν ὅρων οὐδεὶς ἔσται συλλογισμός. συμ-
a ^ ^ ~ 3 3 , * € , L4 *
3o βαίνει yap τὸ B τῷ I ἐξ ἀνάγκης μὴ ὑπάρχειν. ἔστω yap
τὸ μὲν A λευκόν, ἐφ᾽ d δὲ τὸ B ἄνθρωπος, ἐφ᾽ ᾧ δὲ
τὸ Γ κύκνος. τὸ δὴ λευκὸν κύκνῳ μὲν ἐξ ἀνάγκης ὑπάρ-
3, 7 , , , , ‘ » > M
χει, ἀνθρώπῳ δ᾽ ἐνδέχεται μηδενί: καὶ ἄνθρωπος οὐδενὶ
κύκνῳ ἐξ ἀνάγκης. ὅτι μὲν οὖν τοῦ ἐνδέχεσθαι οὐκ ἔστι
, t E 4 E] > 7 , E ,
35 συλλογισμός, φανερόν: τὸ yap ἐξ ἀνάγκης οὐκ ἦν ἐνδε-
χόμενον. ἀλλὰ μὴν οὐδὲ τοῦ ἀναγκαίου: τὸ γὰρ ἀναγκαῖον
H , , ^ a
ἢ ἐξ ἀμφοτέρων ἀναγκαίων ἢ ἐκ τῆς στερητικῆς συνέβαι-
νεν. ἔτι δὲ καὶ ἐγχωρεῖ τούτων κειμένων τὸ B τῷ I ὑπάρ-
xew: οὐδὲν γὰρ κωλύει τὸ μὲν I' ὑπὸ τὸ B εἶναι, τὸ δὲ
aA τῷ μὲν B παντὶ ἐνδέχεσθαι, τῷ δὲ Γ᾽ ἐξ ἀνάγκης
€ , T , M x LJ > 4 M M ^
ὑπάρχειν, otov εἰ τὸ μὲν I’ εἴη ἐγρηγορός, τὸ δὲ B ζῷον,
AM ? » 19) * A Be ~ * ^ > , , , ,
TO δ᾽ ἐφ᾽ ᾧ τὸ A κίνησις. TH μὲν yàp ἐγρηγορότι ἐξ ἀνάγ-
38> «s κίνησις, ζῴῳ δὲ παντὶ ἐνδέχεται: καὶ πᾶν τὸ ἐγρη-
γορὸς ζῷον. φανερὸν οὖν ὅτι οὐδὲ τοῦ μὴ ὑπάρχειν, εἴ-
περ οὕτως ἐχόντων ἀνάγκη ὑπάρχειν. οὐδὲ δὴ τῶν ἀντι-
κειμένων καταφάσεων, ὥστ᾽ οὐδεὶς ἔσται συλλογισμός. ὁμοίως
* , * , , , ^ ~
5 δὲ δειχθήσεται καὶ ἀνάπαλιν τεθείσης τῆς καταφατικῆς.
'Eàv δ᾽ ὁμοιοσχήμονες ὦσιν αἱ προτάσεις, στερητικῶν μὲν
οὐσῶν ἀεὶ γίνεται συλλογισμὸς ἀντιστραφείσης τῆς κατὰ
τὸ ἐνδέχεσθαι προτάσεως καθάπερ ἐν τοῖς πρότερον. εἰ-
λήφθω γὰρ τὸ Α τῷ μὲν Β ἐξ ἀνάγκης μὴ ὑπάρχειν, τῷ
το δὲ Γ᾽ ἐνδέχεσθαι μὴ ὑπάρχειν: ἀντιστραφεισῶν οὖν τῶν προ-
, A * ^ > M t , * ^ *
τάσεων τὸ μὲν B τῷ A οὐδενὶ ὑπάρχει, τὸ δὲ A παντὶ
~ I , δέ : , δὴ 4 ~ ^ hj »
TÓ ἐνδέχεται" γίνεται σὸ πρῶτον σχῆμα. κἂν εἰ
πρὸς τῷ I τεθείη τὸ στερητικόν, ὡσαύτως. ἐὰν δὲ κατη-
γορικαὶ τεθῶσιν, οὐκ ἔσται συλλογισμός. τοῦ μὲν γὰρ μὴ
15 ὑπάρχειν ἢ τοῦ ἐξ ἀνάγκης μὴ ὑπάρχειν φανερὸν ὅτι οὐκ
ἔσται διὰ τὸ μὴ εἰλῆφθαι στερητικὴν πρότασιν μήτ᾽ ἐν τῷ
€ 4 #3 > ^ , > , L4 , > s M
ὑπάρχειν μήτ᾽ ἐν τῷ ἐξ ἀνάγκης ὑπάρχειν. ἀλλὰ μὴν
> ^ ^ , , * L4 , , 3 , ^ a
οὐδὲ τοῦ ἐνδέχεσθαι μὴ ὑπάρχειν: ἐξ ἀνάγκης yap οὕτως
, H ^ ^ , »* , , * *
ἐχόντων τὸ B τῷ I οὐχ ὑπάρξει, olov εἰ τὸ μὲν A re-
20 θείη λευκόν, ἐφ᾽ ᾧ δὲ τὸ B κύκνος, τὸ δὲ I ἄνθρωπος.
Ἀ30 τῶν y d 31 τὸξ et 32 τὸϊ om. d 41 ἐγρήγορσις n 42 τὸξ
om. ABd b4 καταφάσεων n AIPY? : $áceov ABCdPvP 6 ὅμοιο-
σχήμονες ASB*CdP : ὁμοσχήμονες ABn II ὑπάρξει B 16 et 17
μηδ᾽ A
I9. 3828-20. 3013
5, , ~ > , ’ > ^ [4 1
οὐδέ ye τῶν ἀντικειμένων καταφάσεων, ἐπεὶ δέδεικται τὸ
~ , > , > € , > » A
B τῷ Γ ἐξ ἀνάγκης οὐχ ὑπάρχον. οὐκ dpa γίνεται ovA-
λογισμὸς ὅλως.
« , > L4 > ^ ^ > ) ^
Opoiws δ᾽ ἕξει κἀπὶ τῶν ev μέρει συλλογισμῶν"
ὅταν μὲν yap fj τὸ στερητικὸν καθόλου τε καὶ ἀναγκαῖον, 25
ἀεὶ συλλογισμὸς ἔσται καὶ τοῦ ἐνδέχεσθαι καὶ τοῦ μὴ
e P > , A A “- > ^ LU A ^
ὑπάρχειν (ἀπόδειξις δὲ διὰ τῆς ἀντιστροφῆς), ὅταν δὲ τὸ
^
καταφατικόν, οὐδέποτε. τὸν αὐτὸν yap τρόπον δειχθήσεται
« 4 s. ^ ὕ ^ M ^ *, ^ μὲ $055 v
ὃν καὶ ev τοῖς καθόλου, kai διὰ τῶν αὐτῶν ὅρων. οὐδ᾽ ὅταν
3 , ^ * t M x [4 , ^
ἀμφότεραι ληφθῶσι Katagatixat? Kat yap τούτου ἡ αὐτὴ 3o
ἀπόδειξις 7) καὶ πρότερον. ὅταν δὲ ἀμφότεραι μὲν στερητι-
καί, καθόλου δὲ καὶ ἀναγκαία ἡ τὸ μὴ ὑπάρχειν σημαί-
νουσα, δι᾽ αὐτῶν μὲν τῶν εἰλημμένων οὐκ ἔσται τὸ ἀναγ-
καῖον, ἀντιστραφείσης δὲ τῆς κατὰ τὸ ἐνδέχεσθαι προτά-
σεως ἔσται συλλογισμός, καθάπερ ἐν τοῖς πρότερον. ἐὰν as
> > , 3 , ^ , , ~ *, L4
δ᾽ ἀμφότεραι ἀδιόριστοι ἢ ev μέρει τεθῶσιν, οὐκ ἔσται ovÀ-
, 2 , > - > ΝΣ b * ~ , ^ e
λογισμός. ἀπόδειξις δ᾽ ἡ αὐτὴ kal διὰ τῶν αὐτῶν ὅρων.
Φανερὸν οὖν ἐκ τῶν εἰρημένων ὅτι τῆς μὲν στερητικῆῖς
τῆς καθόλου τιθεμένης ἀναγκαίας ἀεὶ γίνεται συλλογι-
M > , ^ > ὃ 7 θ 4 Lx a > M M
σμὸς οὐ μόνον τοῦ ἐνδέχεσθαι μὴ ὑπάρχειν, ἀλλὰ καὶ 4o
τοῦ μὴ ὑπάρχειν, τῆς δὲ καταφατικῆς οὐδέποτε. καὶ ὅτι
τὸν αὐτὸν τρόπον ἐχόντων ἔν τε τοῖς ἀναγκαίοις καὶ ἐν τοῖς
ὑπάρχουσι γίνεταί τε καὶ οὐ γίνεται συλλογισμός. δῆλον 505
δὲ καὶ ὅτι πάντες ἀτελεῖς οἱ συλλογισμοί, καὶ ὅτι τελει-
οὔνται διὰ τῶν προειρημένων σχημάτων.
20 Ἔν δὲ τῷ τελευταίῳ σχήματι καὶ ἀμφοτέρων ἐν-
δεχομένων καὶ τῆς ἑτέρας ἔσται συλλογισμός. ὅταν μὲν ς
οὖν ἐνδέχεσθαι σημαίνωσιν αἱ προτάσεις, καὶ τὸ συμπέρα-
Ww , , * ΩΣ ἣν M » , ε 3
opa ἔσται ἐνδεχόμενον: kai ὅταν ἡ μὲν ἐνδέχεσθαι ἡ ὃ
φ , Ld > [4 € , ~ > , LAS M T
ὑπάρχειν. ὅταν δ᾽ ἡ ἑτέρα τεθῇ ἀναγκαία, ἐὰν μὲν ἢ Ka-
^ > ^
ταφατική, οὐκ ἔσται τὸ συμπέρασμα οὔτε ἀναγκαῖον
, ? ^ ^ ,
οὔθ᾽ ὑπάρχον, ἐὰν δ᾽ jj στερητική, Tod μὴ ὑπάρχειν ἔσται το
, ,
συλλογισμός, καθάπερ καὶ ἐν τοῖς πρότερον: ληπτέον δὲ
iT Á, »
kai ἐν τούτοις ὁμοίως τὸ ἐν τοῖς συμπεράσμασιν ἐνδεχό-
μενον.
bar καταφάσεων Al: ἀντιφάνσεων A: ἀποφάνσεων A3BC : ἀντιφάσεων d:
ἀποφάσεων P : καταφάσεων καὶ ἀποφάσεων n ἐπειδὴ C 25 γὰρ om.
d 33 τὸ om. d! 39 τῆς om. 5 39*3 προειρημένων σχημάτων
ΑΒΟΆΡ: εἰρημένων σχημάτων d: ἐν τῷ προειρημένῳ σχήματι coni. Maier
8 ἡς το ἡ Cnl' τοῦ) καὶ τοῦ C II mpórepov-]- a. B. y. Cn
ANAAYTIKQN TIPOTEPQN A
Ἔστωσαν δὴ πρῶτον ἐνδεχόμεναι, καὶ τὸ A καὶ τὸ
4 - , , Li LA 3 * T > ,
15 Β παντὶ τῷ D ἐνδεχέσθω ὑπάρχειν. ἐπεὶ οὖν ἀντιστρέφει
* 4 »,» 8 P ᾿ M M ^ > ,
τὸ καταφατικὸν ἐπὶ μέρους, τὸ δὲ B παντὶ τῷ Γ᾽ ἐνδέ-
" * M ~ > , , LÀ L4 > * 4 *
χεται, καὶ τὸ Γ᾽ wi τῷ B ἐνδέχοιτ᾽ dv. wor εἰ τὸ μὲν
A παντὶ τῷ Γ᾽ ἐνδέχεται, τὸ δὲ I' τινὲ τῷ B, ἀνάγκη καὶ τὸ A
τινὶ τῷ Β ἐνδέχεσθαι: γίγνεται γὰρ τὸ πρῶτον σχῆμα. καὶ
> ^ A ’ , M ^ [4 , t A
20 εἰ TO μὲν A ἐνδέχεται μηδενὶ τῷ I" ὑπάρχειν, τὸ δὲ B
‘ ~ > , ^ 4 ^ » ΄ ‘ t ^
παντὶ τῷ I, ἀνάγκη τὸ A τινὶ τῷ B ἐνδέχεσθαι μὴ ὑπάρ-
Xew* ἔσται γὰρ πάλιν τὸ πρῶτον σχῆμα διὰ τῆς ἀντι-
στροφῆς. εἰ δ᾽ ἀμφότεραι στερητικαὶ τεθείησαν, ἐξ αὐτῶν
μὲν τῶν εἰλημμένων οὐκ ἔσται τὸ ἀναγκαῖον, ἀντιστραφει-
as Gv δὲ τῶν προτάσεων ἔσται συλλογισμός, καθάπερ ἐν
^ rd > A 4 ^ ‘ ^ > , A
τοῖς πρότερον. εἰ yàp τὸ A καὶ τὸ B τῷ Γ᾽ ἐνδέχεται μὴ
LA , ,* ~ M > ΄ t , ¥
ὑπάρχειν, ἐὰν μεταληφθῇ τὸ ἐνδέχεσθαι ὑπάρχειν, πάλιν
ἔσται τὸ πρῶτον σχῆμα διὰ τῆς ἀντιστροφῆς. εἰ δ᾽ 6 μέν
ἐστι καθόλου τῶν ὅρων ὁ δ᾽ ἐν μέρει, τὸν αὐτὸν τρόπον
3. ἐχόντων τῶν ὅρων ὅνπερ ἐπὶ τοῦ ὑπάρχειν, ἔσται τε καὶ
3 LÀ , > , 4 A * A
οὐκ ἔσται συλλογισμός. ἐνδεχέσθω yap τὸ μὲν A παντὶ
τῷ I, τὸ δὲ B τινὶ τῷ I ὑπάρχειν. ἔσται δὴ πάλιν τὸ
πρῶτον σχῆμα τῆς ἐν μέρει προτάσεως ἀντιστραφείσης" εἰ
γὰρ τὸ A παντὶ τῷ I', τὸ δὲ Γ τινὶ τῷ B, τὸ A zi
ἀετῷ B ἐνδέχεται. καὶ εἰ πρὸς τῷ BI τεθείη τὸ καθόλου,
t a ε i 4 * , 4 x * wv A
ὡσαύτως. ὁμοίως δὲ καὶ εἰ τὸ μὲν A I" στερητικὸν εἴη, τὸ
δὲ B I καταφατικόν: ἔσται γὰρ πάλιν τὸ πρῶτον σχῆμα
διὰ τῆς ἀντιστροφῆς. εἰ δ᾽ ἀμφότεραι στερητικαὶ τεθείησαν,
€ A 06. e , , , > , ~ * ~ ,
ἡ μὲν καθόλου ἡ δ᾽ ἐν μέρει, δι’ αὐτῶν μὲν τῶν εἰλημ-
39^ μένων οὐκ ἔσται συλλογισμός, ἀντιστραφεισῶν δ᾽ ἔσται, κα-
θάπερ ἐν τοῖς πρότερον. ὅταν δὲ ἀμφότεραι ἀδιόριστοι ἢ
ἐν μέρει ληφθῶσιν, οὐκ ἔσται συλλογισμός: καὶ γὰρ παντὶ
ἀνάγκη τὸ Α τῷ Β καὶ μηδενὶ ὑπάρχειν. ὅροι τοῦ ὑπάρ-
sxew ζῷον-ἄνθρωπος-λευκόν, τοῦ μὴ ὑπάρχειν ἵππος- ἄν-
θρωπος--λευκόν, μέσον λευκόν.
' Ea δὲ € ^ L4 , L4 δ᾽ , 5 , 0 ,
av δὲ ἡ μὲν ὑπάρχειν ἡ ἐνδέχεσθαι σημαίνῃ
τῶν προτάσεων, τὸ μὲν συμπέρασμα ἔσται ὅτι ἐνδέχεται
414 πρότερον C 15 τῷ βγη 16 τὸ δὲ] καὶ τὸ C 18 τῷ d: τῶν
ABCn ἀνάγκη ΟἬΓ: 0m. Βά — «oi...19 Bom. A τοτῷ Γ: τῶν ςοαά.
ἐνδέχεται A Βά 20 B+ ἐνδέχοιτο Cn 21 τὸ] καὶ τὸ Γ τῷ ABdr:
τῶν Ün 23 ἐὰν... τεθῶσιν C Al 26 γ- παντὶ C 27 τὸ] τὸ By εἰς τὸ
Ο: εἰςτὸ Γ᾽ ὑπάρχειν ABCA: μὴ ὑπάρχειν n, fort. AIP 32 r5? ΑΒάΓ
τῶν πη — 34 rà» B ACdnI" 35 τὸ By Cdn 36 yom. Γ 38 τεθῶσιν C
by ómápxew-r a. B. y. n 5 λευκὸς Ad Tod... 6 Aevxd om. x!
20. 39*14-21. 403
M »,» L4 € LÁ A ΕΣ LÀ * Uu x ,
καὶ οὐχ ὅτι ὑπάρχει, συλλογισμὸς δ᾽ ἔσται τὸν αὐτὸν TpÓ-
mov ἐχόντων τῶν ὅρων ὃν καὶ ἐν τοῖς πρότερον. ἔστωσαν γὰρ
πρῶτον κατηγορικοί, καὶ τὸ μὲν A παντὶ τῷ Γ᾽ ὑπαρχέτω,
A M * , ὧν € , 2 , ks E
τὸ δὲ D παντὶ ἐνδεχέσθω ὑπάρχειν. ἀντιστραφέντος οὖν τοῦ
BI τὸ πρῶτον ἔσται σχῆμα, καὶ τὸ συμπέρασμα ὅτι ἐν-
δέχεται τὸ A τινὶ τῷ B ὑπάρχειν. ὅτε γὰρ ἡ ἑτέρα τῶν
προτάσεων ἐν τῷ πρώτῳ σχήματι σημαίνοι ἐνδέχεσθαι, καὶ
τὸ συμπέρασμα ἦν ἐνδεχόμενον. ὁμοίως δὲ καὶ εἰ τὸ μὲν
BI ὑπάρχειν τὸ δὲ A I ἐνδέχεσθαι, καὶ εἰ τὸ μὲν A T
στερητικὸν τὸ δὲ BI κατηγορικόν, ὑπάρχοι δ᾽ ὁποτερονοῦν,
ἀμφοτέρως ἐνδεχόμενον ἔσται τὸ συμπέρασμα: γίνεται γὰρ
πάλιν τὸ πρῶτον σχῆμα, δέδεικται δ᾽ ὅτι τῆς ἑτέρας προ-
τάσεως ἐνδέχεσθαι σημαινούσης ἐν αὐτῷ καὶ τὸ συμπέρασμα
ἔσται ἐνδεχόμενον. εἰ δὲ τὸ στερητικὸν τεθείη πρὸς
A w Ld -^ * L4 , , »
τὸ ἔλαττον ἄκρον, ἢ kai ἀμῴφω ληφθείη στερητικά, δι
αὐτῶν μὲν τῶν κειμένων οὐκ ἔσται συλλογισμός, ἀντιστρα-
φέντων δ᾽ ἔσται, καθάπερ ἐν τοῖς πρότερον.
’ , t A * ~ , € , » ,
Ei δ᾽ ἡ μὲν καθόλου τῶν προτάσεων ἡ δ᾽ ἐν μέρει,
κατηγορικῶν μὲν οὐσῶν ἀμφοτέρων, ἢ τῆς μὲν καθόλου
στερητικῆς τῆς δ᾽ ἐν μέρει καταφατικῆς, 6 αὐτὸς τρόπος
ἔσται τῶν συλλογισμῶν: πάντες γὰρ περαίνονται διὰ τοῦ
πρώτου σχήματος. ὥστε φανερὸν ὅτι τοῦ ἐνδέχεσθαι καὶ οὐ
~ € , L4 e , 5 > € A ii
τοῦ ὑπάρχειν ἔσται ὁ συλλογισμός. εἰ δ᾽ ἡ μὲν καταφατικὴ
καθόλον ἡ δὲ στερητικὴ ἐν μέρει, διὰ τοῦ ἀδυνάτου ἔσται
Li 2 58 e , M x A B M ^ D ^ A
ἡ ἀπόδειξις. ὑπαρχέτω yap τὸ μὲν B παντὶ τῷ FD, τὸ δὲ
2 Li A ^ Al e L4 > 4 zx X >
A ἐνδεχέσθω τινὶ τῷ I μὴ ὑπάρχειν: ἀνάγκη δὴ τὸ A év-
δέχεσθαι rwi τῷ B μὴ ὑπάρχειν. εἰ γὰρ παντὶ τῷ B τὸ
Α « , > > 74 A A M ^ ^ L4 ,ὕ
ὑπάρχει ἐξ ἀνάγκης, τὸ 86 B παντὶ τῷ Γ᾽ κεῖται ὑπάρ-
M εἶ ^ 3, tJ rà € , ^ A
xew, τὸ A παντὶ τῷ I ἐξ ἀνάγκης ὑπάρξει: τοῦτο yap
, 3 , [4 , M > , A
δέδεικται πρότερον. ἀλλ᾽ ὑπέκειτο τινὶ ἐνδέχεσθαι μὴ
ὑπάρχειν.
, > , J» ^
Ὅταν δ᾽ ἀδιόριστοι ἢ ἐν μέρει ληφθῶσιν ἀμφότεραι,
, ν , 2 [4 > € LEA ^ M 3 a
οὐκ ἔσται συλλογισμός. ἀπόδειξις δ᾽ ἡ αὐτὴ 7) Kal ἐν τοῖς
πρότερον, καὶ διὰ τῶν αὐτῶν ὅρων.
bro ὃν καὶ ἐν ABAAI*: ὡς ἐν C: ὃν ἐν ': om. m 12 παντὶ τῷ y C
14 r&v B ABdnT 16 ἦν om. A 17 BD... pévom. nb ὑπάρχει n?
2276 n AIP: - ἐνδεχόμενον ABCd, coni. P. 316 0m. AC 33 τῷ μὲν πὶ
34 τινὶ τῷ B ἐνδέχεσθαι ( 36 ὑπάρχοι Cn 4071 ἀόριστοι A 2 ἐν τοῖς
πρότερον sCrlpsi: ἐν τοῖς καθόλου codd. ALP: ἐπὶ τῶν ἐξ ἀμφοτέρων ἐνδε-
χομένων coni. Al
IO
15
20
25
3o
35
40*
ANAAYTIKQN IIPOTEPON A
» 3 , X e M $ , ~ , € 3 2
Εἰ δ᾽ ἐστὶν ἡ μὲν ἀναγκαία τῶν προτάσεων ἡ δ᾽ ἐν- 22
5 δεχομένη, κατηγορικῶν μὲν ὄντων τῶν ὅρων ἀεὶ τοῦ ἐνδέχε-
σθαι ἔσται συλλογισμός, ὅταν δ᾽ ἦ τὸ μὲν κατηγορικὸν τὸ
δὲ στερητικόν, ἐὰν μὲν ἦ τὸ καταφατικὸν ἀναγκαῖον, τοῦ ἐν-
δέχεσθαι μὴ ὑπάρχειν, ἐὰν δὲ τὸ στερητικόν, καὶ τοῦ ἐνδέ-
χεσθαι καὶ τοῦ μὴ ὑπάρχειν. τοῦ δ᾽ ἐξ ἀνάγκης
10 μὴ ὑπάρχειν οὐκ ἔσται συλλογισμός, ὥσπερ οὐδ᾽ ἐν τοῖς
€
ἑτέροις σχήμασιν.
LÀ M i] ^ € σ
Ἔστωσαν δὴ κατηγορικοὶ πρῶτον οἱ ὅροι,
4 ‘A b x ^ € Hi > > * 4 ^
καὶ τὸ μὲν A παντὶ τῷ I ὑπαρχέτω ἐξ ἀνάγκης, τὸ δὲ
Β M 4 25 , 0 [4 , » M - M Lo A A
παντὶ ἐνδεχέσθω ὑπάρχειν. ἐπεὶ οὖν τὸ μὲν παντὶ
τῷ l' ἀνάγκη, τὸ δὲ TI rwi τῷ B ἐνδέχεται, καὶ τὸ A
is τινὶ τῷ B ἐνδεχόμενον ἔσται καὶ οὐχ ὑπάρχον: οὕτω γὰρ
συνέπιπτεν ἐπὶ τοῦ πρώτου σχήματος. ὁμοίως δὲ δειχθήσε-
ται καὶ εἰ τὸ μὲν BI τεθείη ἀναγκαῖον, τὸ 8€ A I év-
δεχόμενον. πάλιν ἔστω τὸ μὲν κατηγορικὸν τὸ δὲ στερητικόν,
ἀναγκαῖον δὲ τὸ κατηγορικόν: καὶ τὸ μὲν A ἐνδεχέσθω μη-
M ^ [4 , M *. A t L4 2 3 ᾽ὔ
2ο δενὲ τῷ I ὑπάρχειν, τὸ δὲ B παντὲ ὑπαρχέτω ἐξ ἀνάγ-
Kns. ἔσται δὴ πάλιν τὸ πρῶτον σχῆμα: καὶ γὰρ ἡ στερη-
τικὴ πρότασις ἐνδέχεσθαι σημαίνει: φανερὸν οὖν ὅτι τὸ συμ-
πέρασμα ἔσται ἐνδεχόμενον: ὅτε γὰρ οὕτως ἔχοιεν αἱ προ-
τάσεις ἐν τῷ πρώτῳ σχήματι, καὶ τὸ συμπέρασμα ἦν
,ὔ
25 ἐνδεχόμενον. εἰ δ᾽ ἡ στερητικὴ πρότασις ἀναγκαία, τὸ συμ-
πέρασμα ἔσται καὶ ὅτι ἐνδέχεται τινὶ μὴ ὑπάρχειν καὶ ὅτι
, ? , J AS M ^ A e a , 2 ᾽ὔ
οὐχ ὑπάρχει. κείσθω γὰρ τὸ Α τῷ Γ μὴ ὑπάρχειν ἐξ ἀνάγ-
κης, τὸ δὲ B παντὶ ἐνδέχεσθαι. ἀντιστραφέντος οὖν τοῦ B
Γ καταφατικοῦ τὸ πρῶτον ἔσται σχῆμα, καὶ ἀναγκαία ἡ
30 στερητικὴ πρότασις. ὅτε δ᾽ οὕτως ἔχοιεν αἱ προτάσεις, συνέ-
i] e^ ‘A x d * * * L4 , x ^
Bowe τὸ A τῷ Γ᾽ kai ἐνδέχεσθαι τινὲ μὴ ὑπάρχειν καὶ μὴ
ὑπάρχειν, ὥστε καὶ τὸ A τῷ Β ἀνάγκη τινὶ μὴ ὑπάρχειν.
ὅταν δὲ τὸ στερητικὸν τεθῇ πρὸς τὸ ἔλαττον ἄκρον, ἐὰν μὲν
» P L4 ^ , ^ ,
ἐνδεχόμενον, ἔσται συλλογισμὸς μεταληφθείσης τῆς mpord-
^ 4 LÀ
35 σεως, καθάπερ ἐν τοῖς πρότερον, ἐὰν δ᾽ ἀναγκαῖον, οὐκ ἔσται"
σ
καὶ γὰρ παντὶ ἀνάγκη καὶ οὐδενὶ ἐνδέχεται ὑπάρχειν. ὅροι
88 ἐνδέχεσθαι ἩΓ: +H ὑπάρχειν ABCA 11 δὴ] γὰρ δὴ d 13
παντὶ] τῷ y παντὶ A: παντὶ τῷ yn 1 ΒΓΙβτῷγ Γ 20 τῷ ^
CnT: τῶν ABdP παντὶ τῷ y C 21 γὰρ codd. Al*: secl. Tredennick
25 τὸ] καὶ τὸ C 28 παντὶ τῷγοα 29 καὶ -- yap C 30 εἶχον
fmP¢ συμβαίνει d 31 καὶ μὴ ὑπάρχειν om. A 32 Kat
om. C
22. 40°4-23. 40°30
^ a [4 Fa Ld e a L4 ^
τοῦ παντὶ ὑπάρχειν Ümvos-Urmos καθεύδων-ἄνθρωπος, τοῦ
μηδενὶ ὕπνος--ππος ἐγρηγορώς- ἄνθρωπος.
Ὅ L4 δ᾽ σ A * e * 06. -^ ν L4 ΕἸ
roles ἔξει kai εἰ ὃ μὲν καθόλου τῶν ὅρων ὃ ὃ
ἐν μέρει πρὸς τὸ μέσον: κατηγορικῶν. μὲν γὰρ ὄντων ἀμ- 40
, a 3 δέ 0 E > - € 7 Pj λλ o>
ἔρων τοῦ ἐνδέχεσθαι καὶ οὐ τοῦ ὑπάρχειν ἔσται συλλογι- 4
, M L4 A] A 4 05 M] A
σμός, kal ὅταν τὸ μὲν στερητικὸν ληφθῇ τὸ δὲ καταῴφα-
τικον, ἀναγκαῖον δὲ τὸ καταφατικόν. ὅταν δὲ τὸ στερητικὸν
ἀναγκαῖον, καὶ τὸ συμπέρασμα ἔσται τοῦ μὴ ὑπάρχειν: ὁ γὰρ
» \ / L4 ^ id M , M M ,
αὐτὸς τρόπος ἔσται τῆς δείξεως kai καθόλου Kal μὴ καθόλου 5
τῶν ὅρων ὄντων. ἀνάγκη γὰρ διὰ τοῦ πρώτου σχήματος τε-
λειοῦσθαι τοὺς συλλογισμούς, ὥστε καθάπερ ἐν ἐκείνοις, καὶ
> 3
ἐπὶ τούτων ἀναγκαῖον συμπίπτειν. ὅταν δὲ τὸ στερητικὸν
00A λ θὲ θῃ ^ s EX » »* M »
καθόλου ληφθὲν τεθῇ πρὸς τὸ ἔλαττον ἄκρον, ἐὰν μὲν év-
δεχόμενον, ἔσται συλλογισμὸς διὰ τῆς ἀντιστροφῆς, ἐὰν δ᾽ το
ἀναγκαῖον, οὐκ ἔσται. δειχθήσεται δὲ τὸν αὐτὸν τρόπον ὃν
καὶ ἐν τοῖς καθόλου, καὶ διὰ τῶν αὐτῶν ὅρων. φανερὸν
- ‘ LJ ^ ^
οὖν Kal ἐν τούτῳ τῷ σχήματι πότε kai πῶς ἔσται συλλο-
γισμός, καὶ πότε τοῦ ἐνδέχεσθαι καὶ πότε τοῦ ὑπάρχειν.
δῆλον δὲ καὶ ὅτι πάντες ἀτελεῖς, καὶ ὅτι τελειοῦνται διὰ 15
τοῦ πρώτου σχήματος.
Ὅ A - * 2 , -^ tA Ao =
23 T. μὲν οὖν of ἐν τούτοις τοῖς σχήμασι συλλογι
* ~ , A ~ > ~ , ,
cuoi τελειοῦνταί τε διὰ τῶν ἐν TH πρώτῳ σχήματι καθόλου
- ~ ^ ,
συλλογισμῶν καὶ εἰς τούτους ἀνάγονται, δῆλον ἐκ τῶν εἰ-
ρημένων: ὅτι δ᾽ ἁπλῶς πᾶς συλλογισμὸς οὕτως ἕξει, νῦν 20
ἔσται φανερόν, ὅταν δειχθῇ πᾶς γινόμενος διὰ τούτων τινὸς
τῶν σχημάτων.
᾿Ανάγκη δὴ πᾶσαν ἀπόδειξιν καὶ πάντα συλλογισμὸν
ἢ ὑπάρχον τι ἢ μὴ ὑπάρχον δεικνύναι, καὶ τοῦτο ἢ καθόλου
- M , v -* ^ - > € , ^ , ?
ἢ κατὰ μέρος, ἔτι ἢ δεικτικῶς ἢ ἐξ ὑποθέσεως. τοῦ δ᾽ ἐξ 25
ὑποθέσεως μέρος τὸ διὰ τοῦ ἀδυνάτου. πρῶτον οὖν εἴπω-
μεν περὶ τῶν δεικτικῶν: τούτων γὰρ δειχθέντων φανερὸν
v M 9». 4 ^ > A 3 , * Ld ^ > €
ἔσται kai ἐπὶ τῶν els τὸ ἀδύνατον kai ὅλως τῶν ἐξ ὑπο-
θέσεως.
a ^ , n € ,
Ei δὴ δέοι τὸ A xarà τοῦ B συλλογίσασθαι ἢ ὑπάρ- 30
837 τοῦτ δὲ Cr bs kai .. . μὴ} ὥσπερ kai i "καὶ καθόλου om. Ct
καὶ μὴ... 6 ὄντων] τῶν ὅρων ὄντων ABCidD: τῶν ὅρων ὄντων xai μὴ
καθόλου B* 14 ἐνδέχεται C 17 οὖν om. ὦ 18 re om. Ad
καθόλου A Bdn* Al: om. Cn 19 ἄγονται Ad! 20 πᾶς om. Bt
ἔχει Waitz 24 τινὶ 4Γ: τί τινι Al 25-6 τοῦ... . ὑποθέσεως om. πὶ
26 μέρος -ἰ- ἐστὶ Cn τοῦ om. Β 27 τούτων γὰρ δειχθέντων om. C
ANAAYTIKQN IIPOTEPON A
xov ἢ μὴ ὑπάρχον, ἀνάγκη λαβεῖν τι κατά τινος. εἰ μὲν
οὖν τὸ Α κατὰ τοῦ Β ληφθείη, τὸ ἐξ ἀρχῆς ἔσται εἰλημ-
Li *, de A ^ I. a δὲ DI M δ , δ᾽
μένον. εἰ δὲ κατὰ τοῦ D, τὸ δὲ κατὰ μηδενός, μὴ
Là > > , x 4 ^ bd > ^ »
ἄλλο κατ᾽ ἐκείνου, μηδὲ κατὰ τοῦ A ἕτερον, οὐδεὶς ἔσται
, ^ MJ a > E—5 ^ > xX
35 συλλογισμός: τῷ yap ἕν καθ᾽ ἑνὸς ληφθῆναι οὐδὲν συμ-
βαίνει ἐξ ἀνάγκης. ὥστε προσληπτέον καὶ ἑτέραν πρότα-
σιν. ἐὰν μὲν οὖν ληφθῇ τὸ A κατ᾽ ἄλλου ἢ ἄλλο κατὰ
^ -^ i] ~ σ x X , *
ToU A, ἢ κατὰ τοῦ I ἕτερον, εἶναι μὲν συλλογισμὸν οὐδὲν
r4 Ἂν * A ᾽ wv ^ ^ » Li
κωλύει, πρὸς μέντοι τὸ B οὐκ ἔσται διὰ τῶν εἰλημμένων.
29? L4 ‘ € ^ > ^ L4 t ^ [XN À ‘
4o οὐδ᾽ ὅταν τὸ l' ἑτέρῳ, κἀκεῖνο ἄλλῳ, καὶ τοῦτο ἑτέρῳ, μὴ
41 συνάπτῃ δὲ πρὸς τὸ B, οὐδ᾽ οὕτως ἔσται πρὸς τὸ B συλ-
λογισμός. ὅλως γὰρ εἴπομεν ὅτι οὐδεὶς οὐδέποτε ἔσται
συλλογισμὸς ἄλλου κατ᾽ ἄλλου μὴ ληφθέντος τινὸς μέ-
σου, ὃ πρὸς ἑκάτερον ἔχει πως ταῖς κατηγορίαις: 6 μὲν
^ A € ~ 3 , , , e δὲ M
s yàp συλλογισμὸς ἁπλῶς ἐκ προτάσεών ἐστιν, 6 δὲ πρὸς
τόδε συλλογισμὸς ἐκ τῶν πρὸς τόδε προτάσεων, ὁ δὲ τοῦδε
A , A ~ Lej Ἂς , , 3 , ^
πρὸς τόδε διὰ τῶν τοῦδε πρὸς τόδε προτάσεων. ἀδύνατον δὲ
πρὸς τὸ Β λαβεῖν πρότασιν μηδὲν μήτε κατηγοροῦντας
?, ^ 4? ? , a , - A A
αὐτοῦ μήτ᾽ ἀπαρνουμένους, 7) πάλιν τοῦ A πρὸς τὸ B μη-
MJ ^ Li » > Li , Li LÀ
το δὲν κοινὸν λαμβάνοντας ἀλλ᾽ ἑκατέρου ἴδια ἅττα κατη-
γοροῦντας ἢ ἀπαρνουμένους. ὥστε ληπτέον τι μέσον ἀμφοῖν,
ὃ συνάψει τὰς κατηγορίας, εἴπερ ἔσται τοῦδε πρὸς τόδε συλ-
, > + > 4 , ^ 4 L4 La
λογισμός. εἰ οὖν ἀνάγκη μέν τι λαβεῖν πρὸς ἄμφω κοινόν,
LJ 3 , ’ ^ * M * ^ * 4
τοῦτο δ᾽ ἐνδέχεται τριχῶς (3 yàp τὸ A τοῦ Γ καὶ τὸ Γ
15700 B κατηγορήσαντας, 7) τὸ Γ᾽ κατ᾽ ἀμφοῖν, ἢ ἄμφω
κατὰ τοῦ I), ταῦτα δ᾽ ἐστὶ τὰ εἰρημένα σχήματα, φα-
νερὸν ὅτι πάντα συλλογισμὸν ἀνάγκη γίνεσθαι διὰ τούτων
τινὸς τῶν σχημάτων. ὁ γὰρ αὐτὸς λόγος καὶ εἰ διὰ πλει-
όνων συνάπτοι πρὸς τὸ Β' ταὐτὸ γὰρ ἔσται σχῆμα καὶ
20 ἐπὶ τῶν πολλῶν.
"Or 4 in καὶ Ld 8 ‘ , 8 a ~ ,
ι μὲν οὖν οἱ δεικτικοὶ περαίνονται διὰ τῶν προειρημέ-
, , Ld ^ ^ € > ^ , * ^
νων σχημάτων, $avepóv: ὅτι δὲ Kai of eis τὸ ἀδύνατον, δῆ-
λον ἔσται διὰ τούτων. πάντες γὰρ οἱ διὰ τοῦ ἀδυνάτου περαΐί-
Ay ^ ^
vovres τὸ μὲν ψεῦδος συλλογίζονται, τὸ δ᾽ ἐξ ἀρχῆς ἐξ
as ὑποθέσεως δεικνύουσιν, ὅταν ἀδύνατόν τι συμβαίνῃ τῆς ἀντι-
φάσεως τεθείσης, οἷον ὅτι ἀσύμμετρος ἡ διάμετρος διὰ τὸ γί-
b31 ἣ μὴ ὑπάρχον om. A} 3380 τ τὸα C 35 τὸ Ad 39 διὰ om. B!
4131 ovAdoytapds+ τοῦ a B 2 εἴπωμεν AYB 7 7681) τόνδε B!
12 65 A 17 ὅτι] οὖν ὅτι (1: ὡς d γενέσθαι d 18 εἰ om. C1
21 ot om. d
23. 40°31-24. 41520
νεσθαι τὰ περιττὰ ἴσα τοῖς ἀρτίοις συμμέτρου τεθείσης. TO μὲν
οὖν ἴσα γίνεσθαι τὰ περιττὰ τοῖς ἀρτίοις συλλογίζεται, τὸ
δ᾽ ἀσύμμετρον εἶναι τὴν διάμετρον ἐξ ὑποθέσεως δείκνυσιν,
, * ^ L4 A ^ ? 2 ~ A
ἐπεὶ ψεῦδος συμβαίνει διὰ τὴν ἀντίφασιν. τοῦτο yap ἦν
* A ~ ? , , a ^ ^ > (A
τὸ διὰ τοῦ ἀδυνάτου συλλογίσασθαι, τὸ δεῖξαί τι ἀδύνα-
A A 7 > ~ L4 , LÀ » » " ~ , Φ'
τον διὰ τὴν ἐξ ἀρχῆς ὑπόθεσιν. ὥστ᾽ ἐπεὶ τοῦ ψεύδους γί-
vera, συλλογισμὸς δεικτικὸς ἐν τοῖς εἰς τὸ ἀδύνατον ἀπ-
, A > , 2 ^ , [4 , , AY M
αγομένοις, τὸ δ᾽ ἐξ ἀρχῆς ἐξ ὑποθέσεως δείκνυται, τοὺς δὲ
, ~
δεικτικοὺς πρότερον εἴπομεν ὅτι διὰ τούτων περαίνονται τῶν
, M bd * t M ^ ,
σχημάτων, φανερὸν ὅτι καὶ of διὰ τοῦ ἀδυνάτου συλλο-
γισμοὶ διὰ τούτων ἔσονται τῶν σχημάτων. ὡσαύτως δὲ
A] Lj L4 Lj t >, € , » a X L4
καὶ οἱ ἄλλοι πάντες of ἐξ ὑποθέσεως: ἐν ἅπασι yap ὁ
A ‘ , ^ M [4 ‘
μὲν συλλογισμὸς γίνεται πρὸς τὸ μεταλαμβανόμενον, τὸ
» *, > ~ , > L4 , L4 Ld e
δ᾽ ἐξ ἀρχῆς περαίνεται δι’ ὁμολογίας ἤ τινος ἄλλης ὑπο-
rg 3 4 ~ 3 > , ^ » , * ,
θέσεως. εἰ δὲ τοῦτ᾽ ἀληθές, πᾶσαν ἀπόδειξιν καὶ πάντα
συλλογισμὸν ἀνάγκη γίνεσθαι διὰ τριῶν τῶν προειρημένων
, , x , “- ε ν
σχημάτων. τούτου δὲ δειχθέντος δῆλον ὡς ἅπας τε συλ-
λογισμὸς ἐπιτελεῖται διὰ τοῦ πρώτου σχήματος καὶ ἀν-
ἄγεται εἰς τοὺς ἐν τούτῳ καθόλου συλλογισμούς.
Ἔτι τε ἐν ἅπαντι δεῖ κατηγορικόν τινα τῶν ὅρων el-
* A , [4 Léo LZ X ^ cal ^
vat Kai τὸ καθόλου ὑπάρχειν: ἄνευ yap τοῦ καθόλου ἢ
+ LÀ 4 hal > 4 A , ^ A , >
οὐκ ἔσται συλλογισμὸς 7) οὐ πρὸς TO κείμενον, ἢ τὸ ἐξ dp-
χῆς αἰτήσεται. κείσθω γὰρ τὴν μουσικὴν ἡδονὴν εἶναι σπου-
δαίαν. εἰ μὲν οὖν ἀξιώσειεν ἡδονὴν εἶναι σπουδαίαν μὴ προσ-
θεὶς τὸ πᾶσαν, οὐκ ἔσται συλλογισμός: εἰ δὲ τινὰ ἡδο-
, , A » ᾽ b 4 ^ , > , > A
viv, εἰ μὲν ἄλλην, οὐδὲν πρὸς τὸ κείμενον, εἰ δ᾽ αὐτὴν
ταύτην, τὸ ἐξ ἀρχῆς λαμβάνει. μᾶλλον δὲ γίνεται φα-
νερὸν ἐν τοῖς διαγράμμασιν, οἷον ὅτι τοῦ ἰσοσκελοῦς ἴσαι
αἱ πρὸς τῇ βάσει. ἔστωσαν εἰς τὸ κέντρον ἠγμέναι ai A Β.
εἰ οὖν ἴσην λαμβάνοι τὴν A I' γωνίαν τῇ B 4 μὴ ὅλως
> , LÀ ^ ~ [4 , * , A
ἀξιώσας ἴσας τὰς τῶν ἡμικυκλίων, καὶ πάλιν τὴν Γ
^ ' ^ ^ M ^ , » ?,
τῇ 4 μὴ πᾶσαν προσλαβὼν τὴν τοῦ τμήματος, ἔτι ὃ
> > LÀ > ~ ^ Ld - M LJ » ,
ἀπ’ ἴσων οὐσῶν τῶν ὅλων γωνιῶν καὶ ἴσων ἀφῃρημένων
LÀ MJ ^ ^ ‘ , > ~ > f
ἴσας εἶναι tas λοιπὰς τὰς E Z, τὸ ἐξ ἀρχῆς αἰτήσε-
436 φανερὸν -᾿- οὖν Bl 40 ἄλλης τινὸς d b2 τῶν τριῶν C 5
καθόλου secl. Maier 6 ὅτι π re om. d τὸν ὅρον B 7 yàp4
ἄν C τῆς d 8 προκειμένου C 10 προσθῇ B! 12 mpoxei-
μενον Cd 15 B] y fecit B 16 λαμβάνει Cd: λαμβάνῃ d? 17 τὰς
om.d 18 προλαβὼν n δ᾽ om. A Bdn 19 ἴσων") τῶν n 20 Tas
εἴ ABCnI AIP, fecit d: secl. Waitz
30
35
40
41*
IO
I5
20
ANAAYTIKQN IIPOTEPON A
?* * 7 > 4 ~ LÀ LÀ > ,
Tat, ἐὰν μὴ λάβῃ ἀπὸ τῶν ἴσων ἴσων ἀφαιρουμένων
LÀ , ^ ? Ld > Ed ^ M ,
ἴσα λείπεσθαι. φανερὸν οὖν ὅτι ἐν ἅπαντι δεῖ τὸ καθόλου
€ rd 1 Ld * * , H t , ~ Ld
ὑπάρχειν, Kal ὅτι τὸ μὲν καθόλου ἐξ ἁπάντων τῶν ὅρων
, ; d M , > , * " » , σ >
καθόλου δείκνυται, τὸ δ᾽ ἐν μέρει καὶ οὕτως κἀκείνως, ὥστ
25 ἐὰν μὲν jj τὸ συμπέρασμα καθόλον, καὶ τοὺς ὅρους ἀνάγκη
, aA ΕΣ L4 Ld , , , M ,
καθόλου εἶναι, ἐὰν δ᾽ of ὅροι καθόλου, ἐνδέχεται τὸ συμπέ-
A , ^ ^4 mJ > "
ρασμα μὴ εἶναι καθόλου. δῆλον δὲ kai ὅτι ἐν ἅπαντι συλλογι-
σμῷ 1j ἀμφοτέρας ἣ τὴν ἑτέραν πρότασιν ὁμοίαν ἀνάγκη γίνε-
σθαι τῷ συμπεράσματι. λέγω δ᾽ οὐ μόνον τῷ καταφατικὴν
3o εἶναι 1j στερητικήν, ἀλλὰ καὶ τῷ ἀναγκαίαν ἢ ὑπάρχουσαν ἢ ἐν-
δεχομένην. ἐπισκέψασθαι δὲ δεῖ καὶ τὰς ἄλλας κατηγορίας.
Φανερὸν δὲ καὶ ἁπλῶς πότ᾽ ἔσται καὶ πότ᾽ οὐκ ἔσται
συλλογισμός, καὶ πότε δυνατὸς καὶ πότε τέλειος, καὶ ὅτι
συλλογισμοῦ ὄντος ἀναγκαῖον ἔχειν τοὺς ὅρους κατά τινα
35 τῶν εἰρημένων τρόπων.
Δῆλον δὲ καὶ ὅτι πᾶσα ἀπόδειξις ἔσται διὰ τριῶν ὅρων 25
καὶ οὐ πλειόνων, ἐὰν μὴ δι’ ἄλλων καὶ ἄλλων τὸ αὐτὸ
συμπέρασμα γίνηται, οἷον τὸ E διά τε τῶν A B καὶ διὰ
τῶν Γ A, ἢ διὰ τῶν A B καὶ AT À- πλείω γὰρ μέσα τῶν
Ἵ ~ , * L4 , 3 x > 3 A
4o αὐτῶν οὐδὲν εἶναι κωλύει. τούτων δ᾽ ὄντων οὐχ εἷς ἀλλὰ
425 πλείους εἰσὶν οἱ συλλογισμοί. ἢ πάλιν ὅταν ἑκάτερον τῶν A B
διὰ συλλογισμοῦ ληφθῇ (olov τὸ A διὰ τῶν 4 E καὶ πά-
Aw τὸ B διὰ τῶν Ζ ΘῚ, ἢ τὸ μὲν ἐπαγωγῇ, τὸ δὲ συλλογι-
~ 3 * ^ [L4 , Hi d , ^
σμῷ. ἀλλὰ καὶ οὕτως πλείους οἱ συλλογισμοί: πλείω yap
s τὰ συμπεράσματα ἐστιν, οἷον τό τε A καὶ τὸ B καὶ τὸ T.
Εἰ δ᾽ οὖν μὴ πλείους ἀλλ᾽ εἷς, οὕτω μὲν ἐνδέχεται γενέσθαι
διὰ πλειόνων τὸ αὐτὸ συμπέρασμα, ὡς δὲ τὸ I διὰ τῶν
A B, ἀδύνατον. ἔστω γὰρ τὸ E συμπεπερασμένον ἐκ τῶν
ABI A. οὐκοῦν ἀνάγκη τι αὐτῶν ἄλλο πρὸς ἄλλο εἰλῆφθαι,
^ M [3 Ld A > € , ^ ^ fl ,
1076 μὲν ws ὅλον τὸ δ᾽ ὡς μέρος: τοῦτο yap δέδεικται mpd-
τερον, ὅτι ὄντος συλλογισμοῦ ἀναγκαῖον οὕτως τινὰς ἔχειν
~ L4 3. * ^ " 4 ^ » Ld ,
τῶν ὅρων. ἐχέτω οὖν τὸ A οὕτως πρὸς τὸ B. ἔστιν dpa τι ἐξ
, ^ , , ~ Y M -^ ^ , a
αὐτῶν συμπέρασμα. οὐκοῦν ἤτοι τὸ E ἣ τῶν Γ 4 θάτερον 7j
ἄλλο τι παρὰ ταῦτα. καὶ εἰ μὲν τὸ E, ἐκ τῶν A B μό-
hl w Ld , ^ b > ^ LÀ " σ >
15 vov dv ein 6 συλλογισμός. τὰ δὲ Γ A εἰ μὲν ἔχει οὕτως ὥστ
bor τῶν om. d ἴσων om. A 27 καθόλου εἶναι d? 28 ἀνάγκη
ὁμοίως d 29T9?] ron 3oróom.n a18econi. 5D 34 Twas d!
39 AIA scripsi: By Bd: ay C ; fecit A: ay xai By BPC AIP: By καὶ ay d?
40 οὐχὶ α 4236 γίνεσθαι Cdn 8e+ron 9 dAdo? om. 1B!
12 dpa] πάντως d 144B]8/on μόνων APC 15ó6o0m.d! ἔχῃ γι
24. 41>21-25. 4210
A 4A « Ld * > LA , w ‘ , , ,
εἶναι τὸ μὲν ὡς ὅλον τὸ δ᾽ ὡς μέρος, ἔσται τι kai ἐξ ἐκεί-
νων, καὶ ἤτοι τὸ E ἣ τῶν A B θάτερον ἢ ἄλλο τι παρὰ
~ x > X ^ bal ^ , - , L4
ταῦτα. kai εἰ μὲν τὸ E ἢ τῶν A B θάτερον, 7j πλείους éaov-
€ , n t > a > a A ,
Tra. of συλλογισμοί, ἢ ὡς ἐνεδέχετο ταὐτὸ διὰ πλειόνων
e , , » ΕΣ LA x ^
ὅρων περαίνεσθαι συμβαΐει: εἰ δ᾽ ἄλλο τι παρὰ ταῦτα, 20
ἊΝ LÀ x > 4 e ^ A > δ
πλείους ἔσονται καὶ ἀσύναπτοι οἱ συλλογισμοὶ πρὸς ἀλλή-
λους. εἰ δὲ μὴ οὕτως ἔχοι τὸ Γ πρὸς τὸ 4 ὥστε ποιεῖν συλ-
λογισμόν, μάτην ἔσται εἰλημμένα, εἰ μὴ ἐπαγωγῆς ἢ κρύ-
pews ἢ τινος ἄλλου τῶν τοιούτων χάριν. 24
Ei 9 ἐκ τῶν A Ba
μὴ τὸ E ἀλλ᾽ ἄλλο .τι γίγνεται συμπέρασμα, ἐκ δὲ τῶν Ἂς
I' 4 ἢ τούτων θάτερον 7j ἄλλο παρὰ ταῦτα, πλείους τε οἱ
συλλογισμοὶ γίνονται καὶ οὐ τοῦ ὑποκειμένου: ὑπέκειτο γὰρ
^ $ , 2 M E , , ^ M
εἶναι τοῦ E τὸν συλλογισμόν. €i δὲ μὴ γίνεται ἐκ τῶν Γ 4 μηδὲν
συμπέρασμα, μάτην τε εἰλῆφθαι αὐτὰ συμβαΐει καὶ μὴ
^ * > ~ 4 , σ x Ld ~
τοῦ ἐξ ἀρχῆς εἶναι τὸν συλλογισμόν. ὥστε φανερὸν ὅτι πᾶσα 30
ἀπόδειξις καὶ πᾶς συλλογισμὸς ἔσται διὰ τριῶν ὅρων μόνον.
Τούτον δ᾽ ὄντος φανεροῦ, δῆλον ὡς καὶ ἐκ δύο προ-
τάσεων καὶ οὐ πλειόνων (οἱ γὰρ τρεῖς ὅροι δύο προτάσεις), εἰ
εἶ 4 , , » ^ > > ^ Y ὁ
μὴ προσλαμβάνοιτό τι, καθάπερ ἐν τοῖς ἐξ ἀρχῆς ἐλέχθη,
πρὸς τὴν τελείωσιν τῶν συλλογισμῶν. φανερὸν οὖν ὡς ἐν ᾧ 35
λόγῳ συλλογιστικῷ μὴ ἄρτιαί εἰσιν αἱ προτάσεις δι’ ὧν γί-
νεται τὸ συμπέρασμα τὸ κύριον (ἔνια γὰρ τῶν ἄνωθεν συμ-
περασμάτων ἀναγκαῖον εἶναι προτάσεις), οὗτος ὁ λόγος ἢ
od συλλελόγεσται ἢ πλείω τῶν ἀναγκαίων ἠρώτηκε πρὸς τὴν
θέσιν. 40
Κατὰ μὲν οὖν τὰς κυρίας προτάσεις λαμβανομένων 42>
τῶν συλλογισμῶν, ἅπας ἔσται συλλογισμὸς ἐκ προτάσεων
^ t ^
μὲν dpriwy ἐξ ὅρων δὲ περιττῶν- ἑνὶ yap πλείους οἱ ὅροι τῶν
προτάσεων. ἔσται δὲ καὶ τὰ συμπεράσματα ἡμίση τῶν προ-
τάσεων. ὅταν δὲ διὰ προσυλλογισυμῶν περαίνηται ἢ διὰ ς
πλείονων μέσων συνεχῶν, οἷον τὸ Α Β διὰ τῶν Γ 4, τὸ
μὲν πλῆθος τῶν ὅρων ὡσαύτως ἑνὶ ὑπερέξει τὰς προτάσεις
^ ^ v ^ » * , , [4 , L4
(ἢ yàp ἔξωθεν ἢ eis τὸ μέσον τεθήσεται 6 παρεμπίπτων ὅρος"
> , A L4 € Y 7 MJ /,
d épws δὲ συμβαίνει evi ἐλάττω εἶναι τὰ διαστήματα
τῶν ὅρων), αἱ δὲ προτάσεις ἴσαι τοῖς διαστήμασιν": οὐ μέντοι τὸ
521 mAeioust+reC οἱ Cn Al: om. ABd 22T98n 25 γένηται d
δὲ fecit n 26 ἣ τοῦτο B 28 τοῦ] τὸ A4! y9 ABCd AIP: αβ coni.
Al, fecit n μηδὲ ἕν n 34 τι Pl: om. codd. ἐλέχθη om. A 35
οὖν-Ἐ ὅτι π 92 ἐστὶ d 6 μέσων Cn Al: +n ΑΒΟΊΔΡ: καὶ I
ANAAYTIKQN IIPOTEPON A
αἰεὶ αἱ μὲν ἄρτιαι ἔσονται οἱ δὲ περιττοί, ἀλλ᾽ ἐναλλάξ,
ὅταν μὲν αἱ προτάσεις ἄρτιαι, περιττοὶ οἱ ὅροι, ὅταν δ᾽ οἱ
ὅροι ἄρτιοι, περιτταὶ αἱ προτάσεις: ἅμα γὰρ τῷ ὅρῳ μία
προστίθεται πρότασις, ἂν ὁποθενοῦν προστεθῇ 6 ὅρος, ὥστ᾽ ἐπεὶ
ε ^ w Lj δὲ a - > y ,
τς αἱ μὲν ἄρτιαι of δὲ περιττοὺ ἦσαν, ἀνάγκη παραλλάττειν
τῆς αὐτῆς προσθέσεως γινομένης. τὰ δὲ συμπεράσματα οὐκέτι
τὴν αὐτὴν ἕξει τάξιν οὔτε πρὸς τοὺς ὅρους οὔτε πρὸς τὰς προ-
εν a
τάσεις- ἑνὸς yàp ὅρου προστιθεμένου συμπεράσματα προσ-
, ~ m
τεθήσεται evi ἐλάττω τῶν προὐπαρχόντων ὅρων" πρὸς μόνον
20 γὰρ τὸν ἔσχατον οὐ ποιεῖ συμπέρασμα, πρὸς δὲ τοὺς dÀ-
4 » ~ , * *, AY '
λους πάντας, olov εἰ τῷ A BI πρόσκειται τὸ A, εὐθὺς Kai
συμπεράσματα δύο πρόοκειται, τό τε πρὸς τὸ A καὶ τὸ πρὸς
* B € , δὲ ? 5 ~ LÀ ^ » A , M
τὸ B. ὁμοίως δὲ κἀπὶ τῶν ἄλλων. κἂν eis TO μέσον δὲ παρ-
ἐμπίπτῃ, τὸν αὐτὸν τρόπον: πρὸς ἕνα γὰρ μόνον οὐ ποιήσει
25 συλλογισμόν. ὥστε πολὺ πλείω τὰ συμπεράσματα καὶ τῶν
ὅρων ἔσται καὶ τῶν προτάσεων.
᾿Επεὶ δ᾽ ἔχομεν περὶ ὧν οἱ συλλογισμοί, καὶ ποῖον ἐν 26
ἑκάστῳ σχήματι καὶ ποσαχῶς δείκνυται, φανερὸν ἡμῖν ἐστὶ
καὶ ποῖον πρόβλημα χαλεπὸν καὶ ποῖον εὐεπιχείρητον: τὸ
30 μὲν γὰρ ἐν πλείοσι σχήμασι καὶ διὰ πλειόνων πτώσεων πε-
, ta s δ᾽ 5» ki L4 M , » , 8
ραινόμενον ῥᾷον, TO ἐν ἐλάττοσι καὶ δι᾿ ἐλαττόνων δυσ-
# A * 7T ^ M , A ~
επιχειρητότερον. τὸ μὲν οὖν καταφατικὸν τὸ καθόλου διὰ τοῦ
πρώτου σχήματος δείκνυται μόνου, καὶ διὰ τούτου μοναχῶς"
τὸ δὲ στερητικὸν διά τε τοῦ πρώτου καὶ διὰ τοῦ μέσου, καὶ
35 διὰ μὲν fod πρώτου μοναχῶς, διὰ δὲ τοῦ μέσου διχῶς" τὸ
δ᾽ ? , ‘ 8 ~ , * ^ ~ , ,
ἐν μέρει καταφατικὸν διὰ τοῦ πρώτου καὶ διὰ τοῦ ἐσχά-
του, μοναχῶς μὲν διὰ τοῦ πρώτου, τριχῶς δὲ διὰ τοῦ ἐσχά-
του. τὸ δὲ στερητικὸν τὸ κατὰ μέρος ἐν ἅπασι τοῖς σχήμασι
δείκνυται, πλὴν ἐν μὲν τῷ πρώτῳ μοναχῶς, ἐν δὲ τῷ μέσῳ
4o καὶ τῷ ἐσχάτῳ ἐν τῷ μὲν διχῶς ἐν τῷ δὲ τριχῶς. φανε-
43" pov οὖν ὅτι τὸ καθόλου κατηγορικὸν κατασκευάσαι μὲν χα-
, ^ » LJ
λεπώτατον, ἀνασκευάσαι δὲ ῥᾷστον. ὅλως δ᾽ ἐστὶν ἀναιροῦντι
, ^ * X M
μὲν τὰ καθόλου τῶν ἐν μέρει paw καὶ yàp ἣν μηδενὶ καὶ
ἣν τινὶ μὴ ὑπάρχῃ, ἀνήρηται: τούτων δὲ τὸ μὲν τινὶ μὴ ἐν
ς ἅπασι τοῖς σχήμασι δείκνυται, τὸ δὲ μηδενὶ ἐν τοῖς δυσῶ.
brr αἱ μὲν om. Ad! I3 περιτταὶ om. Al 22 δύο om. B! προσ-
κείσεται ἢ 24 ποιεῖ d 27 dv-+etain καὶ... 28 €criom. A
πτώσεων fecit B 36 διὰ!) xai διὰ B 39 μοναχῶς ἢ εἴ ut vid.
Al: ἅπαξ A BCd 40 16? om. n! 43*1 τὸ om. A Zet 4 ἣν) εἰ
?: wl
25. 4211-27. 43°41
A » A * , > * ^ - 4 M > i]
τὸν αὐτὸν δὲ τρόπον κἀπὶ τῶν στερητικῶν: Kal yàp ei παντὶ
^ LI , 3 , A 3 . Lj ~ 3 7T , , ,
καὶ εἰ τινί, ἀνήρηται τὸ ἐξ ἀρχῆς" τοῦτο δ᾽ ἦν ἐν δύο σχή-
μασιν. ἐπὶ δὲ τῶν ἐν μέρει μοναχῶς, ἢ παντὶ. 7) μηδενὶ δεί-
favra ὑπάρχειν. κατασκευάζοντι δὲ paw τὰ ἐν μέρει: καὶ
γὰρ ἐν πλείοσι σχήμασι καὶ διὰ πλειόνων τρόπων. ὅλως τε 10
, ‘ , L4 3 , ^ > > ta L4 *
od Set λανθάνειν ὅτι ἀνασκευάσαι μὲν δι’ ἀλλήλων ἔστι kai
M / M ~ > , M ^ M ^ ,
τὰ καθόλου διὰ τῶν ἐν μέρει καὶ ταῦτα διὰ τῶν καθόλου,
κατασκευάσαι δ᾽ οὐκ ἔστι διὰ τῶν κατὰ μέρος τὰ καθόλου,
, ? a A A^ L4 L4 * ^ σ M M 2
δι’ ἐκείνων δὲ ταῦτ᾽ ἔστιν. ἅμα δὲ δῆλον ὅτι καὶ τὸ ἀνα-
σκευάζειν ἐστὶ τοῦ κατασκευάζειν ῥᾷον. 15
Πῶς μὲν οὖν γίνεται πᾶς συλλογισμὸς καὶ διὰ πόσων
ὅρων καὶ προτάσεων, καὶ πῶς ἐχουσῶν πρὸς ἀλλήλας, ἔτι
δὲ ποῖον πρόβλημα ἐν ἑκάστῳ σχήματι καὶ ποῖον ἐν πλείοσι
καὶ ποῖον ἐν ἐλάττοσι δείκνυται, δῆλον ἐκ τῶν εἰρημένων.
27 πῶς δ᾽ εὐπορήσομεν αὐτοὶ πρὸς τὸ τιθέμενον ἀεὶ συλλογι- 20
σμῶν, καὶ διὰ ποίας ὁδοῦ ληψόμεθα τὰς περὶ ἕκαστον ἀρ-
χάς, νῦν ἤδη λεκτέον: οὐ γὰρ μόνον ἴσως δεῖ τὴν γένεσιν
θεωρεῖν τῶν συλλογισμῶν, ἀλλὰ καὶ τὴν δύναμιν ἔχειν τοῦ
ποιεῖν.
« 5, 4 ~ L4 Xx ta > ~ L4 M
Andvrwy δὴ τῶν ὄντων τὰ μέν ἐστι τοιαῦτα ὥστε κατὰ 25
μηδενὸς ἄλλου κατηγορεῖσθαι ἀληθῶς καθόλου (οἷον Κλέων
καὶ Καλλίας καὶ τὸ καθ᾽ ἕκαστον καὶ αἰσθητόν), κατὰ δὲ
, » a x L4 * ^ t , ,
τούτων ἄλλα (xai yàp ἄνθρωπος kai ζῷον ἑκάτερος τούτων
3 L4 M > > ^ x ? L4 ^ ‘ A
éori)’ τὰ δ᾽ αὐτὰ μὲν κατ᾽ ἄλλων κατηγορεῖται, κατὰ δὲ
, L4 , , ^ ^ ^ * , ^ L4
τούτων ἄλλα πρότερον οὐ κατηγορεῖται" τὰ δὲ Kal αὐτὰ dA- 3o
L3 > ^ Ὁ ? L4 * ^ > f
λων καὶ αὐτῶν ἕτερα, οἷον ἄνθρωπος Καλλίου kai ἀνθρώπου
^ L4 bi T LÀ ~ Ld , > * , H
ζῷον. ὅτι μὲν οὖν ἔνια τῶν ὄντων κατ᾽ οὐδενὸς πέφυκε λέγε-
σθαι, δῆλον: τῶν γὰρ αἰσθητῶν σχεδὸν ἕκαστόν ἐστι τοιοῦτον
ὥστε μὴ κατηγορεῖσθαι κατὰ μηδενός, πλὴν ὡς κατὰ συμ-
βεβηκός- φαμὲν γάρ ποτε τὸ λευκὸν ἐκεῖνο Σωκράτην εἶναι 35
‘ A] A] , L4 A A LEA M] LA td
kai τὸ προσιὸν Καλλίαν. ὅτι δὲ kal ἐπὶ τὸ ἄνω πορευομένοις
ἵσταταί ποτε, πάλιν ἐροῦμεν: νῦν δ᾽ ἔστω τοῦτο κείμενον. κατὰ
^ ^ μὴ
μὲν οὖν τούτων οὐκ ἔστιν ἀποδεῖξαι κατηγορούμενον ἕτερον,
πλὴν εἰ μὴ κατὰ δόξαν, ἀλλὰ ταῦτα κατ᾽’ ἄλλων’ οὐδὲ τὰ
καθ᾽ ἕκαστα κατ᾽ ἄλλων, ἀλλ᾽ ἕτερα κατ᾽ ἐκείνων. τὰ δὲ 4o
à! ^ € > , » 3 ^ A , ^ >
μεταξὺ δῆλον ws ἀμφοτέρως ἐνδέχεται (kal yap αὐτὰ κατ
a7 δυσὶ πὶ 8 δείξαντι Α3π 1ο ἐν οἵη. ὁ τρόπων] πτώσεων Waitz
12 τῶν] τῆς d 28 ἑκατέρας n 34 κατὰ om. A 35 Σὼ-
κράτη Bn 36 τὰ ἄνω n
ANAAYTIKQN IIPOTEPON A
ἄλλων καὶ ἄλλα κατὰ τούτων λεχθήσεται)" καὶ σχεδὸν oi
λόγοι καὶ αἱ σκέψεις εἰσὶ μάλιστα περὶ τούτων.
b 4 ^ 4 4 , M μὴ σ > [4
43 et δὴ τὰς προτάσεις περὶ ἕκαστον οὕτως ἐκλαμβάνειν,
ὑποθέμενον αὐτὸ πρῶτον καὶ τοὺς ὁρισμούς τε καὶ ὅσα ἴδια
τοῦ πράγματός ἐστιν, εἶτα μετὰ τοῦτο ὅσα ἕπεται τῷ πρά-
γματι, καὶ πάλιν οἷς τὸ πρᾶγμα ἀκολουθεῖ, καὶ ὅσα μὴ
5 ἐνδέχεται αὐτῷ ὑπάρχειν. οἷς δ᾽ αὐτὸ μὴ ἐνδέχεται, οὐκ
ἐκληπτέον διὰ τὸ ἀντιστρέφειν τὸ στερητικόν. διαιρετέον δὲ καὶ
τῶν ἑπομένων ὅσα τε ἐν τῷ τί ἐστι καὶ ὅσα ἴδια καὶ ὅσα
ὡς συμβεβηκότα κατηγορεῖται, καὶ τούτων ποῖα δοξαστικῶς
καὶ ποῖα κατ᾽ ἀλήθειαν" ὅσῳ μὲν γὰρ ἂν πλειόνων τοιούτων
το εὐπορῇ τις, θᾶττον ἐντεύξεται συμπεράσματι, ὅσῳ δ᾽ ἂν
11 ἀληθεστέρων, μᾶλλον ἀποδείξει.
II Aet δ᾽ ἐκλέγειν μὴ τὰ énó-
, > LI v c ^ 14 or M ,
μενα τινί, ἀλλ᾽ ὅσα ὅλῳ τῷ πράγματι ἕπεται, olov μὴ τί
A > LA ? A , ‘ > , v ^ A ~
τινὲ ἀνθρώπῳ ἀλλὰ Tí παντὶ ἀνθρώπῳ ἕπεται" διὰ yap τῶν
»Ἤ , - /, > , A T Ld
καθόλου προτάσεων ὁ συλλογισμός. ἀδιορίστου μὲν οὖν óv-
Y , , * P4 , b ,
15 Tos ἄδηλον εἰ καθόλου ἡ πρότασις, διωρισμένου δὲ φανερόν.
ε H 3 >? ig b * > A 4 Ld A ‘A ?
ὁμοίως δ᾽ ἐκλεκτέον καὶ οἷς αὐτὸ émerat ὅλοις, διὰ τὴν ei-
P4 Ψ 7 , ἐς 4 M Li P à ? , Ld σ΄
ρημένην αἰτίαν. αὐτὸ δὲ τὸ ἑπόμενον οὐ ληπτέον ὅλον ἔπε-
σθαι, λέγω δ᾽ οἷον ἀνθρώπῳ πᾶν ζῷον ἢ μουσικῇ πᾶσαν ἐπι-
Pa > x , E ~ > ^ , a
στήμην, ἀλλὰ μόνον ἁπλῶς ἀκολουθεῖν, καθάπερ καὶ mpo-
20 τεινόμεθα:- καὶ γὰρ ἄχρηστον θάτερον καὶ ἀδύνατον, οἷον
πάντα ἄνθρωπον εἶναι πᾶν ζῷον ἢ δικαιοσύνην ἅπαν ἀγαθόν.
ἀλλ᾽ d ἕπεται, én’ ἐκείνου τὸ παντὶ λέγεται. ὅταν δ᾽ ὑπό
τινος περιέχηται τὸ ὑποκείμενον ᾧ τὰ ἑπόμενα δεῖ λαβεῖν,
τὰ μὲν τῷ καθόλου ἑπόμενα 7) μὴ ἑπόμενα οὐκ ἐκλεκτέον ἐν
, LÀ A , > lA σ ‘ T * 5
25 τούτοις (εἴληπται yap ἐν ἐκείνοις: ὅσα yap ζῴῳ, kai àv-
σ , A *
θρώπῳ ἕπεται, καὶ doa μὴ ὑπάρχει, ὡσαύτως), rà δὲ
47 i "n » 4 » ~ oN 4
περὶ ἕκαστον ἴδια ληπτέον" ἔστι yap ἅττα τῷ εἴδει ἴδια παρὰ
τὸ γένος: ἀνάγκη γὰρ τοῖς ἑτέροις εἴδεσιν ἴδια ἅττα ὑπάρ-
Ok * ^ , > , " M
χειν. οὐδὲ δὴ τῷ καθόλου ἐκλεκτέον οἷς ἕπεται τὸ περι-
, 3
3o ἐχόμενον, olov ζῴῳ ols ἔπεται ἄνθρωπος: ἀνάγκη yap, εἰ
> , 3 ^ A ~ A , L4 3 ^
ἀνθρώπῳ ἀκολουθεῖ τὸ ζῷον, kai τούτοις ἅπασιν ἀκολουθεῖν,
242 δειχθήσεται n 43 περὶ τούτων εἰσὶ μάλιστα C : μάλιστά εἰσι περὶ
τούτων d by ξκαστον-:- τούτων n 2 ὑποτιθέμενον B? 5 οὐκέτι
ληπτέον n: οὐκέτι ἐκληπτέον ut vid. Al 7 ἴδια codd. D: ὡς ἴδια Bekker
10 dy om. C. 11 ἀληθέστερον Bt 12 ὅλῳ om. πὶ 13 τῇ τῷ
d: τί τῷ Cd? 23 προκείμενον mn 26 ὑπάρχῃ n 29 δεῖ d?
30 ζῷον d ἀνάγκη-Ἐ μὲν ἢ
27. 43°42-28. 44°20
3 4 5 ^ ^ - > » ? ^ £ E:
οἰκειότερα δὲ ταῦτα τῆς τοῦ ἀνθρώπου ἐκλογῆς. ληπτέον δὲ
καὶ τὰ ὡς ἐπὶ τὸ πολὺ ἑπόμενα καὶ οἷς ἕπεται: τῶν
* [i $ a Av A L4 ‘ € *
yàp ws ἐπὶ τὸ πολὺ προβλημάτων Kai 6 συλλογισμὸς
ἐκ τῶν ὡς ἐπὶ τὸ πολὺ προτάσεων, 7j πασῶν ἢ τινῶν: ὅμοιον
γὰρ ἑκάστου τὸ συμπέρασμα ταῖς ἀρχαῖς. ἔτι τὰ πᾶσιν
ἑπόμενα οὐκ ἐκλεκτέον. οὐ γὰρ ἔσται συλλογισμὸς ἐξ αὐτῶν.
,* ^ » > / », ^ Lj ὔ LÀ ^
δι’ ἣν δ᾽ αἰτίαν, ἐν τοῖς ἑπομένοις ἔσται δῆλον.
, M [ à Li , "
28 Karaoxevalew -pev οὖν βουλομένοις κατά τινος ὅλου
τοῦ μὲν κατασκευαζομένου βλεπτέον εἰς τὰ ὑποκείμενα καθ᾽
ὧν αὐτὸ τυγχάνει λεγόμενον, οὗ δὲ δεῖ κατηγορεῖσθαι, ὅσα
τούτῳ ἕπεται" ἂν γάρ τι τούτων ἦ ταὐτόν, ἀνάγκη θάτερον
θατέρῳ ὑπάρχειν. ἣν δὲ μὴ ὅτι παντὶ ἀλλ᾽ ὅτι τινί, οἷς ἕπε-
ται ἑκάτερον: εἰ γάρ τι τούτων ταὐτόν, ἀνάγκη τινὶ ὑπάρ-
bd 4 M L7 € , T * > ^ ©: ,F
xew. ὅταν δὲ μηδενὶ δέῃ ὑπάρχειν, ᾧ μὲν οὐ δεῖ ὑπάρχειν,
, ^ € , a M ^ * € L4 > a Li , ,
εἰς τὰ ἑπόμενα, ὃ δὲ δεῖ μὴ ὑπάρχειν, eis ἃ μὴ ἐνδέχεται
αὐτῷ παρεῖναι: ἢ ἀνάπαλιν, ᾧ μὲν δεῖ μὴ ὑπάρχειν, εἰς ἃ
μὴ ἐνδέχεται αὐτῷ παρεῖναι, ὃ δὲ μὴ ὑπάρχειν, εἰς τὰ
ἑπόμενα. τούτων γὰρ ὄντων τῶν αὐτῶν ὁποτερωνοῦν, οὐδενὶ
ἐνδέχεται θατέρῳ θάτερον ὑπάρχειν" γίνεται γὰρ ὁτὲ μὲν ὃ
ἐν τῷ πρώτῳ σχήματι συλλογισμός, ὁτὲ δ᾽ ὁ ἐν τῷ μέσῳ.
ἐὰν δὲ τινὶ μὴ ὑπάρχειν, ᾧ μὲν δεῖ μὴ ὑπάρχειν, οἷς ἕπεται,
ὃ δὲ μὴ ὑπάρχειν, ἃ μὴ δυνατὸν αὐτῷ ὑπάρχειν: εἰ γάρ
τι τούτων εἴη ταὐτόν, ἀνάγκη τινὶ μὴ ὑπάρχειν.
Μᾶλλον δ᾽
»y POD X. ^ L L4 , L4 M M
ἴσως ὧδ᾽ ἔσται τῶν λεγομένων ἕκαστον φανερόν. ἔστω yap rà
μὲν ἑπόμενα τῷ A ἐφ᾽ ὧν B, οἷς δ᾽ αὐτὸ ἕπεται, ἐφ᾽ ὧν
Γ, ἃ δὲ μὴ ἐνδέχεται αὐτῷ ὑπάρχειν, ef ὧν A- πάλιν
δὲ ~ E ^ M € , » 1» * Z * δ᾽ > M LÀ
€ τῷ τὰ μὲν ὑπάρχοντα, ἐφ᾽ ols Z, ols αὐτὸ ἔπε-
, 5 a ον M > a , ^ € , ?, »
ται, ep ol; H, ἃ δὲ μὴ ἐνδέχεται αὐτῷ ὑπάρχειν, ἐφ
P , 1 5 DE "n - N ὡς > 7
οἷς Θ. εἰ μὲν οὖν ταὐτό τί ἐστι τῶν I τινὶ τῶν Ζ, ἀνάγκη
^ * ^ [4 , + M ^ M ^ ^
τὸ A παντὶ τῷ E ὑπάρχειν: τὸ μὲν yàp Z παντὶ τῷ E, τῷ
* M 4 σ “
δὲ D παντὶ τὸ A, ὥστε παντὶ τῷ E τὸ A. εἰ δὲ τὸ Γ καὶ
M , , > , * ~ ' t , ~ *
τὸ H ταὐτόν, ἀνάγκη τινὶ τῷ E τὸ A ὑπάρχειν: τῷ μὲν
b39 μὲν om. A 40 κατηγορουμένου B? 42 κἂν d* 4452
& ABCdnI Alv? : ὃ mAl οὐ] μὴ P? 3s... ὑπάρχειν codd.
I'Al*? : om. Al ᾧ Al μὴξ fecit B, om. d ἐνδέχεται BCn Alo ;
ἐνδέχηται Ad 4 μὴ A*B’Cdn Alc: om. AB eis B?n 415: om. ABCd
5 ἐνδέχηται d ὃ δὲ μὴ BC?dn, fecit 4:5 δὲ B? 6 ὁποτερωνοῦν
Cn Al* : ὁποτέρων A BCd 9 δεῖ B*CnT': om. ABd μὴ ABC*dnT:
om. B*C 15 ἐφ᾽ ὧν B* Alc 17 ἐστι scripsi: ἔσται codd. 19
τὸ] τῷ Bekker 20 rQ! Al: τῶν codd.
4985
L
35
40
Io
Ir
II
15
20
ANAAYTIKQN IIPOTEPON A
yap Γ τὸ A, τῷ δὲ H τὸ E παντὶ ἀκολουθεῖ. εἰ δὲ τὸ Z
καὶ τὸ 4 ταὐτόν, οὐδενὶ τῶν Ε τὸ Α ὑπάρξει ἐκ προσυλλο-
^ > 4 ^ > , * k] x A ~
γισμοῦ: ἐπεὶ yap ἀντιστρέφει τὸ στερητικὸν καὶ τὸ Z τῷ A
ταὐτόν, οὐδενὶ τῶν Ζ ὑπάρξει τὸ A, τὸ δὲ Ζ παντὶ τῷ Ε.
25 πάλιν εἰ τὸ B καὶ τὸ Θ ταὐτόν, οὐδενὶ τῶν E τὸ A ὑπάρξει"
τὸ yàp B τῷ μὲν A παντί, τῷ δ᾽ ἐφ᾽ ᾧ τὸ E οὐδενὶ ὑπάρ-
£e- ταὐτὸ γὰρ ἦν τῷ Θ, τὸ δὲ O οὐδενὶ τῶν E ὑπῆρχεν.
εἰ δὲ τὸ 4 καὶ τὸ Η ταὐτόν, τὸ A τινὶ τῷ E οὐχ ὑπάρξει"
τῷ γὰρ Η οὐχ trapke, ὅτι οὐδὲ τῷ 4: τὸ δὲ Η ἐστὶν ὑπὸ
3070 E, ὥστε τινὶ τῶν E οὐχ ὑπάρξει. εἰ δὲ τῷ H τὸ B ταὐ-
τόν, ἀντεστραμμένος ἔσται συλλογισμός" τὸ μὲν γὰρ E τῷ
Α ὑπάρξει παντί--τὸ γὰρ Β τῷ Α, τὸ δὲ Ε τῷ Β (ταὐτὸ
γὰρ ἦν τῷ H)—10 δὲ A τῷ E παντὶ μὲν οὐκ ἀνάγκη ὑπάρ-
M δ᾽ > , ὃ ^ ^ > , M 89A
xew, τινὶ δ᾽ ἀνάγκη διὰ τὸ ἀντιστρέφειν τὴν καθόλου κατη-
35 γορίαν τῇ κατὰ μέρος.
Φανερὸν οὖν ὅτι εἰς τὰ προειρημένα βλεπτέον ἑκατέρου
, Ὁ , ‘© a ^ L4 *
καθ᾽’ ἕκαστον πρόβλημα: διὰ τούτων yap ἅπαντες οἱ avÀ-
λογισμοί. δεῖ δὲ καὶ τῶν ἑπομένων, καὶ οἷς ἕπεται ἕκαστον,
, ^ ^ * ^ , , , ^
εἰς τὰ πρῶτα xai rà καθόλου μάλιστα βλέπειν, οἷον τοῦ
4ομὲν E μᾶλλον εἰς τὸ Καὶ Ζ ἢ εἰς τὸ Ζ μόνον, τοῦ δὲ A εἰς
44b τὸ Καὶ Γ ἢ εἰς τὸ Γ μόνον. εἰ μὲν yàp τῷ K Ζ ὑπάρχει τὸ
A, καὶ τῷ Ζ καὶ τῷ E ὑπάρχει: εἰ δὲ τούτῳ μὴ ἕπεται,
> ^ ~ L4 ¢ , * * 58] T π᾿, >
ἐγχωρεῖ τῷ Ζ ἕπεσθαι. ὁμοίως δὲ καὶ ἐφ᾽ ὧν αὐτὸ dxo-
λουθει akemréov: εἰ μὲν γὰρ τοῖς πρώτοις, καὶ τοῖς ὑπ᾽ ἐκεῖνα
5 ἕπεται, εἰ δὲ μὴ τούτοις, ἀλλὰ τοῖς ὑπὸ ταῦτα ἐγχωρεῖ.
Δῆλον δὲ καὶ ὅτι διὰ τῶν τριῶν ὅρων καὶ τῶν δύο προ-
τασεων ἡ σκέψις, καὶ διὰ τῶν προειρημένων σχημάτων ot
x J , A t , * M ^
συλλογισμοὶ πάντες. δείκνυται yàp ὑπάρχειν μὲν mavri τῷ
M ~ ^ ~ 5 v
E τὸ A, ὅταν τῶν Γ καὶ Ζ ταὐτόν τι ληφθῇ. τοῦτο δ᾽ ἔσται
7977)
10 μέσον, ἄκρα δὲ τὸ A καὶ E- γίνεται οὖν τὸ πρῶτον σχῆμα.
τινὶ δέ, ὅταν τὸ Γ καὶ τὸ Η ληφθῇ ταὐτόν. τοῦτο δὲ τὸ ἔσχα-
τον σχῆμα: μέσον γὰρ τὸ Η γίνεται. μηδενὶ δέ, ὅταν τὸ 4
καὶ Ζ ταὐτόν. οὕτω δὲ καὶ τὸ πρῶτον σχῆμα καὶ τὸ μέσον,
Li ‘ ~ Ld » ^ ~ € Ζι M LJ ,
τὸ μὲν πρῶτον ὅτι οὐδενὶ τῷ Z ὑπάρχει τὸ A (εἴπερ ἀντι-
226 rà? A3Cn Al: τὸ ABd: τῶν T 27 τῷ) τὸ Β ὑπάρχειν n 28
τῷ Al: τῶν codd. 20 ὑπάρξει-- τὸ a Cr 31 συλλογισμός ABC Al:
ὁ συλλογισμός dnPc¢ uivom.C « AC Al, fecerunt Bd: Ἡ ΓΡ 32a!
fecit B ὑπάρχει α τὸ uév yàpC B?--mavriC.— 33, rd QC 34-5 τὴν
ἐῶν τῇ BAIP : τῇ καθόλου κατηγορίᾳ τὴν ACdn 39 ró* om.n δι ὑπάρχῃ n
9 καὶ--τῶν C 13 xai τὸ ζ C mpórov4-Corav nD 14 τὸ] καὶ T0 C
28. 44*21-4578
στρέφει τὸ στερητικόν), τὸ δὲ Z παντὶ τῷ E, τὸ δὲ μέσον 15
ὅτι τὸ A τῷ μὲν A οὐδενὶ τῷ δὲ Ε παντὶ ὑπάρχει. τινὶ δὲ μὴ
ε , σ A] ^ » Li ~ 4 ἣν w
ὑπάρχειν, ὅταν τὸ A καὶ Η ταὐτὸν ἧ. τοῦτο δὲ τὸ ἔσχα-
τον σχῆμα: τὸ μὲν yap A οὐδενὶ τῷ Η ὑπάρξει, τὸ δὲ
E παντὶ τῷ Η. φανερὸν οὖν ὅτι διὰ τῶν προειρημένων σχη-
μάτων οἱ συλλογισμοὶ πάντες, καὶ ὅτι οὐκ ἐκλεκτέον ὅσα 20
^ LÀ M * ΤᾺ , ‘ *, ,
πᾶσιν ἕπεται, διὰ τὸ μηδένα γίγνεσθαι συλλογισμὸν ἐξ av-
τῶν. κατασκευάζειν μὲν γὰρ ὅλως οὐκ ἦν ἐκ τῶν ἑπομέ-
3 ^ ? 2 ^ ~
νων, ἀποστερεῖν δ᾽ οὐκ ἐνδέχεται διὰ τοῦ πᾶσιν ἑπομένου"
^ ~ , ~ * € ,
δεῖ yàp τῷ μὲν ὑπάρχειν τῷ δὲ μὴ ὑπάρχειν.
A A ^ L4 L4 Ld , ~ A. ^
Φανερὸν δὲ καὶ ὅτι αἱ ἄλλαι σκέψεις τῶν xarà τὰς 25
ἐκλογὰς ἄχρειοι πρὸς τὸ ποιεῖν συλλογισμόν, οἷον εἰ τὰ
ἑπόμενα ἑκατέρῳ ταὐτά ἐστιν, 7) εἰ οἷς ἕπεται τὸ A καὶ
« 3 ᾽ , ^ - L4 La ^ , ^ Li ,
d μὴ ἐνδέχεται τῷ E, ἢ ὅσα πάλιν μὴ ἐγχωρεῖ ἑκατέρῳ
ὑπάρχειν: οὐ γὰρ γίνεται συλλογισμὸς διὰ τούτων. εἰ μὲν
γὰρ τὰ ἑπόμενα ταὐτά, οἷον τὸ Β καὶ τὸ Ζ, τὸ μέσον 30
γίνεται σχῆμα κατηγορικὰς ἔχον τὰς προτάσεις: εἰ δ᾽ οἷς
σ A * ^ A > * ~ * a
ἕπεται τὸ A καὶ ἃ μὴ ἐνδέχεται τῷ E, olov τὸ Γ᾽ xai
τὸ Θ, τὸ πρῶτον σχῆμα στερητικὴν ἔχον τὴν πρὸς τὸ ἔλατ-
Tov ἄκρον πρότασιν. εἰ δ᾽ ὅσα μὴ ἐνδέχεται ἑκατέρῳ, οἷον
A 4 * M , * € , a“ »
τὸ 4 xai τὸ Θ, στερητικαὶ ἀμφότεραι ai προτάσεις, ἢ ἐν 35
τῷ πρώτῳ 1) ἐν τῷ μέσῳ σχήματι. οὕτως δ᾽ οὐδαμῶς συλ-
λογισμός.
Ll A * ΄ « - * M , A A *
Δῆλον δὲ xai ὅτι ὁποῖα ταὐτὰ ληπτέον τὰ κατὰ THY
ἐπίσκεψιν, καὶ οὐχ ὁποῖα ἕτερα ἢ ἐναντία, πρῶτον μὲν
σ ~ , , [4 , Li ^ M , > ΄
ὅτι τοῦ μέσου χάριν ἡ ἐπίβλεψις, τὸ δὲ μέσον οὐχ ἕτερον 4o
, ^ , A ^ ^ > - ^ , ,
ἀλλὰ ταὐτὸν δεῖ λαβεῖν. εἶτα ἐν ὅσοις xai συμβαίνει yi- 45*
A ^ ~ » ^ ^ M > ,
νεσθαι συλλογισμὸν τῷ ληφθῆναι ἐναντία T) μὴ ἐνδεχόμενα
τῷ αὐτῷ ὑπάρχειν, εἰς τοὺς προειρημένους ἅπαντα ἀνα-
, , , A ^ * LJ , a“ M
χθήσεται τρόπους, olov εἰ τὸ B xai τὸ Z ἐναντία ἣ μὴ
ἐνδέχεται τῷ αὐτῷ ὑπάρχειν: ἔσται μὲν γὰρ τούτων λη- 5
‘ ,
φθέντων συλλογισμὸς ὅτι οὐδενὲ τῶν E τὸ A ὑπάρχει, ἀλλ᾽
, , ᾽ ^ > , ? ^ £, , M A
οὐκ ἐξ αὐτῶν ἀλλ᾽ ἐκ τοῦ προειρημένου τρόπου: τὸ yàp B
~ A M ~ A 2 M € ^ σ * , , , M
τῷ μὲν A παντὶ τῷ δὲ E οὐδενὶ ὑπάρξει: ὥστ᾽ ἀνάγκη ταὐτὸ
bar ἐξ αὐτῶν] ἐξ αὐτῶν διὰ τῶν d : διὰ τῶν d* 26 ποιῆσαι d 31 τὰς]
ἀμφοτέρας τὰς f 33 ró! om. A σχῆμα] ἔσται σχῆμα n: σχῆμα ἔσται D
36 οὐδαμῶς -Ἐ ἔσται ΠΓ 48 ὅτι All : om. codd. 'AIP ταὐτὰ AB*C*dnAlP:
ταῦτα ΒΟΓ τὰ om. C?Pc 39 οὐχ codd. P, coni. Al: om. I'Alve
40 ἐπίσκεψις C 4531 καὶ ἐν ὅσοις n: ἐν ὅσοις T 3 ἅπαν Α1Βά:
ἅπαντας B* Ale 4 τὸξ om. πὶ 6 ε τὸ οἴη. ὦ ὃ τὸ μὲν Β
ANAAYTIKQN TIPOTEPQN A
εἶναι τὸ B τινὶ τῷ Θ. [πάλιν εἰ τὸ B καὶ H μὴ ἐγχωρεῖ
τοτῷ αὐτῷ παρεῖναι, ὅτι τινὲ τῷ Ε οὐχ ὑπάρξει τὸ A: καὶ
γὰρ οὕτως τὸ μέσον ἔσται σχῆμα: τὸ γὰρ Β τῷ μὲν Α
‘ ^ A $, ' L4 4 LA , > , A , L4
παντὶ TQ δὲ E οὐδενὶ ὑπάρξει: ὥστ᾽ ἀνάγκη τὸ B ταὐτόν
τινι εἶναι τῶν Θ. τὸ γὰρ μὴ ἐνδέχεσθαι τὸ Β καὶ τὸ H
τῷ αὐτῷ ὑπάρχειν οὐδὲν διαφέρει 7 τὸ B τῶν Θ τινὶ ταὐ-
το τὸν εἶναι: πάντα γὰρ εἴληπται τὰ μὴ ἐνδεχόμενα τῷ E
ὑπάρχειν.
®D 1 T " , > ~ M L4 ~ , ,
avepóv οὖν ὅτι ἐξ αὐτῶν μὲν τούτων τῶν ἐπιβλέ-
, M Le / 3 , 3 , M i] A
ψεων οὐδεὶς γίνεται συλλογισμός, ἀνάγκη δ᾽ εἰ τὸ B καὶ τὸ Z
> L ᾽ / M ^ M ^
ἐναντία, ταὐτόν τινι εἶναι τὸ B τῶν Θ καὶ τὸν συλλογι-
20 σμὸν γίγνεσθαι διὰ τούτων. συμβαίνει δὴ τοῖς οὕτως ἐπισκο-
^ , » € x ^ , , X. ^
moto. προσεπιβλέπειν ἄλλην ὁδὸν τῆς ἀναγκαίας διὰ τὸ
λανθάνειν τὴν ταὐτότητα τῶν Β καὶ τῶν Θ.
Τὸν αὐτὸν δὲ τρόπον ἔχουσι καὶ οἱ εἰς τὸ ἀδύνατον
ἄγοντες συλλογισμοὶ τοῖς δεικτικοῖς" καὶ γὰρ οὗτοι γίνον-
25 ται διὰ τῶν ἑπομένων καὶ οἷς ἕπεται ἑκάτερον. καὶ ἡ αὐτὴ
3 , ?, > ^ ^ M , ^ s M
ἐπίσκεψις ἐν ἀμφοῖν: ὃ yap δείκνυται δεικτικῶς, καὶ διὰ
~ > , L4 L4 A ^ > ~ Ld *
ToU ἀδυνάτου ἔστι συλλογίσασθαι διὰ τῶν αὐτῶν ὅρων, kai
a A ~ 3 , 4 -^ Ld * 2 M
ὃ διὰ τοῦ ἀδυνάτου, kai δεικτικῶς, olov ὅτι τὸ A οὐδενὶ
τῷ E ὑπάρχει. κείσθω γὰρ τινὶ ὑπάρχειν: οὐκοῦν ἐπεὶ τὸ
30 B παντὶ τῷ A, τὸ δὲ A τινὲ τῷ E, τὸ B τινὲ τῶν E
ὑπάρξει. ἀλλ᾽ οὐδενὶ ὑπῆρχεν. πάλιν ὅτι τινὶ ὑπάρχει" εἰ
γὰρ μηδενὶ τῷ E τὸ A, τὸ δὲ E παντὶ τῷ H, οὐδενὶ τῶν
Η ὑπάρξει τὸ A+ ἀλλὰ παντὶ ὑπῆρχεν. ὁμοίως δὲ καὶ ἐπὶ
~ » , LER J X Μ M » Uu €
τῶν ἄλλων προβλημάτων: dei yàp ἔσται kai ἐν ἅπασιν ἡ
35 διὰ τοῦ ἀδυνάτου δεῖξις ἐκ τῶν ἑπομένων καὶ οἷς ἕπεται
ig , * » L4 , L4 » ^4 ,
ἑκάτερον. καὶ καθ᾽ ἕκαστον πρόβλημα ἡ αὐτὴ σκέψις δει-
ἔπ , , ‘ > > 7 3
κτικῶς Te βουλομένῳ συλλογίσασθαι kai εἰς ἀδύνατον aya-
yeiv: ἐκ γὰρ τῶν αὐτῶν ὅρων ἀμφότεραι αἱ ἀποδείξεις, οἷον
, y ^4 t , ~ ^ L4 ,
εἰ δέδεικται μηδενὶ ὑπάρχειν τῷ E τὸ A, ὅτι ovpPaiver
M M] M ^ t ^ e > , ?'* ^
4o καὶ τὸ B τινὲ τῷ E ὑπάρχειν, ὅπερ ἀδύνατον: ἐὰν ληφθῇ
80 τῷ D: τῶν codd. πάλιν... 16 ὑπάρχειν seclusi: habent codd. ΓΑ͂ΙΡ
9xairó nC ἐγχωρῇ Ad 10 τῷξ Αἱ : τῶν codd. II γὰρὶ - καὶ C
I270 εΒηάϊ: η AB*CdP,coni. Al: e τῷ I οὐδενὶ codd. ΓΑ͂ΙΡ:
oj r.i Waitz 17 οὖν] μὲν οὖν m, fort. Al 18 ἀνάγκη δ᾽ εἰ] ἐὰν
δὲ ACd: ἀνάγκη δεῖ Γ τὸδ om. 5 I9 τὸν om. z, fort, Al 21
προεπιβλέπειν A περίοδον d 22 λανθάνειν- ποτὲ nT 24 yap+
kai C 26 éniBAeyus ABd ἐπ᾿ C 27 διὰ) καὶ &à nI* 29 τῷ
Al: τῶν codd. 3o τῷξ)] τῶν ABCdT'P 32 τῷ P : τῶν codd.
τῷ Γ: τῶν codd. 27 cistron 40 τῷ ΓΑ͂Ϊ: τῶν codd.
a b
28. 45°9-29. 45°32
τῷ μὲν E μηδενὶ τῷ δὲ A παντὶ ὑπάρχειν τὸ B, φανερὸν
ὅτι οὐδενὶ τῷ Ε τὸ Α ὑπάρξει. πάλιν εἰ δεικτικῶς συλλε-
λόγισται τὸ A τῷ E μηδενὶ ὑπάρχειν, ὑποθεμένοις trap-
y à E pn pxew, μένοις ὕπαρ
χειν τινὶ διὰ τοῦ ἀδυνάτου δειχθήσεται οὐδενὲ ὑπάρχον.
L4 , * > M ~ LÀ 1 Ld M > , ,
ὁμοίως δὲ κἀπὶ τῶν ἄλλων- ἐν ἅπασι yap ἀνάγκη κοινόν
^ " L4 ^ e à * ^ L4 ~
τινα λαβεῖν ὅρον ἄλλον τῶν ὑποκειμένων, πρὸς ὃν ἔσται τοῦ
ἔς € , L4 >? > , , ^
ψεύδους ὁ συλλογισμός, ὥστ᾽ ἀντιστραφείσης ταύτης τῆς
προτάσεως, τῆς δ᾽ ἑτέρας ὁμοίως ἐχούσης, δεικτικὸς ἔσται
t ‘ ^ ~ , ^ L4 , x [4
ὁ συλλογισμὸς διὰ τῶν αὐτῶν ὅρων. διαφέρει yàp ὁ δει-
κτικὸς τοῦ εἰς τὸ ἀδύνατον, ὅτι ἐν μὲν τῷ δεικτικῷ κατ᾽
ἀλήθειαν ἀμφότεραι τίθενται αἱ προτάσεις, ἐν δὲ τῷ εἰς τὸ
ἀδύνατον ψευδῶς ἡ μία.
Ταῦτα μὲν οὖν ἔσται μᾶλλον φανερὰ διὰ τῶν ἑπο-
μένων, ὅταν περὶ τοῦ ἀδυνάτου λέγωμεν: νῦν δὲ τοσοῦτον
ς ^ v ^ Ld , *, ^ , ὃ ~
ἡμῖν ἔστω δῆλον, ὅτι eis ταὐτὰ βλεπτέον δεικτικῶς te Bov-
, » * > A > £ MY » A
Aopevp συλλογίζεσθαι καὶ eis τὸ ἀδύνατον ἄγειν. ἐν δὲ
^ L4 ^ ^ , Ui ,ὔ T Ld
τοῖς ἄλλοις συλλογισμοῖς τοῖς ἐξ ὑποθέσεως, olov ὅσοι
κατὰ μετάληψιν 7 κατὰ ποιότητα, ἐν τοῖς ὑποκειμένοις,
? > ^ , > ~ > , 3 - ta μὴ
οὐκ ἐν τοῖς ἐξ ἀρχῆς ἀλλ᾽ ἐν τοῖς μεταλαμβανομένοις, ἔσται
€ n € 4 , Lj] > Ἂν ^ > i > ,
ἡ σκέψις, 6 δὲ τρόπος 6 αὐτὸς τῆς ἐπιβλέψεως. ἐπισκέ-
4 ^ 4 ^ ~ fto» L4 L4
ψασθαι δὲ δεῖ καὶ διελεῖν ποσαχῶς of ἐξ ὑποθέσεως.
Δείκνυται μὲν οὖν ἕκαστον τῶν προβλημάτων οὕτως,
ἔστι δὲ καὶ ἄλλον τρόπον ἔνια συλλογίσασθαι τούτων, οἷον
A Fa ^ ~ ^ , > , , L4 ,
τὰ καθόλου διὰ τῆς κατὰ μέρος ἐπιβλέψεως ἐξ ὑποθέσεως.
> M A * A > A » , x , =
εἰ yap τὸ Γ kai τὸ H ταὐτὰ εἴη, μόνοις δὲ ληφθείη rois
H τὸ E ὑπάρχειν, παντὲ dv τῷ E τὸ A ὑπάρχοι: καὶ
πάλιν εἰ τὸ 4 καὶ H ταὐτά, μόνων δὲ τῶν H τὸ E κα-
^ ΄ > 4 - * [4 4 A T L4
τηγοροῖτο, ὅτι οὐδενὶ τῷ E τὸ A ὑπάρξει. φανερὸν οὖν ὅτι
καὶ οὕτως ἐπιβλεπτέον. τὸν αὐτὸν δὲ τρόπον καὶ ἐπὶ τῶν
ἀναγκαίων καὶ τῶν ἐνδεχομένων: ἡ γὰρ αὐτὴ σκέψις, καὶ
διὰ τῶν αὐτῶν ὅρων ἔσται τῇ τάξει τοῦ τ᾽ ἐνδέχεσθαι καὶ
τοῦ ὑπάρχειν 6 συλλογισμός. ληπτέον δ᾽ ἐπὶ τῶν ἐνδεχο-
μένων καὶ τὰ μὴ ὑπάρχοντα δυνατὰ δ᾽ ὑπάρχειν: δέ-
ὃς τινὶ B et ut vid. AIP : om. ACdn 4 ἀνάγκη - τοῖς δι᾿’ ἀδυνάτου n
ς ἐστι Β 7 δεικτικῶς d ἐστι Β 8 δ' om.C 1I ψευδὴς d
12 μᾶλλον φανερώτερα Cd 14 ταὐτὰ C3 Al: ταῦτα 4 BCdnT Bovdo-
μένοις ἩΓ 15 ἀγαγεῖν ABCA 16-17 olov . . . ποιότητα codd.
I'AlP : secl. Maier 20 δὲ om. n! δεῖ om. A 24 10... τὸ n Ál:
rà... rà ABCd 26 τὸ A Al: ra BCdn μόνον Cd τὰ nt 27
TQ Al: ràv codd. 31 ὁ om. ἢ
45^
5
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15
20
25
30
ANAAYTIKQN IIPOTEPQN A
8 8 Ld * 8 A , , t - » ,
eura, yàp ὅτι kal διὰ τούτων γίνεται ὁ τοῦ ἐνδέχεσθαι
συλλογισμός. ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων Karn-
ἃς γοριῶν.
Φανερὸν οὖν ἐκ τῶν εἰρημένων οὐ μόνον ὅτι ἐγχωρεῖ
διὰ ταύτης τῆς ὁδοῦ γίνεσθαι πάντας τοὺς συλλογισμούς,
ἀλλὰ καὶ ὅτι δι’ ἄλλης ἀδύνατον. ἅπας μὲν γὰρ συλλο-
γισμὸς δέδεικται διά τινος τῶν προειρημένων σχημάτων γι-
, ^ > » » ^ , Ld ^ M
4o vopevos, ταῦτα δ᾽ οὐκ ἐγχωρεῖ δι’ ἄλλων συσταθῆναι πλὴν
διὰ τῶν ἑπομένων καὶ οἷς ἕπεται ἕκαστον" ἐκ τούτων γὰρ
L4 , * * ~ 4 ^ LÀ 3 IO
46% ai προτάσεις xai ἡ τοῦ μέσου λῆψις, dor οὐδὲ συλλογι-
, » ^ , > w
σμὸν ἐγχωρεῖ γίνεσθαι δι᾽ ἄλλων.
. A *T Ld ^ * ἊΝ € » M M M
H μὲν οὖν ὁδὸς κατὰ πάντων ἡ αὐτὴ καὶ περὶ φι-
λοσοφίαν καὶ περὶ τέχνην ὁποιανοῦν καὶ μάθημα" δεῖ γὰρ
ςτὰ ὑπάρχοντα καὶ οἷς ὑπάρχει περὶ ἑκάτερον ἀθρεῖν, καὶ
τούτων ὡς πλείστων εὐπορεῖν, καὶ ταῦτα διὰ τῶν τριῶν ὅρων
^ 3 4 A « d , * € ,
σκοπεῖν, ἀνασκευάζοντα μὲν wot, κατασκευάζοντα δὲ wot,
M * > , » ^ > 3 2, ,
κατὰ μὲν ἀλήθειαν ἐκ τῶν κατ᾽ ἀλήθειαν διαγεγραμμένων
7 , > 4 A a AY » a A
ὑπάρχειν, eis δὲ τοὺς διαλεκτικοὺς συλλογισμοὺς ἐκ τῶν κατὰ
, 4 € , > M ^ ~ ,
10 80fav προτάσεων. ai δ᾽ ἀρχαὶ τῶν συλλογισμῶν καθόλου
μὲν εἴρηνται, ὃν τρόπον τ᾽ ἔχουσι καὶ ὃν τρόπον δεῖ θηρεύ-
ew αὐτάς, ὅπως μὴ βλέπωμεν εἰς ἅπαντα τὰ λεγόμενα,
μηδ᾽ εἰς ταὐτὰ κατασκευάζοντες καὶ ἀνασκευάζοντες, μηδὲ
κατασκευάζοντές τε κατὰ παντὸς ἢ τινὸς καὶ ἀνασκευάζον-
> * , bal ^ * > > , , ^ € ,
ig TES ἀπὸ πάντων ἢ τινῶν, ἀλλ᾽ εἰς ἐλάττω Kal ὡρισμένα,
> bd ^ , , a * ^ » ^ a
καθ᾽ ἕκαστον δὲ ἐκλέγειν τῶν ὄντων, olov περὶ ἀγαθοῦ 7
> , M > € ᾿ t ^ 8 M ^
ἐπιστήμης. ἴδιαι δὲ καθ᾽ ἑκάστην αἱ πλεῖσται. διὸ τὰς
μὲν ἀρχὰς τὰς περὶ ἕκαστον ἐμπειρίας ἐστὶ παραδοῦναι,
λέγω δ᾽ οἷον τὴν ἀστρολογικὴν μὲν ἐμπειρίαν τῆς ἀστρολογι-
20 κῆς ἐπιστήμης (ληφθέντων γὰρ ἱκανῶς τῶν φαινομένων οὕτως
ε L/ € > M , 7, ig $ ^ 4 ^
εὑρέθησαν ai ἀστρολογικαὶ ἀποδείξεις), ὁμοίως δὲ καὶ περὶ
L4 Lj ^ wv , 1 3? , σ , oN ^
ἄλλην ὁποιανοῦν ἔχει τέχνην τε καὶ ἐπιστήμην" ὥστ᾽ ἐὰν ληφθῇ
‘ σ € LÀ ^ * *,
τὰ ὑπάρχοντα περὶ ἕκαστον, ἡμέτερον ἤδη Tas ἀποδείξεις
Lj , , , > A ^ ^ A t ,
ἑτοίμως ἐμφανίζειν. εἰ yàp μηδὲν κατὰ τὴν ἱστορίαν mapa-
, ^ > ^ € , ^ , L4
25 λειφθείη τῶν ἀληθῶς ὑπαρχόντων τοῖς πράγμασιν, ἕξομεν
b34 δ᾽ τ ἔξει nl 4633 μέθοδος π 5 ἑκάτερον A BCdn Al: ἕκαστον mu:
ἕκαστον ἑκάτερον Ale 12 πάντα C 13 αὐτὰ 4 xai ἀνασκευάζοντες
om. A 14 re] τὸ π 16 xai καθ᾽ n 17 ἴδιαι AIP: ἰδίᾳ codd.
καθ᾽ AC*dn Al: xai καθ’ BC ἕκαστον 5 ai Al: εἰσὶν ai codd. Γ
18 éxaerov--8& d 19 ἀστρονομικὴν ἐμπειρίαν Cd τῇ ἀστρολογικῇ
ἐπιστήμῃ ACld 24 παραλης, θῇ d! : παραληφθείη ri)
40
21
b b
29. 45°33-31. 46°19
* μι T? 4 LÀ 3 , 4^ t ^ A 3
περὶ ἅπαντος οὗ μὲν ἔστιν ἀπόδειξις, ταύτην εὑρεῖν καὶ ἀπο-
δεικνύναι, οὗ δὲ μὴ πέφυκεν ἀπόδειξις, τοῦτο ποιεῖν φανερόν.
Καθόλου μὲν οὖν, ὃν δεῖ τρόπον τὰς προτάσεις ἐκλέ-
LÀ , 3 » , ^ L4 , ~
yew, εἴρηται σχεδόν- δι’ ἀκριβείας δὲ διεληλύθαμεν ἐν τῇ
πραγματείᾳ τῇ περὶ τὴν διαλεκτικήν.
Ὅ δ᾽ Li 8 M ^ ^ , , , ,
τι ἡ διὰ τῶν γενῶν διαίρεσις μικρόν τι μόριόν
> ~ > ,ὔ , cr ? ^ L4 a € ig
ἐστι τῆς εἰρημένης μεθόδου, ῥᾷάδιον ἰδεῖν: ἔστι yap ἡ διαίρε-
> 4 , a M ^ ^ ^ ,
ats olov ἀσθενὴς συλλογισμός: ὃ μὲν yàp δεῖ δεῖξαι ai-
^ , > > » ^ " ^ > fx ας
τεῖται, συλλογίζεται δ᾽ ἀεί τι τῶν ἄνωθεν. πρῶτον δ᾽ αὐτὸ
τοῦτο ἐλελήθει τοὺς χρωμένους αὐτῇ πάντας, καὶ πείθειν
, , e L4 - ^ , , » / ,
ἐπεχείρουν ὡς ὄντος δυνατοῦ περὶ οὐσίας ἀπόδειξιν γενέσθαι
+. ~ a , L4 LI L4 - 3 Li ,
καὶ τοῦ Tí ἐστιν. ὥστ᾽ οὔτε 6 τι ἐνδέχεται συλλογίσασθαι
διαιρουμένοις ξυνίεσαν, οὔτε ὅτι οὕτως ἐνεδέχετο ὥσπερ εἰ-
, 3 A ^ ^ à ΄, σ ,
ρήκαμεν. ev μὲν οὖν ταῖς ἀποδείξεσιν, ὅταν δέῃ τι ovMo-
, L4 , ^ M , ? τ , L4
γίσασθαι ὑπάρχειν, δεῖ τὸ μέσον, δι’ οὗ γίνεται 6 συλλο-
γισμός, καὶ ἧττον ἀεὶ εἶναι καὶ μὴ καθόλου τοῦ πρώτου
τῶν ἄκρων: ἡ δὲ διαίρεσις τοὐναντίον βούλεται: τὸ γὰρ κα-
θόλου λαμβάνει μέσον. ἔστω γὰρ ζῷον ἐφ' οὗ A, τὸ
δὲ θνητὸν ἐφ᾽ οὗ B, καὶ ἀθάνατον ἐφ᾽ οὗ Γ, ὁ δ᾽ ἀνθρω-
πος, οὗ τὸν λόγον δεῖ λαβεῖν, ἐφ᾽ οὗ τὸ 4. ἅπαν δὴ ζῷον
λαμβάνει ἢ θνητὸν ἢ ἀθάνατον: τοῦτο δ᾽ ἐστίν, ὃ ἂν ἦ Α,
oe * ud LA a Ld » «4 4
ἅπαν εἶναι ἢ Ban Γ. πάλιν τὸν ἄνθρωπον dei διαιρούμενος
[/ ^ - σ ^ ~ + , [4 P
τίθεται ζῷον εἶναι, ὥστε κατὰ τοῦ 4 τὸ A λαμβάνει ὑπάρ-
L4 p. ^ , > Ld a * a L4
xew. ὃ μὲν οὖν συλλογισμός ἐστιν ὅτι τὸ 4 ἢ Β ἢ Γ ἅπαν
v LÀ * LÀ n *& A ^ , , >
ἔσται, ὥστε τὸν ἄνθρωπον ἢ θνητὸν μὲν ἢ ἀθάνατον avay-
^ ^ 4 bi 2 > ^ 3 » ? ^
καῖον εἶναι, ζῷον θνητὸν δὲ οὐκ ἀναγκαῖον, ἀλλ᾽ αἰτεῖται"
τοῦτο δ' ἦν ὃ ἔδει συλλογίσασθαι. καὶ πάλιν θέμενος τὸ
μὲν A ζῷον θνητόν, ἐφ᾽ οὗ δὲ τὸ B ὑπόπουν, ἐφ' οὗ δὲ
τὸ l' ἄπουν, τὸν δ᾽ ἄνθρωπον τὸ 4, ὡσαύτως λαμβάνει
^ A w > ~ - 2 ~ L4 ^ ^
τὸ μὲν A ἤτοι ἐν τῷ Β ἣ ἐν τῷ IT εἶναι (ἅπαν yap ζῷον
4 “a e , - L4 > , 4 a ~ M ‘
θνητὸν ἢ ὑπόπουν ἢ ἄπουν ἐστί), κατὰ δὲ τοῦ 4 τὸ A (τὸν
γὰρ ἄνθρωπον ζῷον θνητὸν εἶναι ἔλαβεν): ὥσθ᾽ ὑπόπουν μὲν
ἢ ἄπουν εἶναι ζῷον ἀνάγκη τὸν ἄνθρωπον, ὑπόπουν δ᾽ οὐκ
ἀνάγκη, ἀλλὰ λαμβάνει: τοῦτο δ᾽ ἦν ὃ ἔδει πάλιν δεῖξαι.
426 παντὸς "i 28 μὲν om. d 29 ἐληλύθαμεν dt 30 διαλεκτήν
A 32 ἰδεῖν fecit n 36 γίνεσθαι A BCd 37 9 τι codd. AIP: ὅτι
Waitz ἐνδέχεσθαι d 38 διαιρουμένοις scripsi, fort. habuerunt
AIP: διαιρούμενοι AB: διαιρουμένους dn, fecit C, fort. ALP 39 δέῃ
nAl: δέηται ABCA ba ζῷον-- μὲν nT 5 τὸν ὅρον n τὸ Om. f
7 ἀεὶ om. n 95 Bom.d! 10 3) θνητὸν μὲν] ἢ θνητὸν ἢ ἀθάνατον δεῖ
λαβεῖν θνητὸν μὲν n : ζῷον μὲν 3 θνητὸν T 16 τοῦ] τὸ 41
3
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40
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wn
5
ANAAYTIKQN IIPOTEPON A
M ^ * M H LEA] [4 A 4 ,
zo καὶ τοῦτον δὴ τὸν τρόπον dei διαιρουμένοις TO μὲν καθόλου
συμβαίνει αὐτοῖς μέσον λαμβάνειν, καθ᾽ οὗ δ᾽ ἔδει δεῖξαι
x ^ M » r4 , d e A^) LÀ M
καὶ τὰς διαφορὰς ἄκρα. τέλος δέ, ὅτι τοῦτ᾽ ἔστιν ἄνθρωπος
na e > nn 7T Y a , * , * LÀ 2
3j 9 τι ποτ᾽ ἂν ἢ τὸ ζητούμενον, οὐδὲν λέγουσι σαφὲς dor
ἀναγκαῖον elvav καὶ γὰρ τὴν ἄλλην ὁδὸν ποιοῦνται πᾶσαν,
25 οὐδὲ τὰς ἐνδεχομένας εὐπορίας ὑπολαμβάνοντες ὑπάρχειν.
Φανερὸν δ᾽ ὅτι οὔτ᾽ ἀνασκευάσαι ταύτῃ τῇ μεθόδῳ ἔστιν, οὔτε
H , M γον, , LÀ b 1d
περὶ συμβεβηκότος ἢ ἰδίου συλλογίσασθαι, οὔτε περὶ yé-
vous, οὔτ᾽ ἐν οἷς ἀγνοεῖται τὸ πότερον «0i ἢ ὡδὶ ἔχει, οἷον
4.5 € , > ,ὔ ^ , LA! M Ld σ σ΄
ἄρ᾽ ἡ διάμετρος ἀσύμμετρος ἢ σύμμετρος. ἐὰν γὰρ λάβῃ ὅτι ἅπαν
3δομῆκος ἢ σύμμετρον ἣ ἀσύμμετρον, ἡ δὲ διάμετρος μῆκος,
συλλελόγισται ὅτι ἀσύμμετρος ἢ σύμμετρος ἡ διάμε-
τρος. εἰ δὲ λήψεται ἀσύμμετρον, ὃ ἔδει συλλογίσασθαι
λήψεται. οὐκ ἄρα ἔστι δεῖξαι: ἡ μὲν γὰρ ὁδὸς αὕτη, διὰ
ταύτης δ᾽ οὐκ ἔστιν. τὸ ἀσύμμετρον ἢ σύμμετρον ἐφ᾽
^ , Ὕ εἰ 7 L4 L4 ^ ^
35 A, μῆκος B, διάμετρος I'. φανερὸν οὖν ὅτι οὔτε πρὸς má-
σαν σκέψιν ἁρμόζει τῆς ζητήσεως ὁ τρόπος, οὔτ᾽ ἐν οἷς μά-
λιστα δοκεῖ πρέπειν, ἐν τούτοις ἐστὶ χρήσιμος.
» ,ὔ εἶ 4 ε > 7 ,ὔ x ^
Ek τίνων μὲν οὖν αἱ ἀποδείξεις γίνονται καὶ πῶς,
4 » € ^ , > e 4 A
καὶ εἰς ὅποῖα βλεπτέον καθ᾽ ἕκαστον πρόβλημα, φανερὸν
4o ἐκ τῶν εἰρημένων: πῶς δ᾽ ἀνάξομεν τοὺς συλλογισμοὺς εἰς 32
47" τὰ προειρημένα ᾿σχήματα, λεκτέον àv εἴη μετὰ ταῦτα'
λοιπὸν γὰρ ἔτι τοῦτο τῆς σκέψεως. εἰ γὰρ τήν τε γένεσιν
τῶν συλλογισμῶν θεωροῖμεν καὶ τοῦ εὑρίσκειν ἔχοιμεν δύνα-
μιν, ἔτι δὲ τοὺς γεγενημένους ἀναλύοιμεν εἰς τὰ προειρημένα
ςσχήματα, τέλος ἄν ἔχοι ἡ ἐξ ἀρχῆς πρόθεσις. συμβήσε-
ται δ᾽ ἅμα καὶ τὰ πρότερον εἰρημένα ἐπιβεβαιοῦσθαι καὶ
φανερώτερα εἶναι ὅτι οὕτως ἔχει, διὰ τῶν νῦν λεχθησομέ-
^ M ^ * > x 3X € ^ € ,
νων: δεῖ yap πᾶν τὸ ἀληθὲς αὐτὸ ἑαυτῷ ὁμολογούμενον
εἶναι πάντῃ.
10 Πρῶτον μὲν οὖν δεῖ πειρᾶσθαι τὰς δύο προτάσεις ἐκ-
λαμβάνειν τοῦ συλλογισμοῦ (ῥᾷον γὰρ εἰς τὰ μείζω διε-
^ ^ M X 2 , x A , ^ , «
λεῖν ἢ τὰ ἐλάττω, μείζω δὲ τὰ συγκείμενα ἢ ἐξ ὧν),
b20 xai om. B δὲ C 21 αὐτοὺς ἢ δὲ δεῖ Cd: δὲ δέοι π: δὲ B:
ἔδει Γ 2] ἢ] τι ἢ λογίσασθαι dt 28 ὧδε Cdn: ὅτι ὧδε A
ἢ ài scripsi: ἢ ὧδε BCdn: om. A 29 3) σύμμετρος om. ACA 31
ὅτι- ἢ ἡ διάμετρος om. n 33 αὐτὴ f 34 ἔστι- δεῖξαι Cn
σύμμετρον ἢ ἀσύμμετρον Cn: σύμμετρον a. B. y. ἣ ἀσύμμετρον D 35 B]
ἐφ᾽ οὗ BC ΓῚ ἐφ᾽ οὗ ya. β. y. Cty a. B. y. n 4722 τῆς] τὸ τῆς
ABC 3 θεωροῦμεν d 11 ῥᾷον C?nT AIP : paw ABCA 12
ἐξ) τὰ ἐξ Ἡ Γ ὧν- σύγκειται A
31. 46^20-32. 4752
εἶτα σκοπεῖν ποτέρα ἐν ὅλῳ καὶ ποτέρα ἐν μέρει, καί, et
b L4 > a 8 LH A ». s LENA
μὴ ἄμφω εἰλημμέναι εἶεν, αὐτὸν τιθέναι τὴν ἑτέραν. ἐνίοτε
γὰρ τὴν καθόλου προτείναντες τὴν ἐν ταύτῃ οὐ λαμβάνου-
σιν, οὔτε γράφοντες οὔτ᾽ ἐρωτῶντες: ἢ ταύτας μὲν προτεί-
νουσι, δι’ ὧν δ᾽ αὗται περαίνονται, παραλείπουσιν, ἄλλα
> ~
δὲ μάτην ἐρωτῶσιν. σκεπτέον οὖν εἴ τι περίεργον εἴληπται
καὶ εἴ τι τῶν ἀναγκαίων παραλέλειπται, καὶ τὸ μὲν θετέον
^ > > , L4 nn 2 T , Le
TO δ᾽ ἀφαιρετέον, ἕως dv ἔλθῃ eis τὰς δύο προτάσεις"
v , a ,
ἄνευ yap τούτων οὐκ ἔστιν ἀναγαγεῖν τοὺς οὕτως ἠρωτημένους λό-
» 7; * T 4 » ^ ^ * / L4 M ,
yous. ἐνίων μὲν οὖν ῥᾷδιον ἰδεῖν τὸ ἐνδεές, ἔνιοι δὲ λανθάνουσι
M ~ , * ^ > ^ ΙΑ
καὶ δοκοῦσι συλλογίζεσθαι διὰ τὸ ἀναγκαῖόν τι συμβαί-
νειν ἐκ τῶν κειμένων, οἷον εἰ ληφθείη μὴ οὐσίας ἀναιρουμέ-
M 3 ^ > , , T > > M , Y "
vys μὴ ἀναιρεῖσθαι οὐσίαν, ἐξ ὧν δ᾽ ἐστὶν ἀναιρουμένων, καὶ
τὸ ἐκ τούτων φθείρεσθαι: τούτων γὰρ τεθέντων ἀναγκαῖον
$i kl 3 , / 4 z= 2 3 M id X
μὲν τὸ οὐσίας μέρος εἶναι οὐσίαν, οὐ μὴν συλλελόγισται διὰ
τῶν εἰλημμένων, ἀλλ᾽ ἐλλείπουσι προτάσεις. πάλιν εἰ ἀν-
θρώπου ὄντος ἀνάγκη ζῷον εἶναι καὶ ζῴου οὐσίαν, ἀνθρώπου
* > L4 , , 3, > 4 , 3 M
ὄντος ἀνάγκη οὐσίαν εἶναι: ἀλλ᾽ οὔπω συλλελόγισται: οὐ yap
ἔχουσιν αἱ προτάσεις ὡς εἴπομεν.
2 A > > -
"Amarope0o, 8^ ἐν rois τοι-
P4 M ^ > al ? > ^ , Ld
ούτοις διὰ τὸ ἀναγκαῖόν τι συμβαίνειν ἐκ τῶν κειμένων, ὅτι
A € M > at , 2 V [ἢ M M >
καὶ 6 συλλογισμὸς ἀναγκαῖόν ἐστιν. ἐπὶ πλέον δὲ τὸ ἀναγ-
^ ^ >
Katov ἢ 6 συλλογισμός: 6 μὲν yàp συλλογισμὸς πᾶς ἀναγ-
- ^ ^ σ >
καῖον, τὸ δ᾽ ἀναγκαῖον οὐ πᾶν συλλογισμός. ὥστ᾽ οὐκ εἴ τι
, θέ ~ , , , ἡθύ. > M
συμβαίνει τεθέντων τινῶν, πειρατέον ἀνάγειν εὐθύς, ἀλλὰ
πρῶτον ληπτέον τὰς δύο προτάσεις, εἶθ᾽ οὕτω διαιρετέον εἰς
τοὺς ὅρους, μέσον δὲ θετέον τῶν ὅρων τὸν ἐν ἀμφοτέραις
ταῖς προτάσεσι λεγόμενον: ἀνάγκη γὰρ τὸ μέσον ἐν ἀμ-
φοτέραις ὑπάρχειν ἐν ἅπασι τοῖς σχήμασιν.
"Ea * 4
ἂν μὲν οὖν
^ ~ a M
κατηγορῇ kai κατηγορῆται τὸ μέσον, ἢ αὐτὸ μὲν κατη-
^ > ^ ^ ^ » ^
γορῇ, ἄλλο δ᾽ ἐκείνου ἀπαρνῆται, τὸ πρῶτον ἔσται σχῆμα:
814 τιθέντα ABdn 15 προτείναντας d τὴν Cn Ál*, fecerunt AB:
rod ταύτῃ BnÁl*: αὐτῇ BC, fecit A: τούτῳ d 16-17 οὔτε...
περαίνονται om, Al 18 οὖν] δὲ n 19 εἴ om. ABCd 20 ἔλθῃ
Ἔτις Cant 21 ἀναγαγεῖν BC? Alc: ἀγαγεῖν ACdn 22 864-5
ἀπατὴ γίνεται ἢ 23 τι post δοκοῦσι n 24-5 ἀναιρουμένης. ..
ἐστὶν om. C 25 μὴ] οὐκ 28 λείπουσι ri 33 ἀναγκαῖός Cd
34 05... συλλογισμὸς om. A} πᾶς om. ἢ 38 θετέον τὸν ὅρον C
40 οὖν om. C br κατηγοροίη BCd καὶ κατηγορεῖται Bt κατηγο-
ροίη Β 2 ἔστω d
15
20
25
30
31
31
35
40
40
47^
ANAAYTIKQN IIPOTEPON A
ἐὰν δὲ xai κατηγορῇ καὶ ἀπαρνῆται ἀπό τινος, τὸ μέσον"
FA > Ld , , ^ - * 4 3, ~ 4
ἐὰν δ᾽ ἄλλα ἐκείνου κατηγορῆται, ἢ τὸ μὲν ἀπαρνῆται τὸ
5986 κατηγορῆται, τὸ ἔσχατον. οὕτω γὰρ εἶχεν ἐν ἑκάστῳ
σχήματι τὸ μέσον. ὁμοίως δὲ καὶ ἐὰν μὴ καθόλου ὦσιν
αἱ προτάσεις: 6 γὰρ αὐτὸς διορισμὸς τοῦ μέσου. φανερὸν οὖν
ὡς ἐν ᾧ λόγῳ μὴ λέγεται ταὐτὸ πλεονάκις, ὅτι οὐ γίνεται
συλλογισμός: οὐ γὰρ εἴληπται μέσον. ἐπεὶ δ᾽ ἔχομεν ποῖον
10 ép. ἑκάστῳ σχήματι περαίνεται τῶν προβλημάτων, καὶ ἐν
τῶι τὸ καθόλου καὶ ἐν ποίῳ τὸ ἐν μέρει, φανερὸν ὡς οὐκ
E σ΄ . M , 4 — 67 /
eis ἅπαντα τὰ σχήματα βλεπτέον, ἀλλ᾽ ἑκάστου προβλή-
ματος εἰς τὸ οἰκεῖον. ὅσα δ᾽ ἐν πλείοσι περαίνεται, τῇ τοῦ
μέσου θέσει γνωριοῦμεν τὸ σχῆμα.
ις «“ἊΠολλάκις μὲν οὖν ἀπατᾶσθαι συμβαίνει περὶ τοὺς συλ-
λογισμοὺς διὰ τὸ ἀναγκαῖον, ὥσπερ εἴρηται πρότερον, ἐνίοτε
x € , ~ ~ Ld
δὲ παρὰ τὴν ὁμοιότητα τῆς τῶν ὅρων θέσεως" ὅπερ οὐ χρὴ
, € ^ a A ~ M
λανθάνειν ἡμᾶς. οἷον εἰ τὸ A κατὰ τοῦ B λέγεται kai τὸ B
MJ ^ , 4 bad a > , ^ Ed
κατὰ ToU l' δόξειε yap dv οὕτως ἐχόντων τῶν ὅρων εἶναι
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νοητὸς Ἀριστομένης, τὸ δ᾽ ἐφ᾽ ᾧ Γ ᾿Αἀριστομένης. ἀληθὲς δὴ τὸ
A ^ B € » 04 H > 8 1 V Fi 8
τῷ ὑπάρχειν. ἀεὶ γάρ ἐστι διανοητὸς ᾿Αἀριστομένης.
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> f x δ᾽ Α ~ D > € , θ i ,
25 ἀριστομένῃς. τὸ τῷ οὐχ ὑπάρχει: φθαρτὸς γάρ
ἐστιν ὁ Ἰ᾿Αριστομένης. οὐ γὰρ ἐγίνετο συλλογισμὸς οὕτως
ἐχόντων τῶν ὅρων, ἀλλ᾽ ἔδει καθόλου τὴν A B ληφθῆναι
πρότασιν. τοῦτο δὲ ψεῦδος, τὸ ἀξιοῦν πάντα τὸν διανοητὸν
, / 3v 7. 8 ^x Ap een Rcg at dÀ
‘Aptoropevny ἀεὶ εἶναι, φθαρτοῦ ὄντος Apwrouévovs. πάλιν
ϑοἔστω τὸ μὲν ἐφ᾽ ᾧ I Μίκκαλος, τὸ δ᾽ ἐφ᾽ à B “μουσικὸς
Μίκκαλος, ἐφ᾽ d δὲ τὸ A τὸ φθείρεσθαι αὔριον. ἀληθὲς
M Ml ^ ^ € A , , > A
δὴ τὸ B τοῦ I κατηγορεῖν: 6 yap Μίκκαλός ἐστι μουσικὸς
Μίκκαλος. ἀλλὰ καὶ τὸ A τοῦ B- φθείροιτο γὰρ ἂν av-
ριον μουσικὸς Μίκκαλος. τὸ δέ γε Α τοῦ Γ ψεῦδος. τοῦτο
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35 δὴ ταὐτόν ἐστι τῷ πρότερον: οὐ yàp ἀληθὲς καθόλου, Mix-
| Ld , L4 rà * ^
καλος μουσικὸς ὅτι φθείρεται αὔριον: τούτου δὲ μὴ λη-
φθέντος οὐκ ἦν συλλογισμός.
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τῶν ὅρων C 21 Α)τὸα A 22 τὸ.. .᾿Αριστομένης om. ni 23
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33
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32. 47^3-35. 48°32
“ n + e 3 5 " > Say Bj "
Αὕτη μὲν οὖν ἡ ἀπάτη γίνεται ἐν τῷ παρὰ paxpor
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34 700€ παντι vrapxyew, συγχωροῦμεν. πολλακις O€ ιαψεύ- 40
δεσθαι συμπεσεῖται mapa τὸ μὴ καλῶς ἐκτίθεσθαι τοὺς 485
κατὰ τὴν πρότασιν ὅρους, οἷον εἰ τὸ μὲν Α εἴη ὑγίεια, τὸ
δ᾽ ἐφ᾽ ᾧ B νόσος, ἐφ᾽ à δὲ I' ἄνθρωπος. ἀληθὲς yàp εἰ-
^ Ld * » A ~ > , € ΄ , ~
πεῖν ὅτι τὸ A οὐδενὶ τῷ B ἐνδέχεται ὑπάρχειν (οὐδεμιᾷ
‘ , € , L4 , * , σ ^ ‘ ~
yàp νόσῳ ὑγίεια ὑπάρχει), καὶ πάλιν ὅτι τὸ B παντὶ τῷ 5
Γ ὑπάρχει (πᾶς γὰρ ἄνθρωπος δεκτικὸς νόσου). δόξειεν ἂν
7 , a 2 ^ > 7 [4 , [4 ,
οὖν συμβαίνειν μηδενὶ ἀνθρώπῳ ἐνδέχεσθαι ὑγίειαν ὑπάρ-
χειν. τούτου δ᾽ αἴτιον τὸ μὴ καλῶς ἐκκεῖσθαι τοὺς ὅρους
κατὰ τὴν λέξιν, ἐπεὶ μεταληφθέντων τῶν κατὰ τὰς ἕξεις
οὐκ ἔσται συλλογισμός, οἷον ἀντὶ μὲν τῆς ὑγιείας εἰ τεθείη 10
τὸ ὑγιαῖνον, ἀντὶ δὲ τῆς νόσου τὸ νοσοῦν. οὐ γὰρ ἀληθὲς
εἰπεῖν ὡς οὐκ ἐνδέχεται τῷ νοσοῦντι τὸ ὑγιαίνειν ὑπάρξαι.
Y d A x , > L4 , > ^ ~
τούτου δὲ μὴ ληφθέντος οὐ γίνεται συλλογισμός, εἰ μὴ τοῦ
» LÀ ~ , » > if > ΓΑ ^ M
ἐνδέχεσθαι: τοῦτο δ᾽ οὐκ ἀδύνατον: ἐνδέχεται yap μηδενὶ
ἀνθρώπῳ ὑπάρχειν ὑγίειαν. πάλιν ἐπὶ τοῦ μέσου σχήματος τς
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» i^ A x $ Po e L4 L4 > τ " 3 ,
ἀνθρώπῳ δὲ παντὶ ἐνδέχεται ὑπάρχειν, ὥστ᾽ οὐδενὶ ἀνθρώπῳ
νόσον. ἐν δὲ τῷ τρίτῳ σχήματι κατὰ τὸ ἐνδέχεσθαι συμ-
, M m= * A Li , * , ‘ > ,
βαίνει τὸ ψεῦδος, καὶ yap ὑγίειαν καὶ νόσον καὶ ἐπιστή-
μὴν καὶ ἄγνοιαν καὶ ὅλως τὰ ἐναντία τῷ αὐτῷ ἐνδέχεται 20
ὑπάρχειν, ἀλλήλοις δ᾽ ἀδύνατον. τοῦτο δ᾽ ἀνομολογούμενον
τοῖς προειρημένοις: ὅτε γὰρ τῷ αὐτῷ πλείω ἐνεδέχετο ὑπάρ-
» , LI. ,
xew, ἐνεδέχετο καὶ ἀλλήλοις.
Φανερὸν οὖν ὅτι ἐν ἅπασι τούτοις ἡ ἀπάτη γίνεται παρὰ
τὴν τῶν ὅρων ἔκθεσιν: μεταληφθέντων γὰρ τῶν κατὰ τὰς as
" S , ^ a T7 c ‘ 4 "
ἕξεις οὐδὲν γίνεται ψεῦδος. δῆλον οὖν ὅτι κατὰ Tas τοιαύτας
προτάσεις ἀεὶ τὸ κατὰ τὴν ἕξιν ἀντὶ τῆς ἕξεως μεταλη-
πτέον καὶ θετέον ὅρον.
35 Οὐ δεῖ δὲ τοὺς ὅρους ἀεὶ ζητεῖν ὀνόματι ἐκτίθεσθαι-
πολλάκις γὰρ ἔσονται λόγοι οἷς οὐ κεῖται ὄνομα: διὸ χα- 30
λεπὸν ἀνάγειν τοὺς τοιούτους συλλογισμούς. ἐνίοτε δὲ καὶ ἀπα-
^ » ^ * s , - ~
τᾶσθαι συμβήσεται διὰ τὴν τοιαύτην ζήτησιν, olov ὅτι τῶν
b38 ἐν om. A1BICd 4823 δὲ om. B 4 rTàv B n 18 νόσον
A BCn AIP : νόσοι d : νόσος coni. Tredennick TQ om. A} τρίτῳ] y f
20 τῷ] παντὶ τῷ n 21 ἀνομολογούμενον ACdP: ἂν ὁμολογούμενον Bal
22 ἐνδέχοιτο n 27 κατὰ τὴν ξξιν BCdnAl: ἕξιν μὴ ἔχον fecit A: κατὰ τὴν
ἕξιν μετέχον Bt 30 ὀνόματα f διὸ-Ἐ καὶ n
ANAAYTIKQN IIPOTEPON A
ἀμέσων ἔστι συλλογισμός. ἔστω τὸ A δύο ὀρθαί, τὸ ἐφ᾽ ᾧ
B τρίγωνον, ἐφ᾽ ᾧ δὲ Γ ἰσοσκελές. τῷ μὲν οὖν Γ ὑπάρχει
3570 A διὰ τὸ B, τῷ δὲ B οὐκέτι δι’ ἄλλο (καθ᾽ αὑτὸ γὰρ
^ D » , > 4 a > > » , ^
τὸ τρίγωνον ἔχει δύο ὀρθάς), ὥστ᾽ οὐκ ἔσται μέσον τοῦ A B,
ἀποδεικτοῦ ὄντος. φανερὸν γὰρ ὅτι τὸ μέσον οὐχ οὕτως ἀεὶ
, € , > > 3 5, , Ld , > A
ληπτέον ws τόδε τι, ἀλλ᾽ ἐνίοτε λόγον, ὅπερ συμβαίνει κἀπὶ
τοῦ λεχθέντος.
M M € Ἂ t ^ ^ , M ^ ^
4» To δὲ ὑπάρχειν τὸ πρῶτον τῷ μέσῳ καὶ τοῦτο τῷ
La , ὃ ^ λ p , e »* 0 , ἀλλ A.
ἄκρῳ od δεῖ λαμβάνειν ὡς αἰεὶ κατηγορηθησομένων ή
"^ € , , ^ ^ ~ > ^
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M » ^ * [4 , > e , > > Ld ^
του. καὶ ἐπὶ τοῦ μὴ ὑπάρχειν δ᾽ ὡσαύτως. ἀλλ᾽ ὁσαχῶς
^ , M M > X J ^ ? ' ^
τὸ εἶναι λέγεται kal τὸ ἀληθὲς εἰπεῖν αὐτὸ τοῦτο, rooav-
ταχῶς οἴεσθαι χρὴ onuaive καὶ τὸ ὑπάρχειν. οἷον ὅτι
s τῶν ἐναντίων ἔστι μία ἐπιστήμη. ἔστω γὰρ τὸ A τὸ μίαν
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~ t , , e ^ > {3 ^ La > ~
τῷ B ὑπάρχει οὐχ ὥστε rà ἐναντία [τὸ] μίαν εἶναι [αὐτῶν]
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ἐπιστήμην, ἀλλ᾽ ὅτι ἀληθὲς εἰπεῖν Kar’ αὐτῶν μίαν εἶναι
αὐτῶν ἐπιστήμην.
/ 5 x X * + 4 ^ L4 A ~ ,
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θ M δὲ , * o. ^ , * λέ θ * 3
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€ , , * , , - 3 > ~ 2 * € H
ἡ σοφία ἐστὶν ἐπιστήμη, τοῦ δ᾽ ἀγαθοῦ ἐστὶν ἡ σοφία, συμ-
πέρασμα ὅτι τοῦ ἀγαθοῦ ἔστιν ἐπιστήμη: τὸ μὲν δὴ ἀγαθὸν
᾽ » E H t ^ ; 24 > H [E H Li
οὐκ ἔστιν ἐπιστήμη, ἡ δὲ σοφία ἐστὶν ἐπιστήμη. ὁτὲ δὲ τὸ
το μὲν μέσον ἐπὶ τοῦ τρίτου λέγεται, τὸ δὲ πρῶτον ἐπὶ τοῦ μέ-
cov οὐ λέγεται, οἷον εἰ τοῦ ποιοῦ παντὸς ἔστιν ἐπιστήμη 7
ἐναντίου, τὸ δ᾽ ἀγαθὸν καὶ ἐναντίον καὶ ποιόν, συμπέρασμα
μὲν ὅτι τοῦ ἀγαθοῦ ἔστιν ἐπιστήμη, οὐκ ἔστι δὲ τὸ ἀγαθὸν ἐπι-
, 3 A M * , M * > , 3 A t ? ‘ ~
στήμη οὐδὲ TO ποιὸν οὐδὲ τὸ ἐναντίον, ἀλλὰ τὸ ἀγαθὸν ταῦτα.
i. ^ a - a ^
20 ἔστι δὲ μήτε τὸ πρῶτον κατὰ τοῦ μέσου μήτε τοῦτο κατὰ τοῦ
τρίτοῦ, τοῦ πρώτου κατὰ τοῦ τρίτου ὁτὲ μὲν λεγομένου ὁτὲ δὲ μὴ
λεγομένου. οἷον εἰ οὗ ἐπιστήμη ἔστιν, ἔστι τούτου γένος, τοῦ δ᾽
ἀγαθοῦ ἔστιν ἐπιστήμη, συμπέρασμα ὅτι τοῦ ἀγαθοῦ ἔστι γένος"
^ T Ww
κατηγορεῖται δ᾽ οὐδὲν κατ᾽ οὐδενός. εἰ δ᾽ οὗ ἔστιν ἐπιστήμη,
25 γένος ἐστὶ τοῦτο, τοῦ δ᾽ ἀγαθοῦ ἔστιν ἐπιστήμη, συμπέρασμα
933 ἔστι ABCdP: éoratn:om, Ale 6 συλλογισμός AICP τὸ om.d
Tó48' C 34 δὲ - τὸ A 37 ἀποδεικτικοῦ A BlCdn yap} οὖν (3
be δ᾽ om. Bt 3 αὐτὸ om. Alc 6 τὰ- δ᾽ A*nI' ἐναντία-: rois 418
Β]τὸ Bd 7 ὥστε τὰ ἐναντία μίαν εἶναι scripsi, fort. habet Al: ὡς τὰ ἐναντία
(+éor nD) τὸ μίαν εἶναι αὐτῶν codd. P 12-13 ἐστὶν! . . . τοῦ om. A?
12 cogia®+ ἐπιστήμη ABCn AIP 20 δὲ ABdnI': δὲ ὅτε B*C Alc
a a
35. 48°33-38. 49°18
- , , , ,ὔ x x ‘ - L4 ~
ὅτι τἀγαθόν ἐστι γένος: κατὰ μὲν δὴ τοῦ ἄκρου κατηγορεῖ-
* ~ » 5 , 2 , Ψ.
ται τὸ πρῶτον, κατ᾽ ἀλλήλων δ᾽ οὐ λέγεται. 27
Tov αὐτὸν δὴ 27
Ἐ & LAN ^ » Li , Li , M LEA J
τρόπον kal ἐπὶ τοῦ μὴ ὑπάρχειν ληπτέον. od yap ἀεὶ ση-
, 4 A [4 [4 , ^ M P , > »
paives τὸ μὴ ὑπάρχειν τόδε τῷδε μὴ εἶναι τόδε τόδε, ἀλλ
, 7 * bi 4 , ^ - 4 ^ - ΕΣ LÀ
ἐνίοτε τὸ μὴ εἶναι τόδε τοῦδε ἢ τόδε τῷδε, olov ὅτι οὐκ ἔστι 30
κινήσεως κίνησις ἢ γενέσεως γένεσις, ἡδονῆς δ᾽ ἔστιν" οὐκ ἄρα
ἡ ἡδονὴ γένεσις. ἢ πάλιν ὅτι γέλωτος μὲν ἔστι σημεῖον, ση-
μείου δ᾽ οὐκ ἔστι σημεῖον, ὥστ᾽ οὐ σημεῖον 6 γέλως. ὁμοίως
δὲ κἀν τοῖς ἄλλοις ἐν ὅσοις ἀναιρεῖται τὸ πρόβλημα τῷ
λέγεσθαί πως πρὸς αὐτὸ τὸ γένος. πάλιν ὅτι ὁ καιρὸς οὐκ 35
ἔστι χρόνος δέων- θεῷ γὰρ καιρὸς μὲν ἔστι, χρόνος δ᾽ οὐκ
L4 , 4 A] \ ^ > / L4 * ^
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θετέον καιρὸν καὶ χρόνον δέοντα καὶ θεόν, τὴν δὲ πρότασιν
ληπτέον κατὰ τὴν τοῦ ὀνόματος πτῶσιν. ἁπλῶς γὰρ τοῦτο
λέγομεν κατὰ πάντων, ὅτι τοὺς μὲν ὅρους ἀεὶ θετέον κατὰ 4o
τὰς κλήσεις τῶν ὀνομάτων, οἷον ἄνθρωπος ἢ ἀγαθόν 7) évav-
, , 2 , ~ 5 ^x 25 , H x , a
Tia, οὐκ ἀνθρώπου ἢ ἀγαθοῦ ἢ ἐναντίων, τὰς δὲ προτάσεις 49
ληπτέον κατὰ τὰς ἑκάστου πτώσεις: ἢ γὰρ ὅτι τούτῳ, οἷον
M LÀ bal L4 , A , ^ Ld ^
τὸ ἴσον, ἢ ὅτι τούτου, olov τὸ διπλάσιον, ἢ ὅτι τοῦτο, olov
^ u ^ ἷ “5 ^ ΄ T Lj vw ^ -
TO τύπτον ἢ ὁρῶν, ἢ ὅτι οὗτος, olov ὁ dvOpurtos ζῷον, ἢ
εἴ πως ἄλλως πίπτει τοὔνομα κατὰ τὴν πρότασιν. 5
37; Τὸ δ᾽ ὑπάρχειν τόδε τῷδε καὶ τὸ ἀληθεύεσθαι τόδε
κατὰ τοῦδε τοσαυταχῶς ληπτέον ὁσαχῶς αἱ κατηγορίαι
διήρηνται, καὶ ταύτας 7) πῇ ἢ ἁπλῶς, ἔτι T) ἁπλᾶς ἢ συμ-
πεπλεγμένας- ὁμοίως δὲ καὶ τὸ μὴ ὑπάρχειν. ἐπισκεπτέον
δὲ ταῦτα καὶ διοριστέον βέλτιον. το
428 Τὸ δ᾽ ἐπαναδιπλούμενον ἐν ταῖς προτάσεσι πρὸς τῷ
a L4 , > 4 ^ , , > », ΄
πρώτῳ ἄκρῳ θετέον, οὐ πρὸς τῷ μέσῳ. λέγω δ᾽ οἷον εἰ γέ-
vovro συλλογισμὸς ὅτι τῆς δικαιοσύνης ἔστιν ἐπιστήμη ὅτι
> , a oe 3 , nn > , ‘ ~ , ,
ἀγαθόν, τὸ ὅτι ἀγαθόν ἢ jj ἀγαθόν πρὸς τῷ πρώτῳ θετέον.
ἔστω γὰρ τὸ A ἐπιστήμη ὅτι ἀγαθόν, ἐφ᾽’ ᾧ δὲ B ἀγαθόν, 15
}83 T * a ‘ A > Li ^ ^
ἐφ᾽ ᾧ δὲ Γ δικαιοσύνη. τὸ δὴ A ἀληθὲς τοῦ B κατηγορῆ-
^ ^ > ^ ww > , LÀ » 3 ^ M
cav τοῦ yàp ἀγαθοῦ ἔστιν ἐπιστήμη ὅτι ἀγαθόν. ἀλλὰ καὶ
M ^ € A , 4 > Ff L4 M T ,
τὸ Β τοῦ I^ ἡ yàp δικαιοσύνη ὅπερ ἀγαθόν. οὕτω μὲν οὖν yi-
bag τῷδε] τόδε C τόδε] τῷδε n, fecit B 30 τὸ om. ἢ 35
γένος codd. AIP: μέσον coni. Al 37 ὠφέλιμα n 41 κλήσεις
CdnAl: κλίσεις AB τἀναντία ἢ 4933 ór) om. 1 4T -Ὁ τὸ γῖ
8 ἢ n Alc: om. ABCA 12 οἷον] ὅτι ABCd 14 ἢ om. Ct 15
ἐφ᾽... ἀγαθόν om. πὶ
ANAAYTIKON IIPOTEPON A
vera, ἀνάλυσις. «i δὲ πρὸς τῷ B τεθείη τὸ ὅτι ἀγαθόν, οὐκ
ao ἔσται: τὸ μὲν yap A κατὰ τοῦ B ἀληθὲς ἔσται, τὸ δὲ B
^ ~ > > b w 4 x > 1 Ld > 4
κατὰ τοῦ l' οὐκ ἀληθὲς ἔσται: τὸ γὰρ ἀγαθὸν ὅτι ἀγαθὸν
κατηγορεῖν τῆς δικαιοσύνης ψεῦδος καὶ οὐ συνετόν. ὁμοίως δὲ
* > 4 € x , Ld μὲ , 3 > , ^
καὶ εἰ τὸ ὑγιεινὸν δειχθείη ὅτι ἔστιν ἐπιστητὸν ἦ ἀγαθόν, 7
τραγέλαφος $ μὴ ov, 1$ ὁ ἄνθρωπος φθαρτὸν jj
as αἰσθητόν: ἐν ἅπασι γὰρ τοῖς ἐπικατηγορουμένοις πρὸς τῷ
ἄκρῳ τὴν ἐπαναδίπλωσιν θετέον.
, € » b * , ~ Ed Ld Li ~
Οὐχ ἡ αὐτὴ δὲ θέσις τῶν ὅρων ὅταν ἁπλῶς τι συλ-
^ εν , ^ ^*^ ^ 4 > t e
Aoyio καὶ ὅταν τόδε τι 7 πῇ 9 πώς, λέγω δ᾽ olov ὅταν
τἀγαθὸν ἐπιστητὸν δειχθῇ καὶ ὅταν ἐπιστητὸν ὅτι ἀγα-
, * , > 4 € ^ > M an , 2, ^
3o 0óv- GAN’ εἰ μὲν ἁπλῶς ἐπιστητὸν δέδεικται, μέσον θετέον τὸ
" » ,* @ > , M ow L4 ^ M A Lj ,
ὄν, εἰ δ᾽ ὅτι ἀγαθόν, τὸ τὶ ὄν. ἔστω yap τὸ μὲν A ἐπιστήμη
ὅτι τὶ ὄν, ἐφ᾽ à δὲ B ov τι, τὸ δ᾽ ἐφ᾽ à I ἀγαθόν. ἀλη-
θὲς δὴ τὸ Α τοῦ B κατηγορεῖν: ἦν γὰρ ἐπιστήμη τοῦ τινὸς ὄν-
τος ὅτι τὶ ὄν. ἀλλὰ καὶ τὸ B τοῦ I" τὸ γὰρ ἐφ᾽ ᾧ Γ ὅν
LÀ M ^ ^ w L4 > , > ~ e
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> , 7 H EH INE ES γα 7 a >? > 1 [I
dyaÜóv- ἦν yap τὸ τὶ ὃν τῆς ἰδίου σημεῖον οὐσίας. εἰ δὲ τὸ
ὃν μέσον ἐτέθη καὶ πρὸς τῷ ἄκρῳ τὸ ὃν ἁπλῶς καὶ μὴ τὸ
M ^ , Li *, hj T 3 Ld v > , >
Ti ὃν ἐλέχθη, οὐκ dv ἦν συλλογισμὸς ὅτι ἔστιν ἐπιστήμη τά-
γαθοῦ ὅτι ἀγαθόν, ἀλλ᾽ ὅτι ὄν, οἷον ἐφ᾽ à τὸ A ἐπιστήμη
49^ ὅτι óv, ἐφ’ ᾧ B ὄν, ἐφ᾽ à I' ἀγαθόν. φανερὸν οὖν ὅτι ἐν
τοῖς ἐν μέρει συλλογισμοῖς οὕτως ληπτέον τοὺς ὅρους.
Δεῖ δὲ καὶ μεταλαμβάνειν ἃ τὸ αὐτὸ δύναται, ὀνό- 30
ματα ἀντ᾽ ὀνομάτων καὶ λόγους ἀντὶ λόγων καὶ ὄνομα καὶ
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s Àóyov, Kat del ἀντὶ τοῦ λόγου τοὔνομα λαμβάνειν: pdcv ydp
€ ~ -" w ¢ > * , , ^ M Li
ἡ τῶν ὅρων ἔκθεσις. olov εἰ μηδὲν διαφέρει εἰπεῖν τὸ ὑπολη-
πτὸν τοῦ δοξαστοῦ μὴ εἶναι γένος 7 μὴ εἶναι ὅπερ ὑποληπτόν
τι τὸ δοξαστόν (ταὐτὸν γὰρ τὸ σημαινόμενον), ἀντὶ τοῦ λόγου
~ , ^ e A M x ¥ L4 Á,
τοῦ λεχθέντος τὸ ὑποληπτὸν Kal τὸ δοξαστὸν ὅρους θετέον.
> ^ , > *, , 3 ἣ, Y € A > ^ ^
10 ᾿Επεὶ δ᾽ οὐ ταὐτόν ἐστι τὸ εἶναι τὴν ἡδονὴν ἀγαθὸν xai 40
τὸ εἶναι τὴν ἡδονὴν τὸ ἀγαθόν, οὐχ ὁμοίως θετέον τοὺς ὅρους,
» , ᾽ , , « M L4 L4 € ‘ , , >
ἀλλ᾽ εἰ μέν ἐστιν ὁ συλλογισμὸς ὅτι ἡ ἡδονὴ τἀγαθόν, τά-
Ψ' > » o > , , , a 5 a - L4
γαθόν, εἰ δ᾽ ὅτι ἀγαθόν, ἀγαθόν. οὕτως κἀπὶ τῶν ἄλλων.
a20-1 T0*. . . ἔσται om. "ἢ: ἔσται om. C 23 ἐπιστητόν ἐστιν PC;
ἐπιστητὸν n 24 ἡ ABCd et ut vid. AIP: δοξαστὸν ἡ B* Ale: μὴ ὃν $n
àv 4- Bo£aaróv d? ὁ om. n Ale 28 kai... πῇ om. πὶ 29 ὅτι
n et ut vid. P: τι ὅτι ABC 32 ri fecit B 3389]dvm — Fu] ἡ π
34 τὶ om. πὶ 36 ἀγαθόν) τι ὄν B? 39 οἷον om. An 5 ῥᾷον n
8 τὸ) τόδε B! γάρ: τι n: ἐστὶ Γ 9 ληφθέντος n I3 οὕτω
T86 nt
38. 49°19-42. 50°6
41 Οὐκ ἔστι δὲ ταὐτὸν οὔτ᾽ εἶναι οὔτ᾽ εἰπεῖν, ὅτι ᾧ τὸ
ὑπάρχει, τούτῳ παντὶ τὸ A ὑπάρχει, καὶ τὸ εἰπεῖν τὸ ᾧ τ5
AY
^ A Li , * M * € , ;$
παντὶ τὸ B ὑπάρχει, καὶ τὸ A παντὶ ὑπάρχει: οὐδὲν yap
τυ
κωλύει τὸ B τῷ I ὑπάρχειν, μὴ παντὶ δέ. οἷον ἔστω τὸ B
καλόν, τὸ δὲ I" λευκόν. εἰ δὴ λευκῷ τινὶ ὑπάρχει καλόν,
ἀληθὲς εἰπεῖν ὅτι τῷ λευκῷ ὑπάρχει καλόν: ἀλλ᾽ οὐ παντὶ
” > A T A ^ L4 4 M * ^ > φ
ἴσως. εἰ μὲν οὖν τὸ A τῷ Β ὑπάρχει, μὴ παντὶ δὲ καθ᾽ οὗ 20
^ w > > M ^ A wo» > , Ui ,
τὸ B, οὔτ᾽ εἰ παντὶ τῷ I’ τὸ B, οὔτ᾽ εἰ μόνον ὑπάρχει,
ἀνάγκη τὸ Α οὐχ ὅτι οὐ παντί, ἀλλ᾽ οὐδ᾽ ὑπάρχειν. εἰ δὲ
καθ᾽ οὗ ἂν τὸ B λέγηται ἀληθῶς, τούτῳ παντὶ ὑπάρχει
γηται ἀληθῶς, τούτῳ i ὑπάρχει,
συμβήσεται τὸ A, καθ᾽ οὗ παντὸς τὸ B λέγεται, κατὰ
τούτου παντὸς λέγεσθαι. εἰ μέντοι τὸ A λέγεται καθ᾽ οὗ ἂν 25
M , 4A d RAND! , ~ t ,
τὸ B λέγηται κατὰ παντός, οὐδὲν κωλύει τῷ I ὑπάρχειν
‘ A ‘ x A] a Ld ^ L4 , » M ^
TO B, μὴ παντὶ δὲ τὸ A ἢ ὅλως μὴ ὑπάρχειν. ἐν δὴ rois
τρισὶν ὅροις δῆλον ὅτι τὸ καθ᾽ οὗ τὸ B παντὸς τὸ A λέγε-
^ L4 > Ld a , ^ ££ ,
σθαι τοῦτ᾽ ἔστι, καθ᾽ ὅσων τὸ B λέγεται, κατὰ πάντων Aé-
* ^ * > * ^ 4 M] M &
γεσθαι xai τὸ A. καὶ ef μὲν κατὰ παντὸς τὸ B, καὶ τὸ 30
A οὕτως: εἰ δὲ μὴ κατὰ παντός, οὐκ ἀνάγκη τὸ A κατὰ
παντός.
Οὐ δεῖ δ᾽ οἴεσθαι παρὰ τὸ ἐκτίθεσθαί τι ovpPaivew
LÀ $, * a Ed ^ , > LI
ἄτοπον: οὐδὲν yap προσχρώμεθα τῷ τόδε τι εἶναι, GAA
ὥσπερ ὁ γεωμέτρης τὴν ποδιαίαν καὶ εὐθεῖαν τήνδε καὶ 35
2 À! ^ Hu λέ ΕΣ L4 ἀλλ᾽ > e ~ LÀ
ἀπλατῇ εἶναι λέγει οὐκ οὔσας, οὐχ οὕτως χρῆται ὡς
, , , Ld A a ^ L4 € Ld
ἐκ τούτων συλλογιζόμενος. ὅλως yap ὃ μὴ ἔστιν ὡς ὅλον
"ἢ , * Ld x — e , 4 Ld >,
πρὸς μέρος καὶ ἄλλο πρὸς τοῦτο ws μέρος πρὸς ὅλον, ἐξ
οὐδενὸς τῶν τοιούτων δείκνυσιν ὁ δεικνύων, ὥστε οὐδὲ γίνεται
συλλογισμός. τῷ δ᾽ ἐκτίθεσθαι οὕτω χρώμεθα ὥσπερ καὶ 505
^ ? , M] , > > , , A L4 «
τῷ αἰσθάνεσθαι, τὸν μανθάνοντ᾽ ἀλέγοντες" οὐ γὰρ οὕτως ὡς
L4 , > , > > ~ LÀ > φ e
ἄνευ τούτων οὐχ οἷόν τ᾽ ἀποδειχθῆναι, ὥσπερ ἐξ ὧν ὁ συλ-
λογισμός.
42 Mi λανθανέτω δ᾽ ἡμᾶς ὅτι ἐν τῷ αὐτῷ συλλογισμῷ s
οὐχ ἅπαντα τὰ συμπεράσματα δι᾽ ἑνὸς σχήματός ἐστιν,
διότῷβ Βὶ οὐδὲσ ιτιϑγετὸᾳΒβ ig97Hom.n = 21 εἴ3- τινὶ Ale
22 ὑπάρχειν- τῷ y nT 23 παντὶ 4- ró a BL 26 τῷ] εἰ τῷ CI Al
ὑπάρχει C Al 27 ἢ ABC*n?P: om. Cn Alc 8e C 28 ro! om. A
29 πάντων- τούτων Cc 32 Tavrós Al, Aldina : παντὸς a. B. y. codd.
35 xai 4- τὴν Cn τήνδε-ἰ εἶναι ἩΓ 36 εἶναι om. Cn” οὖσαν Bt
οὐχ B*C*d AIP et ante ὡς n; om. ABC 39 were] o? yap n So?1
ἐκτίθεσθαι προσχρώμεθα Al 2 τὸν μανθάνοντ᾽ ἀλέγοντες scripsi: τὸν
μανθάνοντα λέγοντες codd. AIP: πρὸς τὸν μανθάνοντα λέγοντες Pacius 3
τούτων BAL: τούτου ACrI” 6 εἰσίν ABC
ANAAYTIKQN TIPOTEPQN A
ἀλλὰ τὸ μὲν διὰ τούτου τὸ δὲ δι’ ἄλλου. δῆλον οὖν ὅτι καὶ
τὰς ἀναλύσεις οὕτω ποιητέον. ἐπεὶ δ᾽ οὐ πᾶν πρόβλημα ἐν
ἅπαντι σχήματι ἀλλ᾽ ἐν ἑκάστῳ τεταγμένα, φανερὸν ἐκ τοῦ
το συμπεράσματος ἐν ᾧ σχήματι ζητητέον.
15
20
25
20
35
40
Τούς τε πρὸς ὁρισμὸν τῶν λόγων, ὅσοι πρὸς ἕν τι Tvy- 43
, ὃ ιλ , ~ > - " ^ a ὃ Δ 0
χάνουσι διειλεγμένοι τῶν ἐν TH ὅρῳ, πρὸς ὃ διείλεκται θε-
,
τέον ὅρον, kai οὐ τὸν ἅπαντα Aóyov: ἧττον yàp συμβήσε-
, θ ἣν x ^ f » ^ y^! Lá "
ται ταράττεσθαι διὰ τὸ μῆκος, olov εἰ τὸ ὕδωρ ἔδειξεν ὅτι
ὑγρὸν ποτόν, τὸ ποτὸν καὶ τὸ ὕδωρ ὅρους θετέον.
“BE * AY , Li θέ, λλι * u é
τι δὲ τοὺς ἐξ ὑποθέσεως συλλογισμοὺς οὐ πειρατέον 44
ἀνάγειν: οὐ γὰρ ἔστιν ἐκ τῶν κειμένων ἀνάγειν. οὐ γὰρ διὰ
συλλογισμοῦ δεδειγμένοι εἰσίν, ἀλλὰ διὰ συνθήκης ὦμο-
,
λογημένοι πάντες. olov εἰ ὑποθέμενος, dv δύναμίς τις pia
4 ~ , [4 , H , , fh t διαλι
μὴ $ τῶν ἐναντίων, μηδ᾽ ἐπιστήμην μίαν εἶναι, εἶτα ε-
χθείη ὅτι οὐκ ἔστι πᾶσα δύναμις τῶν ἐναντίων, olovel τοῦ ὑγιεινοῦ
καὶ τοῦ νοσώδους- ἅμα γὰρ ἔσται τὸ αὐτὸ ὑγιεινὸν καὶ vo-
σῶδες. ὅτι μὲν οὖν οὐκ ἔστι μία πάντων τῶν ἐναντίων δύναμις,
3 Li μι 3 » 5 ΕΣ Mw > L4 r
ἐπιδέδεικται, ὅτι δ᾽ ἐπιστήμη οὐκ ἔστιν, οὐ δέδεικται. καίτοι
ὁμολογεῖν ἀναγκαῖον ἀλλ᾽ οὐκ ἐκ συλλογισμοῦ, ἀλλ᾽ ἐξ
ὑποθέσεως. τοῦτον μὲν οὖν οὐκ ἔστιν ἀναγαγεῖν, ὅτι δ᾽ οὐ μία
δύναμις, €orw: οὗτος γὰρ ἴσως καὶ ἦν συλλογισμός, ἐκεῖνο
δ᾽ ὑπόθεσις.
Lj , b 3 So. ἃ ^ ὃ A ^ 3 , ,
Ομοίως δὲ καὶ ἐπὶ τῶν διὰ τοῦ ἀδυνάτου περαινομένων"
δὲ A , . L4 > αλ » ἀλλὰ 3 M » X 18 4,
οὐδὲ yàp τούτους οὐκ ἔστιν ἀναλύειν, ἀλλὰ τὴν μὲν eis TO ἀδύ-
νατον ἀπαγωγὴν ἔστι (συλλογισμῷ γὰρ δείκνυται), θάτερον
δ᾽ , LÀ , ς L4 A , , M
οὐκ ἔστιν: ἐξ ὑποθέσεως yap περαίνεται. διαφέρουσι δὲ
τῶν προειρημένων ὅτι ἐν ἐκείνοις μὲν δεῖ προδιομολογήσα-
σθαι, εἰ μέλλει συμφήσειν, οἷον ἂν δειχθῇ μία δύναμις
^ , * [4 M , ^ 3,
τῶν ἐναντίων, καὶ ἐπιστήμην εἶναι τὴν αὐτήν- ἐνταῦθα δὲ καὶ
μὴ προδιομολογησάμενοι συγχωροῦσι διὰ τὸ φανερὸν εἶναι
τὸ ψεῦδος, οἷον τεθείσης τῆς διαμέτρου συμμέτρου τὸ τὰ
A ,
περιττὰ ἴσα εἶναι τοῖς ἀρτίοις.
Π. A ' δὲ ' L4 , > [4 θέ ^
oAÀoi δὲ Kai ἕτεροι περαίνονται ἐξ ὑποθέσεως, οὕς
, ^ A^. ^ RA
ἐπισκέψασθαι δεῖ καὶ διασημῆναι καθαρῶς. τίνες μὲν οὖν αἱ
a7 καὶ om. ACnI 9 τεταγμένον Bn 11 ὁρισμοὺς Clin I5
ὑγρὸν] oU 2: οὐχ ὑγρὸν Γ 19-20 μὴ ἢ plan: μία ἡ C 20 διαλεχθῇ C
21 πᾶσα ABCnAL: μία A? ΒΒΟΞΓ: πάντων A3 οἷον ἡ π 24 ἐπιδέ-
δεικται] ἀποδέδεικται AC 26 τοῦτον AB Alc : τοῦτο Cn ἀνάγειν (
οὐδὲ" 27 ἦν- ὁ Ὁ. 30 οὐκ om. Cin 37 olov 4- ὅτι G 38 εἶναι
ica C 40 oiv] τούτων C at om. a
42. 50*7-45. 50°36
ὃ * , * ~ 7, M s. L4 L4 b
ιαφοραὶ τούτων, Kal ποσαχῶς γίνεται τὸ ἐξ ὑποθέσεως, 50
σ ? ^ ~ ^ ^
ὕστερον ἐροῦμεν" viv δὲ τοσοῦτον ἡμῖν ἔστω φανερόν, ὅτι οὐκ ἔστιν
3 uA ᾽
ἀναλύειν εἰς τὰ σχήματα τοὺς τοιούτους συλλογισμούς. καὶ
δι᾿ ἣν αἰτίαν, εἰρήκαμεν.
“ "
45 Ὅσα δ᾽ ἐν πλείοσι σχήμασι δείκνυται τῶν προβλη- s
, ^ ^
μάτων, ἢν ev θατέρῳ συλλογισθῇ, ἔστιν ἀναγαγεῖν τὸν συλ-
, ^
λογισμὸν eis θάτερον, οἷον τὸν ἐν τῷ πρώτῳ στερητικὸν εἰς τὸ
, > ^ ^
δεύτερον, Kal τὸν ἐν τῷ μέσῳ εἰς τὸ πρῶτον, οὐχ ἅπαντας
δὲ ἀλλ᾽ » 3; L4 δὲ ‘ > ^ € Li 3 ^
é ἐνίους. ἔσται δὲ φανερὸν ev τοῖς ἑπομένοις. εἰ yàp
M ^ ^ ^
τὸ A μηδενὶ τῷ B, τὸ δὲ B παντὶ τῷ Γ, τὸ A οὐδενὶ τῷ τὸ
Γ. οὕτω μὲν οὖν τὸ πρῶτον σχῆμα, ἐὰν δ᾽ ἀντιστραφῇ τὸ
στερητικόν, τὸ μέσον ἔσται: τὸ γὰρ Β τῷ μὲν Α οὐδενί, τῷ
δὲ Γ᾿ παντὶ ὑπάρχει. ὁμοίως δὲ καὶ εἰ μὴ καθόλου ἀλλ᾽ ἐν
μέρει ὁ συλλογισμός, οἷον εἰ τὸ μὲν A μηδενὶ τῷ B, τὸ δὲ
Β τινὶ τῷ Γ' ἀντιστραφέντος γὰρ τοῦ στερητικοῦ τὸ μέσον 15
ἔσται σχῆμα.
Τῶν δ᾽ ἐν τῷ δευτέρῳ συλλογισμῶν οὗ μὲν καθόλον
ἀναχθήσονται εἰς τὸ πρῶτον, τῶν δ᾽ ἐν μέρει ἅτερος μόνος.
M ^ A ^ x 4 ^ X. 5. e ,
ἔστω yap τὸ A τῷ μὲν Β μηδενὶ τῷ δὲ Γ᾽ παντὶ ὑπάρχον.
ἀντιστραφέντος οὖν τοῦ στερητικοῦ τὸ πρῶτον ἔσται σχῆμα" τὸ 20
μὲν yàp B οὐδενὶ τῷ A, τὸ δὲ A παντὶ τῷ Γ᾽ ὑπάρξει. ἐὰν
δὲ τὸ κατηγορικὸν ἢ πρὸς τῷ B, τὸ δὲ στερητικὸν πρὸς τῷ
- Ld 4 M ^ 4 > M ^ X, A
I’, πρῶτον ὅρον θετέον τὸ I τοῦτο yap οὐδενὶ τῷ A, τὸ δὲ
A παντὶ τῷ B- ὥστ᾽ οὐδενὶ τῷ Bro I. οὐδ᾽ dpa τὸ Bre D
, > /, M 4 » rr , , / T t
οὐδενί: ἀντιστρέφει yàp τὸ στερητικόν. ἐὰν δ᾽ ἐν μέρει ἦ ὁ 25
συλλογισμός, ὅταν μὲν ἢ τὸ στερητικὸν πρὸς τῷ μείζονι
ἄκρῳ, ἀναχθήσεται εἰς τὸ πρῶτον, οἷον εἰ τὸ Α μηδενὶ τῷ
Β, τῷ δὲ Γ τινί: ἀντιστραφέντος γὰρ τοῦ στερητικοῦ τὸ πρῶ-
LÀ ^ A M M ^. M ^ \ M 4
Tov ἔσται σχῆμα: TO μὲν yàp B οὐδενὶ τῷ A, τὸ δὲ A τινὶ
^ e M M , , > , φ , ii
τῷ Γ΄. ὅταν δὲ τὸ κατηγορικόν, οὐκ ἀναλυθήσεται, olov εἰ τὸ 3o
A ^ 4 B , ^ * I ᾽ , L4 ^ δέ
τῷ μὲν Β παντί, τῷ δὲ Γ οὐ παντί: οὔτε γὰρ δέχεται
3 Ἁ M L4 ΄ LÀ ,
ἀντιστροφὴν τὸ A B, οὔτε γενομένης ἔσται συλλογισμός.
Πάλιν οἱ μὲν ἐν τῷ τρίτῳ σχήματι οὐκ ἀναλυθήσον-
ται πάντες εἰς τὸ πρῶτον, οἱ δ᾽ ἐν τῷ πρώτῳ πάντες εἰς τὸ
, € , ^ X M ^ A x * ^
τρίτον. ὑπαρχέτω yap τὸ A παντὶ τῷ B, τὸ δὲ B τινὶ τῷ 35
I. οὐκοῦν ἐπειδὴ ἀντιστρέφει τὸ ἐν μέρει κατηγορικόν, ὑπάρ-
br τούτων om. C τὸ om. πὲ 6 ἣν] ἵν᾽ Β: εἰ Βὲ 8 τὸν]
τὸ" ἅπαντα t 9 ἀλλ᾽ -᾿ ἐπ᾿ nD ἐνίων ἐνίοτε n 18 μόνον A
27 ἀναλυθήσεται ΒΓ 31 ἐπιδέχεται Alc 33 ἐν om. A 34 of δ᾽
A*Cn Ál: οὐδ᾽ of AB 36 τὸ] καὶ τὸ ἩΓ
4985 Μ
ANAAYTIKON IIPOTEPON A
fe τὸ Γ rui τῷ B- τὸ δὲ A παντὶ ὑπῆρχεν, ὥστε γίνεται
τὸ τρίτον σχῆμα. καὶ εἰ στερητικὸς 6 συλλογισμός, ὡσαύ-
τως" ἀντιστρέφει γὰρ τὸ ἐν μέρει κατηγορικόν, ὥστε τὸ μὲν
40 A οὐδενὶ τῷ Β, τὸ δὲ Γ τινὶ ὑπάρξει.
51. Τῶν δ᾽ ἐν τῷ τελευταίῳ σχήματι συλλογισμῶν εἷς
, ΕΣ > adv , ^ ~ Ld ^ 66A θῇ
μόνος οὐκ ἀναλύεται εἰς τὸ πρῶτον, ὅταν μὴ καθόλου τεθῇ
^ , € δ᾽ ἄλλ. Fi > , , 6.
τὸ στερητικόν, οἱ οἱ πάντες ἀναλύονται. κατηγορείσθω
A A ~ A M A | ^ > , L:
yàp παντὸς τοῦ Γ τὸ A καὶ τὸ B: οὐκοῦν ἀντιστρέψει τὸ D
ς πρὸς ἑκάτερον ἐπὶ μέρους: ὑπάρχει dpa rui τῷ B. ὥστ᾽
ἔσται τὸ πρῶτον σχῆμα, εἰ τὸ μὲν Α παντὶ τῷ Γ, τὸ δὲ
Γ τινὶ τῷ B. καὶ εἰ τὸ μὲν A παντὶ τῷ Γ, τὸ δὲ B τινί,
€ » A , 2 , ‘A ^ εἶ M LA b
ὁ αὐτὸς λόγος" ἀντιστρέφει yàp πρὸς τὸ B τὸ I. ἐὰν δὲ
^ * B M ^ EL i δὲ A b ^ I. ~ Ld
τὸ μὲν B παντὶ τῷ I, τὸ δὲ τινὶ τῷ I, πρῶτος ὅρος
το θετέος τὸ Β' τὸ γὰρ Β παντὶ τῷ Γ, τὸ δὲ Γ τινὶ τῷ A, ὥστε
^ M ^ > M > Ld , * > L4 " M
τὸ B τινὶ τῷ A. ἐπεὶ δ᾽ ἀντιστρέφει τὸ ἐν μέρει, καὶ τὸ A
τινὶ TQ B ὑπάρξει. καὶ εἰ στερητικὸς 6 συλλογισμός, κα-
θόλου τῶν ὅρων ὄντων, ὁμοίως ληπτέον. ὑπαρχέτω γὰρ τὸ
B παντὶ τῷ D, τὸ δὲ A μηδενί: οὐκοῦν τινὶ τῷ B ὑπάρξει
1370 Γ, τὸ δὲ A οὐδενὶ τῷ Γ᾽, ὥστ᾽ ἔσται μέσον τὸ Γ΄. ὁμοίως
δὲ καὶ εἰ τὸ μὲν στερητικὸν καθόλου, τὸ δὲ κατηγορικὸν ἐν
μέρει" τὸ μὲν yap A οὐδενὶ τῷ I, τὸ δὲ Γ τινὶ τῶν B ὑπάρ-
2A LI 3, L4 ~ A , > » > ,
fe. ἐὰν δ᾽ ἐν μέρει ληφθῇ τὸ στερητικόν, οὐκ ἔσται ἀνάλυ-
A 8 Ἂς ^ * X A M * La
σις, οἷον εἰ τὸ μὲν B παντὶ τῷ Γ, τὸ δὲ A τινὶ μὴ ὑπάρ-
> , A ^ > , t ,
20 χει: ἀντιστραφέντος yàp τοῦ B I ἀμφότεραι αἱ προτάσεις
ἔσονται κατὰ μέρος.
Φανερὸν δὲ καὶ ὅτι πρὸς τὸ ἀναλύειν εἰς ἄλληλα τὰ
σχήματα ἡ πρὸς τῷ ἐλάττονι ἄκρῳ πρότασις ἀντιστρεπτέα
ἐν ἀμφοτέροις τοῖς σχήμασι: ταύτης γὰρ μετατιθεμένης
25 ἡ μετάβασις ἐγίνετο.
Τῶν δ᾽ ἐν τῷ μέσῳ σχήματι ἅτερος μὲν ἀναλύεται,
σ , , , , ’ A LA Ld |! ‘A a ^
ἅτερος δ᾽ οὐκ ἀναλύεται, εἰς τὸ τρίτον. ὅταν μὲν yàp ἢ TO
καθόλου στερητικόν, ἀναλύεται. εἰ γὰρ τὸ Α μηδενὶ τῷ Β,
^ δὲ Γ , 2 , « z > / M M A
τῷ δὲ τινί, ἀμφότερα ὁμοίως ἀντιστρέφει πρὸς τὸ Α,
LÀ A x B 38 * ^ A a de D /. , L4 M A
3o ὥστε τὸ μὲν B οὐδενὶ τῷ A, τὸ δὲ Γ τινί: μέσον dpa τὸ A.
Ld δὲ M A M ^ B ^ δι Γ M A € p ,
Grav δὲ τὸ A παντὶ τῷ B, τῷ δὲ Γ τινὲ μὴ ὑπάρχῃ, οὐκ
ba? τῶν Bn ὑπῆρχε- τὸ Bn 5197 τῷ CI: τῶν ABn δγτὸβ
A'Ban} 9 πρῶτον ὅρον θετέον A2C 14 τῶν Bn 18 ἔστιν Al
19 ὑπάρχῃ (ut solet) B 25 γίνεται C 27 yàp om. 5. 30 7o?
fecit 1
45. 50°37-46. 51°26
L4 > : d > , ^ ^ , > ^ ,
ἔσται ἀνάλυσις" οὐδετέρα yàp τῶν προτάσεων ἐκ τῆς ἀντι-
στροφῆς καθόλου.
Κι * Lj , -^ , A , , , ,
αἱ of ἐκ τοῦ τρίτου δὲ σχήματος ἀναλυθήσονται εἰς
* , - , X ,ὔ » AY
τὸ μέσον, Grav jj καθόλου τὸ στερητικόν, olov εἰ τὸ A μη-
^ ~ A * à 0 , x ^ A ~ M
sei τῷ Γ, τὸ δὲ B τινὶ ἢ παντί. καὶ yàp τὸ Γ τῷ μὲν A
> , ^ * a Li , »* > > ' , a
οὐδενί, TH δὲ B τινὶ ὑπάρξει. ἐὰν δ᾽ ἐπὶ μέρους ἦ τὸ στε-
ρητικόν, οὐκ ἀναλυθήσεται: οὐ γὰρ δέχεται ἀντιστροφὴν τὸ
ἐν μέρει ἀποφατικόν.
Φ. A 7 Ld t > M M > » ,
avepóv οὖν ὅτι οἱ αὐτοὶ συλλογισμοὶ οὐκ ἀναλύονται
» a , ^ »
ἐν τούτοις τοῖς σχήμασιν οἵπερ οὐδ᾽ εἰς τὸ πρῶτον ἀνελύοντο,
M ^ ^ ^ ^
καὶ ὅτι εἰς τὸ πρῶτον σχῆμα τῶν συλλογισμῶν ἀναγομέ-
νων οὗτοι μόνοι διὰ τοῦ ἀδυνάτου περαίνονται.
Πῶς μὲν οὖν δεῖ τοὺς συλλογισμοὺς ἀνάγειν, καὶ ὅτι
> , ^ , , Ld * , ~ ,
ἀναλύεται τὰ σχήματα εἰς ἄλληλα, φανερὸν ἐκ τῶν εἰ-
46 ρημένων. διαφέρει δέ τι ἐν τῷ κατασκευάζειν ἢ ἀνασκευά-
ζειν τὸ ὑπολαμβάνειν ἢ ταὐτὸν ἢ ἕτερον σημαίνειν τὸ μὴ
εἶναι τοδὶ καὶ εἶναι μὴ τοῦτο, οἷον τὸ μὴ εἶναι λευκὸν τῷ
A , > ^ , * , γῸ} ν , ,
εἶναι μὴ λευκόν. οὐ yàp ταὐτὸν σημαίνει, οὐδ᾽ ἔστιν dmó-
φασις τοῦ εἶναι λευκὸν τὸ εἶναι μὴ λευκόν, ἀλλὰ τὸ μὴ
δ , 4 ΄ σ' € , A LÀ a ,
εἶναι λευκόν. λόγος δὲ τούτου ὅδε. ὁμοίως yap ἔχει τὸ δύ-
ναται βαδίζειν πρὸς τὸ δύναται οὐ βαδίζειν τῷ ἔστι λευκόν
πρὸς τὸ ἔστιν οὐ λευκόν, καὶ ἐπίσταται τἀγαθόν πρὸς τὸ
ἐπίσταται τὸ οὐκ ἀγαθόν. τὸ γὰρ ἐπίσταται τἀγαθόν ἢ ἔστιν
ἐπιστάμενος τἀγαθόν οὐδὲν διαφέρει, οὐδὲ τὸ δύναται βαδί-
- L4 , , - * A > ,
Lew ἢ ἔστι δυνάμενος . βαδίζειν: ὥστε Kai τὰ ἀντικείμενα,
οὐ δύναται βαδίζειν---οὐκ ἔστι δυνάμενος βαδίζειν. εἰ οὖν τὸ
*, LÀ td > 4 , * L4 ,
οὐκ ἔστι δυνάμενος βαδιζειν ταὐτὸ σημαίνει kai ἔστι Suva-
* , hal 4 , LJ , e e ,
μενος οὐ βαδίζειν ἢ μὴ βαδίζειν, ταῦτά ye apa ὑπάρξει
, ^ € i 1 , A , & , * * ,
ταὐτῷ (ὃ yap αὐτὸς δύναται xai βαδίζειν Kai μὴ Badi-
Lew, καὶ ἐπιστήμων τἀγαθοῦ καὶ τοῦ μὴ ἀγαθοῦ ἐστί), φάσις
δὲ καὶ ἀπόφασις οὐχ ὑπάρχουσιν αἱ ἀντικείμεναι ἅμα τῷ
αὐτῷ. ὥσπερ οὖν οὐ ταὐτό ἐστι τὸ μὴ ἐπίστασθαι τἀγαθὸν
" *, 4 6 A 1 » θό δ᾽ f M > 0o *
καὶ ἐπίστασθαι τὸ μὴ ἀγαθόν, οὐδ᾽ εἶναι μὴ ἀγαθὸν xai
A t > 06 , , ~ ‘ > aX ,*5 0 ,
μὴ εἶναι ἀγαθὸν ταὐτόν. τῶν yap ἀνάλογον ἐὰν θάτερα
ἡ ἕ it θά ὑδὲ τὸ εἶναι μὴ ἴσον καὶ τὸ μὴ εἶ-
ἦ ἕτερα, καὶ θάτερα. οὐδὲ τὸ εἶναι μὴ ἴσο μὴ
~ ^ * LJ M
vat toov: τῷ μὲν yap ὑπόκειταί Ti, TH ὄντι μὴ tow, Kal
422 δὲ οἴη. AB. b3 τοὺς λόγους ΗΓ ἡ τόδε n* Ale 12-13 τὸ ἐπίστα-
σθαι Β 18 οὐ om. Αἰ} βαδίζειν 5 om. P 20 xai-- ὁ nl Ale
ἐπιστήμων ABAIS: ἐπιστήμην Cn ἐστί ABnALS : ἔχειν Cn? 21 ἅμα
om. B 24 ἀναλόγων B? 25 ró! om. π
35
40
51»
Io
15
20
25
ANAAYTIKQN IIPOTEPON A
a > v A L4 ^ > 2 L4 , LÀ A - LÀ 3
τοῦτ᾽ ἔστι τὸ ἄνισον, τῷ δ᾽ οὐδέν. διόπερ ἴσον μὲν ἢ ἄνισον οὐ
“- LÀ ? ^ ? LÀ ^. w M LÀ , ^ ,
πᾶν, ἴσον δ᾽ ἢ οὐκ ἴσον πᾶν. ἔτι τὸ ἔστιν οὐ λευκὸν ξύλον
a 3 v t tA 3 σ € 4 > 4 3
καὶ οὐκ ἔστι λευκὸν ξύλον οὐχ ἅμα ὑπάρχει. εἰ γάρ ἐστι
30 ξύλον οὐ λευκόν, ἔσται ξύλον: τὸ δὲ μὴ ὃν λευκὸν ξύλον οὐκ
3 , , LÀ ^ LA > L4 ~ >
ἀνάγκη ξύλον εἶναι. ὥστε φανερὸν ὅτι οὐκ ἔστι τοῦ ἔστιν dya-
θόν τὸ ἔστιν οὐκ ἀγαθόν ἀπόφασις. εἰ οὖν κατὰ παντὸς ἑνὸς
ἢ φάσις ἢ ἀπόφασις ἀληθής, εἰ μὴ ἔστιν ἀπόφασις, δῆ-
λον ὡς κατάφασις ἄν πως εἴη. καταφάσεως δὲ πάσης
35 ἀπόφασις ἔστιν: καὶ ταύτης ἄρα τὸ οὐκ ἔστιν οὐκ ἀγαθόν.
Ἔχει δὲ τάξιν τήνδε πρὸς ἄλληλα. ἔστω τὸ εἶναι ἀγαθὸν
ἐφ᾽ od A, τὸ δὲ μὴ εἶναι ἀγαθὸν ἐφ᾽ οὗ B, τὸ δὲ εἶναι
i! > M 1» T c A ‘ ^ * A: * $
μὴ ἀγαθὸν ἐφ᾽ οὗ I, ὑπὸ τὸ B, τὸ δὲ μὴ εἶναι μὴ áy-
αθὸν ἐφ᾽ οὗ 4, ὑπὸ τὸ A. παντὶ δὴ ὑπάρξει 7) τὸ A ἢ τὸ
4 , M ^ > ~ A ^ M ^ t] M , M
4o B, kai οὐδενὲ τῷ αὐτῷ- kai ἢ τὸ IH τὸ A, kai οὐδενὶ
~ % ~ b T * > , ^ M € , >
τῷ αὐτῷ. καὶ ᾧ τὸ I, ἀνάγκη τὸ B παντὶ ὑπάρχειν (εἰ
525" γὰρ ἀληθὲς εἰπεῖν ὅτι ἐστὶν οὐ λευκόν, καὶ ὅτι οὐκ ἔστι λευκὸν
ἀληθές: ἀδύνατον γὰρ ἅμα εἶναι λευκὸν καὶ εἶναι μὴ λευ-
, n vA ΕΣ * * L4 , ν >
Kóv, ἢ εἶναι ξύλον οὐ λευκὸν καὶ εἶναι ξύλον λευκόν, ὥστ
εἰ μὴ ἡ κατάφασις, ἡ ἀπόφασις ὑπάρξει), τῷ δὲ Β τὸ Γ
,» > 7 ^ 3 e M ta , s P4 L4 » [4
ς οὐκ ἀεί (ὃ yàp ὅλως μὴ ξύλον, οὐδὲ ξύλον ἔσται οὐ λευκόν).
ἀνάπαλιν τοίνυν, ᾧ τὸ A, τὸ 4 παντί (ἢ γὰρ τὸ I ἢ τὸ
4: ἐπεὶ δ᾽ οὐχ οἷόν τε ἅμα εἶναι μὴ λευκὸν καὶ λευκόν,
^ LA , ^ ^ ^ L4 ~ > ^ > ^
τὸ 4 ὑπάρξει: xarà yap τοῦ ὄντος λευκοῦ ἀληθὲς εἰπεῖν
oe *, LÀ , , M M ^ » a * ^
ὅτι οὐκ ἔστιν οὐ λευκόν), κατὰ δὲ τοῦ 4 od παντὸς τὸ A (κατὰ
^ ^ Ld A a L4 , 3 * A > ^ €*
10 yàp Tod ὅλως μὴ ὄντος ξύλου οὐκ ἀληθὲς τὸ A εἰπεῖν, ὡς
ἔστι ξύλον λευκόν, ὥστε τὸ 4 ἀληθές, τὸ δ᾽ A οὐκ ἀλη-
θές, ὅτι ξύλον λευκόν). δῆλον δ᾽ ὅτι καὶ τὸ A I οὐδενὶ
^ 2 ^ ‘ ^ M A , , M ^ ? ~
τῷ αὐτῷ καὶ τὸ B xai τὸ 4 ἐνδέχεται Twi TQ αὐτῷ
ὑπάρξαι.
€ [4 > v * € , M ^
15 ‘Opotws δ᾽ ἔχουσι kai al στερήσεις πρὸς τὰς κατης-
, L4 ^ , » ay? T * , LJ » 1?» ^
yopias ταύτῃ τῇ θέσει. ἴσον ἐφ᾽ οὗ τὸ A, οὐκ ἴσον ἐφ᾽ οὗ
B, ἄνισον ἐφ᾽ οὗ I, οὐκ ἄνισον ἐφ᾽ οὗ A.
Καὶ ἐπὶ πολλῶν δέ, ὧν τοῖς μὲν ὑπάρχει τοῖς δ᾽ οὐχ
ὑπάρχει ταὐτόν, ἡ μὲν ἀπόφασις ὁμοίως ἀληθεύοιτ᾽ ἄν, ὅτι
ΕἸ L4 MJ , ^ - * w ^ σ΄ L4 >
20 οὐκ ἔστι λευκὰ πάντα ἢ ὅτι οὐκ ἔστι λευκὸν ἕκαστον" ὅτι ὃ
b31 φανερὸν ὅτι om. n 4 ἡ n4l* 34-5 nAl* 35 καὶ om. C
5251 ἐστὶν nI': om. ABC 3 0) Aevkóv . . . λευκόν] λευκὸν... οὐ λευκόν t
47° om. Bn τῷ] τὸ A? 9 πάντως Cn I0 a B*Ctn Al, fecit
A: y BCT 11 λευκόν A1TBCnAl: οὐ λευκόν AB? δ᾽ om. #
1 70 B A 19 ἀληϑεύοιτ᾽ ἄν] ἀληθεύει PS
46. 51*27-52^14
* * > A a a , 3 * > 4 ^
ἐστὶν οὐ λευκὸν ἕκαστον ἢ πάντα ἐστὶν οὐ λευκά, ψεῦδος.
Ld i * i. IM ^ ^ , , ki LÀ >
ὁμοίως δὲ καὶ τοῦ ἔστι πᾶν ζῷον λευκόν οὐ τὸ ἔστιν ov Aev-
κὸν ἅπαν ζῷον ἀπόφασις (ἄμφω γὰρ ψευδεῖς), ἀλλὰ τὸ
οὐκ ἔστι πᾶν ζῷον λευκόν. 24
᾿Επεὶ δὲ δῆλον ὅτι ἕτερον σημαί- 24
M LÀ 3 H + , » , ^ M x
veu. τὸ ἔστιν οὐ λευκόν καὶ οὐκ ἔστι λευκόν, Kal TO μὲν Ka- 25
4 M] > > / ^ t € , ig , * ^
τάφασις τὸ δ᾽ ἀπόφασις, φανερὸν ws οὐχ ὁ αὐτὸς τρόπος
τοῦ δεικνύναι ἑκάτερον, οἷον ὅτι ὃ ἂν ἦ ζῷον οὐκ ἔστι λευ-
' ^ ? Ὁ M FZ M Ld > M HJ ^ a
κὸν ἢ ἐνδέχεται μὴ εἶναι λευκόν, καὶ ὅτι ἀληθὲς εἰπεῖν μὴ
λευκόν: τοῦτο γάρ ἐστιν εἶναι μὴ λευκόν. ἀλλὰ τὸ μὲν
ἀληθὲς εἰπεῖν ἔστι λευκόν εἴτε μὴ λευκόν ὁ αὐτὸς τρόπος" 30
κατασκευαστικῶς γὰρ ἄμφω διὰ τοῦ πρώτου δείκνυται σχή-
ματος" τὸ γὰρ ἀληθὲς τῷ ἔστιν ὁμοίως τάττεται: τοῦ γὰρ
ἀληθὲς εἰπεῖν λευκὸν οὐ τὸ ἀληθὲς εἰπεῖν μὴ λευκὸν ἀπόφα-
σις, ἀλλὰ τὸ μὴ ἀληθὲς εἰπεῖν λευκόν. εἰ δὴ ἔσται ἀληθὲς
εἰπεῖν ὃ dv ἦ ἄνθρωπος μουσικὸν εἶναι ἢ μὴ μουσικὸν εἶναι, 35
ὃ av ἢ ζῷον ληπτέον ἢ εἶναι μουσικὸν ἢ εἶναι μὴ μουσικόν,
* Li A * x x an v »
καὶ δέδεικται. τὸ δὲ μὴ εἶναι μουσικὸν ὃ dv 4 ἄνθρωπος, ava-
σκευαστικῶς δείκνυται κατὰ τοὺς εἰρημένους τρόπους τρεῖς:
« ~ 2 Ed Ld μ᾿ ^ * * L4 5 Ld
Ἁπλῶς δ᾽ ὅταν οὕτως ἔχῃ τὸ A καὶ τὸ B ὥσθ᾽ ἅμα
* “ 3 ~ b 2 , * * , , , L4
μὲν TQ αὐτῷ μὴ ἐνδέχεσθαι, παντὶ δὲ ἐξ ἀνάγκης θάτε- 4o
pov, καὶ πάλιν τὸ Γ καὶ τὸ 4 ὡσαύτως, ἕπηται δὲ τῷ Γ 52>
τὸ Α καὶ μὴ ἀντιστρέφῃ, καὶ τῷ Β τὸ 4 ἀκολουθήσει καὶ
5 ἂν £f ^ ^ A Mi X Ψ' ~ " ^
οὐκ ἀντιστρέψει: kai τὸ μὲν A καὶ A ἐνδέχεται τῷ αὐτῷ,
a M * », , , ^ * T " ~
τὸ δὲ B καὶ Γ οὐκ ἐνδέχεται. πρῶτον μὲν οὖν ὅτι τῷ B
^ 4 ? , , > ^ ki * ~
τὸ 4 ἕπεται, ἐνθένδε φανερόν. ἐπεὶ yap παντὶ τῶν Γ 45
θάτερον ἐξ ἀνάγκης, ᾧ δὲ τὸ Β, οὐκ ἐνδέχεται τὸ Γ διὰ
τὸ συνεπιφέρειν τὸ Α, τὸ δὲ Α καὶ Β μὴ ἐνδέχεσθαι τῷ
αὐτῷ, φανερὸν ὅτι τὸ A ἀκολουθήσει. πάλιν ἐπεὶ τῷ A τὸ
Γ οὐκ ἀντιστρέφει, παντὶ δὲ τὸ Γ ἢ τὸ 4, ἐνδέχεται τὸ A
* M] ^ *, ^ e , ki LÀ M * >
καὶ τὸ 4 τῷ αὐτῷ ὑπάρχειν. τὸ δέ ye B καὶ τὸ I οὐκ το
ἐνδέχεται διὰ τὸ συνακολουθεῖν τῷ I τὸ A: συμβαίνει γάρ
τι ἀδύνατον. φανερὸν οὖν ὅτι οὐδὲ τῷ 4 τὸ Β ἀντιστρέφει,
ἐπείπερ ἐγχωρεῖ ἅμα τὸ 4 καὶ τὸ A ὑπάρχειν.
, ? i MM S M > ~ ^ , ^ -
Συμβαίνει δ᾽ ἐνίοτε καὶ ἐν τῇ τοιαύτῃ τάξει τῶν ὅρων
820 τὸ] τοῦ n 31 κατασκευαστικὸς n? 34 ἔσται coni. Jenkinson,
habet ut vid. Al: ἐστιν codd. 35ó0sn avCnAl: ἐὰν AB 36
«va? om. B 39 οὕτως ὅταν C br τὸξ om. n δὲ om. A?
2 ἀντιστρέφει B 4D]r0 y C 5 ἔπεταιτὸδ( gavepov-+ ἔσται C
ὃ τῷ a r0 y ACHP: τὸ 0 1 y ABnT 9 δὲ ἢ n
ANAAYTIKON IIPOTEPON A
, ^ kJ a 4 x > , , 3, ~ EA
15 ἀπατᾶσθαι διὰ τὸ μὴ τὰ ἀντικείμενα λαμβάνειν ὀρθῶς ὧν
> , ^ , e , , A 4 * M
ἀνάγκη παντὶ θάτερον ὑπάρχειν" olov εἰ τὸ A xai τὸ B μὴ
ἐνδέχεται ἅμα τῷ αὐτῷ, ἀνάγκη δ᾽ ὑπάρχειν, ᾧ μὴ θά-
τερον, θάτερον, καὶ πάλιν τὸ Γ᾽ kai τὸ A ὡσαύτως, à δὲ
τὸ I’, παντὶ ἕπεται τὸ A. συμβήσεται yàp à τὸ A, τὸ B
t , , , 4 Ld » 4 A Y y A Li ΄
20 ὑπάρχειν ἐξ ἀνάγκης, ὅπερ ἐστὶ ψεῦδος. εἰλήφθω γὰρ ἀπό-
φασις τῶν A B ἡ éd' ᾧ Z, καὶ πάλιν τῶν I' À ἡ ἐφ᾽
τ LEA a *' ow a - i xn M ' ,
ᾧ O. ἀνάγκη δὴ παντὶ ἢ τὸ A ἢἣ τὸ Ζ' ἢ yàp τὴν φά-
^ A > , ^ d hl M -^ M L4
ow ἣ rjv ἀπόφασιν. καὶ πάλιν 7 τὸ TH τὸ Θ' φάσις
^ M 2 , ^ T7 M M * t€ ,
yàp καὶ ἀπόφασις. καὶ d τὸ I, παντὶ τὸ A ὑπόκειται.
25 ὦστε d τὸ Z, παντὶ τὸ Θ. πάλιν ἐπεὶ τῶν Ζ B παντὶ θά-
τερον καὶ τῶν Θ 4 ὡσαύτως, ἀκολουθεῖ δὲ τῷ Ζ τὸ Θ,
A ^ » , A ~ ^ LÀ Y LÀ ^
καὶ τῷ 4 ἀκολουθήσει τὸ B- τοῦτο yap ἴσμεν. εἰ apa τῷ
Γ τὸ A, καὶ τῷ 4 τὸ B. τοῦτο δὲ ψεῦδος" ἀνάπαλιν γὰρ
ἦν ἐν τοῖς οὕτως ἔχουσιν ἡ ἀκολούθησις. οὐ γὰρ ἴσως ἀνάγκη
3o παντὶ τὸ A 7j τὸ Ζ, οὐδὲ τὸ Z ἣ τὸ Β' οὐ γάρ ἐστιν ἀπό-
~ * - AY > ~ A > 3 A > ,
φασις τοῦ A τὸ Z. τοῦ yàp ἀγαθοῦ τὸ οὐκ ἀγαθὸν amó-
, A] A , , M X > > M ~ w ᾿ > a w 9
φασις" od ταὐτὸ δ᾽ ἐστὶ τὸ οὐκ ἀγαθὸν τῷ οὔτ᾽ ἀγαθὸν oír
οὐκ ἀγαθόν. ὁμοίως δὲ καὶ ἐπὶ τῶν I A: αἱ γὰρ ἀποφά-
σεις αἱ εἰλημμέναι δύο εἰσίν.
Β.
ΕΣ , A L3 , 4 4 , M ,ὔ
Ev πόσοις μὲν οὖν σχήμασι καὶ διὰ ποίων καὶ πό-
σων προτάσεων καὶ πότε καὶ πῶς γίνεται συλλογισμός,
4o ἔτι δ᾽ εἰς ποῖα βλεπτέον ἀνασκευάζοντι καὶ κατασκευά-
53* ζοντι, καὶ πῶς δεῖ ζητεῖν περὶ τοῦ προκειμένου καθ᾽ ὁποιαν-
^ Li w A ^ , t ~ , ‘ *
oüv μέθοδον, ἔτι δὲ διὰ ποίας ὁδοῦ ληψόμεθα τὰς περὶ
LÀ > i M ΄ > M > Lj ‘ ,
ἕκαστον ἀρχάς, ἤδη διεληλύθαμεν. ἐπεὶ δ᾽ oi μὲν καθόλου
^ ^ LE € ^ UJ a t M ,
τῶν συλλογισμῶν εἰσὶν of δὲ κατὰ μέρος, of μὲν καθόλου
, LL , , ^ » ’ , Lj M
ς πάντες αἰεὶ πλείω συλλογίζονται, τῶν δ᾽ ἐν μέρει of μὲν
,
κατηγορικοὶ πλείω, οἱ δ᾽ ἀποφατικοὶ τὸ συμπέρασμα μό-
νον. αἱ μὲν γὰρ ἄλλαι προτάσεις ἀντιστρέφουσιν, ἡ δὲ στε-
ρητικὴ οὐκ ἀντιστρέφει. τὸ δὲ συμπέρασμα τὶ κατά τινός
ἐστιν, ὥσθ᾽ οἱ μὲν ἄλλοι συλλογισμοὶ πλείω συλλογίζον-
big τὰ Waitz τὰ οἵπ. η — à A! 18 θάτερον om. C! 19 ἕπηται
ABn γὰρ om. AB 25 τὸ θ παντὶ τῷ C B? 26 τῷ L τὸ
A* BCn AIP : τὸ ζ τὸ 4: τὸ bre B 27 rà?) τὸ 4! 32 TO οὐκ
ἀγαθὸν om. n! 33 οὐκ ἀγαθόν) κακὸν καὶ τὸ οὐκ ἀγαθόν n: κακόν n?
39 γίνεται ὑ- πᾶς Γ 5333 διεληλύθαμεν- πρότερον n 8 τὶ fecit 2?
46. 52^15-B. 2. 5354
ται, οἷον εἰ τὸ A δέδεικται παντὶ τῷ B ἢ τινί, kai τὸ B
^ ~ > ^ € , ^ > ^ -^ A
τινὶ τῷ A ἀναγκαῖον ὑπάρχειν, kai εἰ μηδενὶ τῷ B τὸ A,
οὐδὲ τὸ B οὐδενὶ τῷ A, τοῦτο δ᾽ ἕτερον τοῦ ἔμπροσθεν: εἰ δὲ
Twi μὴ ὑπάρχει, οὐκ ἀνάγκη καὶ τὸ B τινὲ τῷ A μὴ
ὑπάρχειν: ἐνδέχεται yàp παντὶ ὑπάρχειν.
Αὕτη μὲν οὖν κοινὴ πάντων αἰτία, τῶν τε καθόλου
4 ^ ^ , L4 ^ M ^ - ^ Lá
kai τῶν κατὰ μέρος- ἔστι δὲ περὶ τῶν καθόλου καὶ ἄλλως
εἰπεῖν. ὅσα γὰρ ἢ ὑπὸ τὸ μέσον ἢ ὑπὸ τὸ συμπέρασμά
3 [i L '
ἐστιν, ἁπάντων ἔσται ὁ αὐτὸς συλλογισμός, ἐὰν rà μὲν ἐν
Ὁ μέ a δ᾽ ἐν τῷ 10; θῇ, otov εἰ τὸ A B
τῷ μέσῳ ta δ᾽ ἐν τῷ συμπεράσματι τεθῇ, olov εἰ τὸ
, kí ^ oe L4 * M - 4 » p
συμπέρασμα διὰ τοῦ Γ, ὅσα ὑπὸ τὸ B ἢ τὸ TD ἐστί,
> , ‘A 4 , ‘A ν M A > -
ἀνάγκη κατὰ πάντων λέγεσθαι τὸ A> εἰ yàp τὸ A ἐν ὅλῳ
TQ B, τὸ δὲ B ἐν τῷ A, καὶ τὸ 4 ἔσται ἐν τῷ Α' πά-
λιν εἰ τὸ E ἐν ὅλῳ τῷ D, τὸ δὲ Γ ἐν τῷ A, καὶ τὸ E
? Lal L4 L4 , A b , ‘ L4 *
ἐν τῷ A ἔσται. ὁμοίως δὲ Kai εἰ στερητικὸς 6 συλλογισμός.
ἐπὶ δὲ τοῦ δευτέρου σχήματος τὸ ὑπὸ τὸ συμπέρασμα μό-
νον ἔσται συλλογίσασθαι, οἷον εἰ τὸ Α τῷ Β μηδενί, τῷ
δὲ D' παντί: συμπέρασμα ὅτι οὐδενὶ τῷ Γ τὸ B. εἰ δὴ τὸ
A ὑπὸ τὸ Γ ἐστί, φανερὸν ὅτι οὐχ ὑπάρχει αὐτῷ τὸ B-
~ 2 Li a ‘ Ld , L4 4 > a ^ ~
Trois δ᾽ ὑπὸ τὸ A ὅτι οὐχ ὑπάρχει, od δῆλον διὰ τοῦ συλ-
λογισμοῦ. καίτοι οὐχ ὑπάρχει τῷ E, εἰ ἔστιν ὑπὸ τὸ A:
3 M * x ~ * [4 i x a ^
ἀλλὰ τὸ μὲν τῷ I μηδενὶ ὑπάρχειν τὸ B διὰ τοῦ συλ-
-^ Ló 3 * ~ ‘ i Pd 2 ,
λογισμοῦ δέδεικται, τὸ δὲ τῷ A μὴ ὑπάρχειν ἀναπόδει-
w σ , > M A τ , a
krov εἴληπται, ὥστ᾽ οὐ διὰ τὸν συλλογισμὸν συμβαίνει τὸ
B τῷ E μὴ ὑπάρχειν. ἐπὶ δὲ τῶν ἐν μέρει τῶν μὲν ὑπὸ
τὸ συμπέρασμα οὐκ ἔσται τὸ ἀναγκαῖον (οὐ γὰρ γίνεται
’, -“ m ^ H , ~ » [4 X A
συλλογισμός, ὅταν αὕτη ληφθῇ ἐν μέρει), τῶν δ᾽ ὑπὸ τὸ
μέσον ἔσται πάντων, πλὴν οὐ διὰ τὸν συλλογισμόν" οἷον εἰ
τὸ A παντὶ τῷ B, τὸ δὲ B τινὶ τῷ Γ' τοῦ μὲν γὰρ ὑπὸ
^ , *, L4 , ~ , € M 4 LÀ
TO Γ τεθέντος οὐκ ἔσται συλλογισμός, τοῦ δ᾽ ὑπὸ τὸ B ἔσται,
t4 , *, ^ M : d ε , M 5 M ~ LÀ
ἀλλ᾽ οὐ διὰ τὸν mpoyeyevguévov. ὁμοίως δὲ κἀπὶ τῶν ἄλλων
^ [4 4 L4
σχημάτων: τοῦ μὲν yap ὑπὸ τὸ συμπέρασμα οὐκ ἔσται,
, > L4 ‘ > A * , M .
θατέρου δ᾽ -€orat, πλὴν οὐ διὰ τὸν συλλογισμόν, F xai ἐν
^ , , ^ , ^ Ui A *
τοῖς καθόλου ἐξ dvamoÓe(krov τῆς προτάσεως τὰ ὑπὸ τὸ
, » , Ll LE »9» » ^ ^ $0» 5 ,
μέσον ἐδείκνυτο: ὥστ᾽ ἢ οὐδ᾽ ἐκεῖ ἔσται 7) καὶ ἐπὶ τούτων.
ν E 1 7 e » LÀ » 9 0 ^ t ‘
oT. μὲν οὖν οὕτως ἔχειν ὥστ᾽ ἀληθεῖς εἶναι tas mpo-
aio ἥ.... Bom. nl 11 τῷ ατινὶ C 15 re fecit B 22 bis, 24 ἐν
T nt 25 δευτέρου) B. n 26 ἐστὶ C συλλογισμός A 29
δτιτ τὸ BC 30 εἰ) ὃ Atn 36 αὐτὴ C by 4 ABC
10
I$
20
25
39
35
40
5
I
o
20
25
30
35
ANAAYTIKON IIPOTEPON B
τάσεις δι’ dw ὃ συλλογισμός, ἔστι δ᾽ ὥστε ψευδεῖς, ἔστι δ᾽
" A x 3 ^ i! * -^ ^ ‘ * ^
ὥστε τὴν μὲν ἀληθῆ τὴν δὲ ψευδῆ. τὸ δὲ συμπέρασμα ἢ
ἀληθὲς ἢ ψεῦδος ἐξ ἀνάγκης. ἐξ ἀληθῶν μὲν οὖν οὐκ ἔστι
ψεῦδος συλλογίσασθαι, ἐκ ψευδῶν δ᾽ ἔστιν ἀληθές, πλὴν
οὐ διότι ἀλλ᾽ ὅτι: τοῦ γὰρ διότι οὐκ ἔστιν ἐκ ψευδῶν συλλο-
, *»« > > ¢ 7 ^ Li L /
propos: δι’ ἣν δ᾽ αἰτίαν, ἐν τοῖς ἑπομένοις λεχθήσεται.
Πρῶτον μὲν οὖν ὅτι ἐξ ἀληθῶν οὐχ οἷόν τε ψεῦδος
, , ^ ^ > ^ ~ » > ,
συλλογίσασθαι, ἐντεῦθεν δῆλον. εἰ yap τοῦ A ὄντος ἀνάγκη
1 4 ^ Lo» > 7 Y 1 7 , >
τὸ B εἶναι, τοῦ B μὴ ὄντος ἀνάγκη τὸ A μὴ εἶναι. εἰ oiv
ἀληθές ἐστι τὸ A, ἀνάγκη τὸ B ἀληθὲς εἶναι, ἣ συμβή-
σεται τὸ αὐτὸ ἅμα εἶναί τε καὶ οὐκ εἶναι: τοῦτο δ᾽ ἀδύνα-
TOv. μὴ ὅτι δὲ κεῖται τὸ A εἷς ὅρος, ὑποληφθήτω ἐνδέχε-
σθαι ἑνός τινος ὄντος ἐξ ἀνάγκης τι συμβαίνειν: οὐ γὰρ
οἷόν τε: τὸ μὲν γὰρ συμβαῖνον ἐξ ἀνάγκης τὸ συμπέρα-
σμά ἐστι, δι’ ὧν δὲ τοῦτο γίνεται ἐλαχίστων, τρεῖς ὅροι,
δύο δὲ διαστήματα καὶ προτάσεις. εἰ οὖν ἀληθές, ᾧ τὸ Β
ὑπάρχει, τὸ A παντί, ᾧ δὲ τὸ D, τὸ B, à τὸ I', ἀνάγκη
4 U ts * > ts ~ ^ Ld
TO A ὑπάρχειν καὶ οὐχ οἷόν τε τοῦτο ψεῦδος elvai ἅμα
^ e ,^ > A A > € , A : bl a ^
yàp ὑπάρξει ταὐτὸ kai οὐχ ὑπάρξει. τὸ οὖν A ὥσπερ ἕν κεῖ-
’ , ^ € , * M , M ~
Tat, δύο προτάσεις συλληφθεῖσαι. ὁμοίως δὲ καὶ ἐπὶ τῶν
στερητικῶν ἔχει" οὐ γὰρ ἔστιν ἐξ ἀληθῶν δεῖξαι ψεῦδος.
Ἔκ ψευδῶν δ᾽ ἀληθὲς ἔστι συλλογίσασθαι καὶ ἀμ-
φοτέρων τῶν προτάσεων ψευδῶν οὐσῶν καὶ τῆς μιᾶς, ταύ-
τῆς δ᾽ οὐχ ὁποτέρας ἔτυχεν ἀλλὰ τῆς δευτέρας, ἐάνπερ
ὅλην λαμβάνῃ ψευδῆ: μὴ ὅλης δὲ λαμβανομένης ἔστιν
Lj ~ v M 4 " ^ € , ^ A
ὁποτερασοῦν. ἔστω yap τὸ A ὅλῳ τῷ I" ὑπάρχον, τῷ δὲ
B μηδενί, μηδὲ τὸ B τῷ I. ἐνδέχεται δὲ τοῦτο, οἷον λίθῳ
οὐδενὶ ζῷον, οὐδὲ λίθος οὐδενὶ ἀνθρώπῳ. ἐὰν οὖν ληφθῇ τὸ A
παντὶ τῷ DB καὶ τὸ DB παντὶ τῷ I, τὸ A παντὶ τῷ [D
ὑπάρξει, ὥστ᾽ ἐξ ἀμφοῖν ψευδῶν ἀληθὲς τὸ συμπέρα-
σμα: πᾶς γὰρ ἄνθρωπος ζῷον. ὡσαύτως δὲ καὶ τὸ στερη-
τικόν. ἔστι yap τῷ l' μήτε τὸ A ὑπάρχειν μηδενὶ μήτε τὸ
Β, τὸ μέντοι Α τῷ Β παντί, οἷον ἐὰν τῶν αὐτῶν ὅρων λη-
φθέντων μέσον τεθῇ ὁ ἄνθρωπος: λίθῳ γὰρ οὔτε ζῷον οὔτε
L4 > M LA , 3 ’ * * ~ LÁ > A
ἄνθρωπος οὐδενὶ ὑπάρχει, ἀνθρώπῳ δὲ παντὶ ζῷον. ὥστ᾽ ἐὰν
bg οὐδ᾽ ὅτι Al: οὐ τοῦ διότι B?n. 10 δειχϑήσεται n I2 συλλογίσασθαι
om. n 16 ὑποληφθῇ τῷ ABIL 19 ἐλάχιστον CIT 20 xai]
ai C 21 ὑπάρχειν C 23 ὥσπερ ἔκκειται Bly} 25 ἀληθείας C
26 ἀλήθειαν C 27 τῶν om. ABC 28 ἀλλὰ τῆς δευτέρας om. B:
ἀλλὰ τῆς B n 3o rà? nP: τῶν ABCT 36 ἔστω C
2. 53^5-54'30
ᾧ μὲν ὑπάρχει, λάβῃ μηδενὶ ὑπάρχειν, ᾧ δὲ μὴ ὑπάρχει, 4o
παντὶ ὑπάρχειν, ἐκ ψευδῶν ἀμφοῖν ἀληθὲς ἔσται τὸ συμ-
πέρασμα. ὁμοίως δὲ δειχθήσεται καὶ ἐὰν ἐπί τι ψευδὴς 545
ἑκατέρα ληφθῇ. 2
᾿Εὰν δ᾽ ἡ ἑτέρα τεθῇ ψευδής, τῆς μὲν πρώ- 2
τῆς ὅλης ψευδοῦς οὔσης, οἷον τῆς A Β, οὐκ ἔσται τὸ συμπέ-
ρασμα ἀληθές, τῆς δὲ BI ἔσται. λέγω δ᾽ ὅλην ψευδῆ τὴν
ἐναντίαν, οἷον εἰ μηδενὶ ὑπάρχον παντὶ εἴληπται ἢ εἰ παντὶ
μηδενὶ ὑπάρχειν. ἔστω γὰρ τὸ Α τῷ Β μηδενὶ ὑπάρχον, τὸ
δὲ B τῷ I παντί. av δὴ τὴν μὲν B I' πρότασιν λάβω
ἀληθῆ, τὴν δὲ τὸ A B ψευδῆ ὅλην, καὶ παντὶ ὑπάρχειν τῷ
Β τὸ Α, ἀδύνατον τὸ συμπέρασμα ἀληθὲς εἶναι" οὐδενὶ γὰρ
σι
ὑπῆρχε τῶν I, εἴπερ ᾧ τὸ DB, μηδενὶ τὸ A, τὸ δὲ B παντὶ το
^ € , + 720} A "ἢ ^ ^ € , ^ \
TQ I. ὁμοίως δ᾽ οὐδ᾽ εἰ τὸ A τῷ B παντὶ ὑπάρχει kai τὸ
B τῷ I, ἐλήφθη δ᾽ ἡ μὲν τὸ BI ἀληθὴς πρότασις, ἡ
δὲ τὸ A Β ψευδὴς ὅλη, καὶ μηδενὶ ᾧ τὸ Β, τὸ 4-- τὸ συμ-
LÀ ^ » * ay L4 Ἢ, ~ *
πέρασμα ψεῦδος ἔσται: παντὶ yàp ὑπάρξει τῷ Γ τὸ A,
εἴπερ ᾧ TO B, παντὶ τὸ A, τὸ δὲ B παντὶ τῷ l'. φανερὸν ες
^ r3 a , e ΄ ^ 37
οὖν ὅτι τῆς πρώτης ὅλης λαμβανομένης ψευδοῦς, ἐάν τε Ka-
ταφατικῆς ἐάν τε στερητικῆς, τῆς δ᾽ ἑτέρας ἀληθοῦς, οὐ γίνε-
ται ἀληθὲς τὸ συμπέρασμα. 18
Mn ὅλης δὲ λαμβανομένης 18
~ LÀ , a x ^ * M € , ~
ψευδοῦς ἔσται. εἰ yap τὸ A τῷ μὲν I παντὶ ὑπάρχει τῷ
δὲ B τινί, τὸ δὲ B παντὶ τῷ I, οἷον ζῷον κύκνῳ μὲν παντὶ 20
λευκῷ δὲ τινί, τὸ δὲ λευκὸν παντὶ κύκνῳ, ἐὰν ληφθῇ τὸ Α
παντὶ τῷ DB καὶ τὸ B παντὶ τῷ D', τὸ A παντὶ τῷ Γ᾽ ὑπάρξει
ἀληθῶς. πᾶς γὰρ κύκνος ζῷον. ὁμοίως δὲ καὶ εἰ στερητικὸν
M A , ^ ^ ι ἢ ~ M M e [4
εἴη τὸ A B: ἐγχωρεῖ yap τὸ A τῷ μὲν B τινὶ ὑπάρχειν
τῷ δὲ I μηδενί, τὸ δὲ B παντὶ τῷ I, οἷον ζῷον τινὶ Aev- 25
^ , » + ^ 3 A L4 la , 4 ,
KQ χίονι δ᾽ οὐδεμιᾷ, λευκὸν δὲ πάσῃ χιόνι. εἰ οὖν ληφθείη
τὸ μὲν A μηδενὶ τῷ B, τὸ δὲ Β παντὶ τῷ Γ, τὸ A οὐδενὶ
τῷ Γ ὑπάρξει. 28
᾿Εὰν δ᾽ ἡ μὲν A B πρότασις ὅλη ληφθῇ 28
ἀληθής, ἡ δὲ Β I ὅλη ψευδής, ἔσται συλλογισμὸς ἀλη-
x > 3 ^ f , A ~ M ^ M € ,
θής- οὐδὲν yap κωλύει τὸ A τῷ B καὶ τῷ l' παντὶ ὑπάρ- 30
b4o μὲ dC Ἀὑπάρχει- παντί Γ᾽ μὴ ὑπά ΑἹ δι ὑπάρχειν- τεθῇ π
μὲν e ΡΧ 7) PXT x )
54*5 e] jn 6 ὑπάρχειν] ὑπάρχον n 8 τὸ om. BC A om. I
ὑπάρχον ft 12 τῷ παντὶ ληφθῇ B room. n ἀληθὲς Bt 13 τὸ
om. x ὧν A Bn T0 B B 21 ἐὰν] ἐὰν οὖν n: ἐάνπερ Γ 22 τὸ A
... I om. A τὸ] καὶ τὸ C 23 ἀληθές AC
ANAAYTIKON IIPOTEPON B
4 , ES ~ - ~ > ~ ,
xew, τὸ μέντοι Β μηδενὶ τῷ I, οἷον ὅσα τοῦ αὐτοῦ γένους
wi 4 € » Ww ^ M ^ M LJ M 3 ,
εἴδη μὴ ὑπ᾽ aAAnAa’ τὸ γὰρ ζῷον καὶ ἵππῳ καὶ ἀνθρώπῳ
e , LÀ , > ^ > rg »* T ~ a
ὑπάρχει, ἵππος δ᾽ οὐδενὶ ἀνθρώπῳ. ἐὰν οὖν ληφθῇ τὸ A
^ ^ * ‘A 4 ~ 3 4 " a
παντὶ TQ B καὶ τὸ B παντὶ τῷ Γ᾽, ἀληθὲς ἔσται τὸ cup-
, ~ Ld LÀ ^ id € ,
35 πέρασμα, ψευδοῦς ὅλης οὔσης τῆς B I προτάσεως. ὁμοίως
δὲ καὶ στερητικῆς οὔσης τῆς A B προτάσεως. ἐνδέχεται yap
* , ^ , ^ M e , * M
τὸ A μήτε τῷ B μήτε τῷ Γ᾽ μηδενὶ ὑπάρχειν, μηδὲ τὸ B
4 ~ a > » [4 L4 A P,
μηδενὶ τῷ D, olov τοῖς ἐξ ἄλλου γένους εἴδεσι τὸ γένος"
τὸ γὰρ ζῷον οὔτε μουσικῇ οὔτ᾽ ἰατρικῇ ὑπάρχει, οὐδ᾽
e ^ ^ ^
54^ ἡ μουσικὴ ἰατρικῇ. ληφθέντος οὖν τοῦ μὲν A μηδενὶ τῷ B,
~ * A ~ > A v M , A ,
τοῦ δὲ B παντὶ τῷ I, ἀληθὲς ἔσται τὸ συμπέρασμα. καὶ εἰ
μὴ ὅλη ψευδὴς ἡ BI ἀλλ᾽ ἐπί τι, καὶ οὕτως ἔσται τὸ συμ-
, > , RASS A » * M ^ B ‘ ~
πέρασμα ἀληθές. οὐδὲν yàp κωλύει τὸ A καὶ τῷ B xai τῷ
" 4. , * LÀ M ~ A f ~
5 I ὅλῳ ὑπάρχειν, τὸ μέντοι B τινὶ τῷ D, οἷον τὸ γένος τῷ
* ^ ~ A a ^ * » ^ x
εἴδει καὶ τῇ διαφορᾷ τὸ yap ζῷον παντὶ ἀνθρώπῳ καὶ
* ~ € LI L4 M ~ M > , , 7 A
παντὶ πεζῷ, ὁ δ᾽ ἄνθρωπος τινὶ πεζῷ καὶ οὐ παντί. εἰ οὖν τὸ
A παντὶ τῷ B καὶ τὸ B παντὶ τῷ Γ᾽ ληφθείη, τὸ A παντὶ
^ e , - T 3 j Lj , ^ * ~
TQ I ὑπάρξει: ὅπερ ἦν ἀληθές. ὁμοίως δὲ καὶ στερητικῆς
L4 ~ Fd * » M a * ^
10 otons τῆς A B προτάσεως. ἐνδέχεται yàp τὸ A μήτε τῷ B
, ~ 4 e , A LA M -^
μήτε τῷ D μηδενὶ ὑπάρχειν, τὸ μέντοι Β τινὶ τῷ D, olov
τὸ γένος τῷ ἐξ ἄλλου γένους εἴδει καὶ διαφορᾷ: τὸ γὰρ
ζῷον οὔτε φρονήσει οὐδεμιᾷ ὑπάρχει οὔτε θεωρητικῇ, ἡ δὲ
φρόνησις τινὶ θεωρητικῇ. εἰ οὖν ληφθείη τὸ μὲν A μηδενὶ τῷ
15 B, τὸ δὲ Β παντὶ τῷ I, οὐδενὶ τῷ D τὸ A ὑπάρξει- τοῦτο
δ᾽ ἦν ἀληθές.
, ^ 4 ~ , , ~ ? Li M ~
Emi δὲ τῶν ἐν μέρει συλλογισμῶν ἐνδέχεται καὶ τῆς
, , Ld w ^ ~ ΕΣ es , ^
πρώτης προτάσεως ὅλης οὔσης ψευδοῦς τῆς δ᾽ ἑτέρας ἀληθοῦς
ἀληθὲς εἷναι τὸ συμπέρασμα, καὶ ἐπί τι ψευδοῦς οὔσης τῆς
, ^ , ἀξ. d bs LJ M ^ M > ~ ~
20 πρώτης τῆς δ᾽ ἑτέρας ἀληθοῦς, Kal τῆς μὲν ἀληθοῦς τῆς
δ᾽ ἐν μέρει ψευδοῦς, καὶ ἀμφοτέρων ψευδῶν. οὐδὲν γὰρ κω-
λύει τὸ A τῷ μὲν B μηδενὶ ὑπάρχειν τῷ δὲ D τινί, καὶ
^ ^ , ^ > ~ , ^ A x
τὸ B τῷ Γ᾽ τινί, olov ζῷον οὐδεμιᾷ χιόνι λευκῷ δὲ τινὶ
ὑπάρχει, καὶ ἡ χιὼν λευκῷ τινί. εἰ οὖν μέσον τεθείη ἡ χιών,
25 πρῶτον δὲ τὸ ζῷον, καὶ ληφθείη τὸ μὲν A ὅλῳ τῷ Β ὑπάρ-
χειν, τὸ δὲ B τινὲ τῷ D, ἡ μὲν A B ὅλη ψευδής, ἡ δὲ
337 10 Aom.C μηδὲ] μήτε ABC 38 τὸ] ἕτερον nT 30 μουσικὴ
οὔτ᾽ ἰατρικὴ A bg xai? om, Zi η ὁ... πεζῷ om. At 8 τῷ]
τὸ ( 10 γὰρ- ἅμα n 11 τῷ] τῶν n 20 τῆς... ἀληθοῦςϊ
om.” érépas+ ὅλης Γ μὲν-Ἐ μείζονος C 22-3 xai... rwi Om. ft
24 ov Bekker jom.n
2. 54°31-55*21
B I' ἀληθής, kai τὸ συμπέρασμα ἀληθές. ὁμοίως δὲ xa.
στερητικῆς οὔσης τῆς A B προτάσεως: ἐγχωρεῖ γὰρ τὸ A τῷ
x Ld € , ~ * * * € , * ,
μὲν B ὅλῳ ὑπάρχειν τῷ δὲ Γ rut μὴ ὑπάρχειν, τὸ μέν-
τοι B τινὶ τῷ Γ ὑπάρχειν, οἷον τὸ ζῷον ἀνθρώπῳ μὲν παντὶ 4o
ὑπάρχει, λευκῷ δὲ τινὶ οὐχ ἕπεται, 6 δ᾽ ἄνθρωπος τινὶ
λευκῷ ὑπάρχει, ὥστ᾽ εἰ μέσου τεθέντος τοῦ ἀνθρώπου ληφθείη
τὸ A μηδενὶ τῷ B ὑπάρχειν, τὸ δὲ B τινὶ τῷ I ὑπάρχειν,
ἀληθὲς ἔσται τὸ συμπέρασμα ψευδοῦς οὔσης ὅλης τῆς Α Β
, M , , , ^ € [4 v *
προτάσεως. kai εἰ ἐπί τι ψευδὴς ἡ A B πρότασις, ἔσται τὸ 35
, » , , x ^ ΄ ^ M ^ 4
συμπέρασμα ἀληθές. οὐδὲν yap κωλύει τὸ A καὶ τῷ B xai
~ b] € ΄ M * ~ M . , A
TQ Γ τινὶ ὑπάρχειν, kai τὸ B τῷ Γ τινὶ ὑπάρχειν, olov τὸ
ζῷ i καλῷ καὶ τινὶ iAw, καὶ τὸ καλὸν τινὲ ar
@ov Twi καλῷ καὶ τινὶ μεγάλῳ, kai ὁν τινὲ μεγάλῳ
ὑπάρχειν. ἐὰν οὖν ληφθῇ τὸ A παντὶ τῷ B καὶ τὸ B τινὶ τῷ T,
ἡ μὲν A B πρότασις ἐπί τι ψευδὴς ἔσται, ἡ δὲ BI ἀλη- 555
θής, καὶ τὸ συμπέρασμα ἀληθές. ὁμοίως δὲ καὶ στερητικῆς
οὔσης τῆς A B προτάσεως: οἱ γὰρ αὐτοὶ ὅροι ἔσονται καὶ
ὡσαύτως κείμενοι πρὸς τὴν ἀπόδειξιν. 4
Πάλιν εἰ ἡ μὲ A B,
ἀληθὴς ἡ δὲ BI ψευδής, ἀληθὲς ἔσται τὸ συμπέρασμα. ς
, a A , A ~ * Ld € , ^ ^
οὐδὲν yàp κωλύει τὸ A τῷ μὲν B ὅλῳ ὑπάρχειν τῷ δὲ I
, A A ~ M € , ^ 4
τινί, καὶ τὸ B τῷ I μηδενὶ ὑπάρχειν, olov ζῷον κύκνῳ
A * L4 t , , * , M [ὰ σ > ,
μὲν παντὶ μέλανι δὲ τινί, κύκνος δὲ οὐδενὶ μέλανι. ὥστ᾽ εἰ
ληφθείη παντὶ τῷ B τὸ A καὶ τὸ B τινὲ τῷ I, ἀληθὲς
w 4 , - L4 ~ € , M 4
ἔσται τὸ συμπέρασμα ψευδοῦς ὄντος τοῦ BI’. ὁμοίως δὲ καὶ 1o
στερητικῆς λαμβανομένης τῆς A Β προτάσεως. ἐγχωρεῖ γὰρ
τὸ A τῷ μὲν B μηδενὶ τῷ δὲ D τινὶ μὴ ὑπάρχειν, τὸ
μέντοι Β μηδενὶ τῷ I, οἷον τὸ γένος τῷ ἐξ ἄλλου γένους
LÀ M ~ , ^ [4 ^ PAN M] X ^
εἴδει καὶ τῷ συμβεβηκότι τοῖς αὑτοῦ εἴδεσι: τὸ yàp ζῷον
, ~ A , A [4 ΄ὔ ~ 2 , [4 , 2 M]
ἀριθμῷ μὲν οὐδενὲ ὑπάρχει λευκῷ δὲ τινί, ὁ δ᾽ ἀριθμὸς τς
οὐδενὶ λευκῷ: ἐὰν οὖν μέσον τεθῇ ὁ ἀριθμός, καὶ ληφθῇ τὸ
μὲν A μηδενὶ τῷ B, τὸ δὲ B τινὶ τῷ I, τὸ A τινὶ τῷ TD
οὐχ ὑπάρξει, ὅπερ ἦν ἀληθές. καὶ ἡ μὲν A B πρότασις
ἀληθής, ἡ δὲ BI ψευδής. καὶ εἰ ἐπί τι ψευδὴς ἡ A B,
ψευδὴς δὲ καὶ ἡ B D, ἔσται τὸ συμπέρασμα ἀληθές. οὐδὲν 2o
^ , ‘A - E] M ~ M L4 , Li
yàp κωλύει τὸ A τῷ B τινὶ kai τῷ Γ τινὶ ὑπάρχειν éka-
b28 οὔσης -- ὅλης ΒΓ 45 τὸ om. ABn 37 καὶ... ὑπάρχειν
om. n T9? om. πὶ 55*6 τὸ Bé y A Il orepytixis-+ οὔσης n
12 μὲν om. C 14 αὐτοῦ A: ἑαυτοῦ n 15 τινί codd.: τινὶ οὔ coni.
Jenkinson 16 οὖν oin. B 17 71? ... om. A τινὶ] rim
21 roi! om. n
ANAAYTIKQN IIPOTEPON B
τέρῳ, τὸ δὲ B μηδενὶ τῷ IT, olov εἰ ἐναντίον τὸ B τῷ T,
» b L4 ^ > ^ 7 M A ~ M
ἄμφω δὲ συμβεβηκότα τῷ αὐτῷ γένει: τὸ yap ζῷον τινὶ
λευκῷ καὶ τινὶ μέλανι ὑπάρχει, λευκὸν δ᾽ οὐδενὶ μέλανι.
25 ἐὰν οὖν ληφθῇ τὸ A παντὶ τῷ B καὶ τὸ B τινὶ τῷ I,
ἀληθὲς ἔσται τὸ συμπέρασμα. καὶ στερητικῆς δὲ λαμβανο-
μένης τῆς Α Β ὡσαύτως: οἱ γὰρ αὐτοὶ ὅροι καὶ ὡσαύτως
τεθήσονται πρὸς τὴν ἀπόδειξιν. καὶ ἀμφοτέρων δὲ ψευδῶν
οὐσῶν ἔσται τὸ συμπέρασμα ἀληθές: ἐγχωρεῖ γὰρ τὸ Α τῷ
M M ~ M ΕἸ € , ‘ a M
3o uév B μηδενὶ τῷ δὲ Γ τινὶ ὑπάρχειν, τὸ μέντοι Β μηδενὶ
^ T ' ’,ὔ ~ 2 » [4 sd M -
τῷ Γ, οἷον τὸ γένος τῷ ἐξ ἄλλου γένους εἴδει kai τῷ συμ-
βεβηκότι τοῖς εἴδεσι τοῖς αὑτοῦ: ζῷον γὰρ ἀριθμῷ μὲν
*, * ^ A M [i 4 * € > ^ > M ^|
οὐδενὶ λευκῷ δὲ τινὶ ὑπάρχει, καὶ 6 ἀριθμὸς οὐδενὶ λευκῷ.
ἐὰν οὖν ληφθῇ τὸ A παντὶ τῷ B καὶ τὸ B τινὶ τῷ I, τὸ
εἶ 3; > , * ^ , L4 ^
35 ev συμπέρασμα ἀληθές, at δὲ προτάσεις ἄμφω ψευδεῖς.
« H x ‘ ^ L4 ^ LENA ‘ /
ὁμοίως δὲ kai στερητικῆς οὔσης τῆς A B. οὐδὲν yàp κωλυέι
^ ~ M o * L4 ~ M ‘ * € L4
τὸ A τῷ μὲν B ὅλῳ ὑπάρχειν τῷ δὲ D τινὲ μὴ ὑπάρ-
* ^ M ~ ~ 4 A *
xew, μηδὲ τὸ B μηδενὶ τῷ I', olov ζῷον κύκνῳ μὲν παντὶ
΄ M * , e , , > ΕΣ * , € » »
μέλανι δὲ τινὲ ody ὑπάρχει, κύκνος δ᾽ οὐδενὲ μέλανι. ὥστ᾽ εἰ
4“οληφθείη τὸ A μηδενὶ τῷ B, τὸ δὲ B τινὶ τῷ I, τὸ A ri
55b τῷ I οὐχ ὑπάρξει. τὸ μὲν οὖν συμπέρασμα ἀληθές, αἱ δὲ
προτάσεις ψευδεῖς.
°F δὲ ΄ ,ὔ P4 * , ^ ὃ &
v δὲ TQ μέσῳ σχήματι πάντως ἐγχωρεῖ διὰ ψευ-
δῶν ἀληθὲς συλλογίσασθαι, καὶ ἀμφοτέρων τῶν προτάσεων
ς ὅλων ψευδῶν λαμβανομένων καὶ ἐπί τι ἑκατέρας, καὶ τῆς
μὲν ἀληθοῦς τῆς δὲ ψευδοῦς οὔσης [ὅλης] ὁποτερασοῦν ψευδοῦς τι-
θεμένης, [καὶ εἰ ἀμφότεραι ἐπί τι ψευδεῖς, καὶ εἰ ἡ μὲν ἁπλῶς
ἀληθὴς ἡ δ᾽ ἐπί τι ψευδής, καὶ εἰ ἡ μὲν ὅλη ψευδὴς ἡ
δ᾽ ἐπί τι ἀληθής,] καὶ ἐν τοῖς καθόλου καὶ ἐπὶ τῶν ἐν μέρει
^ , A M ^ \ Y [4 H ^
το συλλογισμῶν. εἰ yàp τὸ A τῷ μὲν B μηδενὶ ὑπάρχει τῷ
δὲ I' παντί, οἷον ζῷον λίθῳ μὲν οὐδενὲ ἵππῳ δὲ παντί, ἐὰν
» , ^ [4 , M ^ Li ^ M
ἐναντίως τεθῶσιν αἱ προτάσεις kai ληφθῇ τὸ A τῷ μὲν B
* ^ M , > ^ L4 ^ H
παντὶ TQ δὲ Γ᾽ μηδενί, ἐκ ψευδῶν ὅλων τῶν προτάσεων
ἀληθὲς ἔσται τὸ συμπέρασμα. ὁμοίως δὲ καὶ εἰ τῷ μὲν Β
* ^ ^ M € , ^ Li ^ > 4 »
i5 παντὶ τῷ δὲ I μηδενὶ ὑπάρχει τὸ A: 6 yap αὐτὸς ἔσται
16 συλλογισμός.
τό Πάλιν εἰ ἡ μὲν ἑτέρα ὅλη ψευδὴς ἡ δ᾽ ἑτέρα
428 ψευδῶν- ὅλων n 2976 Aom.n 32 αὐτοῦ AB 34 οὖν
om. C br ὑπάρξει (Γ: ὑπάρχει ABn 3 μέσῳ] δευτέρῳ C 6 ὅλης
et 7-9 xai . . . ἀληθής seclusi : habent codd. P: 7 «ai . . . ψευδεῖς secl. Waitz
1 εἰ} αἱ π 8-9 xai . . . ἀληθής secl. Waitz
2. 55?22-3. 56713
ὅλη ἀληθής: οὐδὲν yàp κωλύει τὸ A καὶ τῷ B kai τῷ Γ
* € ta * , B 5 M ^ I LJ A ,ὔ
παντὶ ὑπάρχειν, τὸ μέντοι μηδενὶ τῷ D, οἷον τὸ γένος
^ 4 € 2 LÀ LÀ a ^ ^ M ν ‘
τοῖς μὴ ὑπ᾽ ἄλληλα εἴδεσιν. τὸ yap ζῷον καὶ ἵππῳ παντὶ
a > LÀ * , * L4 LÀ »* 7 ^
xai ἀνθρώπῳ, kai οὐδεὶς ἄνθρωπος ἵππος. ἐὰν οὖν ληφθῇ 20
~ M 4 ~ b ^ e $9. € A Ld
τῷ μὲν παντὶ τῷ δὲ μηδενὶ ὑπάρχειν, ἡ μὲν ὅλη wev-
δὴς ἔσται ἡ δ᾽ ὅλη ἀληθής, καὶ τὸ συμπέρασμα ἀληθὲς
πρὸς ὁποτερῳοῦν τεθέντος τοῦ στερητικοῦ. καὶ εἰ ἡ ἑτέρα ἐπί τι
, € , € 4 e >? , > ^ M 1 ^
ψευδής, ἡ δ᾽ ἑτέρα ὅλη ἀληθής. ἐγχωρεῖ yap τὸ A τῷ
Ἂς A € L4 ^ A , * 4 x
μὲν B τινὶ ὑπάρχειν τῷ δὲ I παντί, τὸ μέντοι Β μηδενὶ 25
τῷ Γ, οἷον ζῷον λευκῷ μὲν τινὲ κόρακι δὲ παντί, καὶ τὸ
λευκὸν οὐδενὶ κόρακι. ἐὰν οὖν ληφθῇ τὸ Α τῷ μὲν Β μηδενὶ
τῷ δὲ I ὅλῳ tra ἡ μὲν A Β πρό ἐπί τι ψευ-
7 ? pxew, ἡ μὲν πρότασις ἐπί τι wev
85s, ἡ δ᾽ A D ὅλη ἀληθής, καὶ τὸ συμπέρασμα ἀληθές.
καὶ μετατιθεμένου δὲ τοῦ στερητικοῦ ὡσαύτως" διὰ γὰρ τῶν 30
αὐτῶν ὅρων ἡ ἀπόδειξις. καὶ εἰ ἡ καταφατικὴ πρότασις ἐπί
τι ψευδής, ἡ δὲ στερητικὴ ὅλη ἀληθής. οὐδὲν γὰρ κωλύει τὸ
Α τῷ μὲν B τινὶ ὑπάρχειν τῷ δὲ Γ᾽ ὅλῳ μὴ ὑπάρχειν,
M A M ^ of x ^ ^ xX t H
καὶ τὸ B μηδενὶ τῷ I, otov τὸ ζῷον λευκῷ μὲν τινὲ πίττῃ
δ᾽ οὐδεμιᾷ, καὶ τὸ λευκὸν οὐδεμιᾷ πίττῃ. ὥστ᾽ ἐὰν ληφθῇ τὸ 435
A ὅλῳ τῷ Β ὑπάρχειν τῷ δὲ Γ μηδενί, ἡ μὲν A Β ἐπί τι
ψευδής, ἡ δ᾽ A D ὅλη ἀληθής, καὶ τὸ συμπέρασμα ἀλη-
θές. καὶ εἰ ἀμφότεραι αἱ προτάσεις ἐπί τι ψευδεῖς, ἔσται
M ta 5 4 ? ^ ^ X * ^ 4
τὸ συμπέρασμα ἀληθές. ἐγχωρεῖ yàp τὸ A καὶ τῷ B καὶ
^ M € , ^ x M ^ ^ M
τῷ Γ τινὶ ὑπάρχειν, τὸ δὲ B μηδενὶ τῷ I, olov ζῷον καὶ 4o
λευκῷ τινὶ καὶ μέλανί τινι, τὸ δὲ λευκὸν οὐδενὶ μέλανι. ἐὰν οὖν 564
ληφθῇ τὸ A τῷ μὲν B παντὶ τῷ δὲ Γ᾽ μηδενί, ἄμφω μὲν at
; t » 7 ^ 5$ ΄ > , A
προτάσεις ἐπί τι ψευδεῖς, τὸ δὲ συμπέρασμα ἀληθές. ὁμοίως
δὲ καὶ μετατεθείσης τῆς στερητικῆς διὰ τῶν αὐτῶν ὅρων.
Φανερὸν δὲ καὶ ἐπὶ τῶν ἐν μέρει συλλογισμῶν: οὐδὲν ;
* 4 A ^ b A ^ M M e ,
yàp κωλύει τὸ A τῷ μὲν B παντὶ τῷ δὲ I τινὶ ὑπάρχειν,
M ^ B ^ * M € , b ^ M 3 a
καὶ τὸ B τῷ I τινὲ μὴ ὑπάρχειν, οἷον ζῷον παντὶ ἀνθρώ-
^ 4 , L4 x * ^ 3 € /
πῳ λευκῷ δὲ τινί, ἄνθρωπος δὲ Tui λευκῷ οὐχ ὑπάρξει.
ἐὰν οὖν τεθῇ τὸ Α τῷ μὲν Β μηδενὶ ὑπάρχειν τῷ δὲ Γ τινὶ
c , € ^ L4 , L4 , c > i [d
ὑπάρχειν, ἡ μὲν καθόλου πρότασις ὅλη ψευδής, ἡ δ᾽ ἐν μέ- τὸ
> 055 M τ , aX 0é e ^ δὲ Y
ρει ἀληθής, kai τὸ συμπέρασμα ἀληθές. ὡσαύτως δὲ καὶ
^ , ^ 2 ^ ^ A
καταφατικῆς λαμβανομένης τῆς A Β' ἐγχωρεῖ yap τὸ A
τῷ μὲν Β μηδενὶ τῷ δὲ D τινὲ μὴ ὑπάρχειν, καὶ τὸ B τῷ
oH μη 1 μη pxew, a
big τοῖς om. "ἢ 20 Àné85-I- τὸ ζῷον AT 24 ὅλη om. C 27
τὸ Aom. B μὲν om. C 5674 τεθείσης n! ὁ τῷ ron
I
2
2
3
3
3
3
4
56
ANAAYTIKQN ΠΡΟΤΕΡΩΝ B
I τινὶ μὴ ὑπάρχειν, olov τὸ ζῷον οὐδενὶ ἀψύχῳ, Aev-
ςκῷ δὲ τινί, καὶ τὸ ἄψυχον οὐχ ὑπάρξει τινὶ λευκῷ.
ἐὰν οὖν τεθῇ τὸ Α τῷ μὲν Β παντὶ τῷ δὲ Γ τινὶ μὴ ὑπάρ-
χειν, ἡ μὲν A Β πρότασις, ἡ καθόλου, ὅλη ψευδής, ἡ δὲ
A D ἀληθής, καὶ τὸ συμπέρασμα ἀληθές. καὶ τῆς μὲν κα-
θόλου ἀληθοῦς τεθείσης, τῆς δ᾽ ἐν μέρει ψευδοῦς. οὐδὲν γὰρ
ο κωλύει τὸ Α μήτε τῷ B μήτε τῷ Γ μηδενὶ ἕπεσθαι, τὸ μέν-
τοι Β τινὶ τῷ Γ μὴ ὑπάρχειν, οἷον ζῷον. οὐδενὶ dpi οὐδ᾽
ἀψύχῳ, καὶ ὃ ἀριθμὸς τινὶ ἀψύχῳ οὐχ ἕπεται. ἐὰν οὖν τεθῇ
τὸ Α τῷ μὲν Β μηδενὶ τῷ δὲ Γ τινί, τὸ μὲν συμπέρασμα
ἔσται ἀληθὲς καὶ ἡ καθόλου πρότασις, ἡ δ᾽ ἐν μέρει
ς ψευδής. καὶ καταφατικῆς δὲ τῆς καθόλου τιθεμένης ὡσαύ-
τως. ἐγχωρεῖ γὰρ τὸ A καὶ τῷ B καὶ τῷ Γ᾽ ὅλῳ ὑπάρχειν,
τὸ μέντοι B. τιρὶ τῷ Γ μὴ ἕπεσθαι, οἷον τὸ γένος τῷ εἴδει
καὶ τῇ διαφορᾷ- τὸ γὰρ ζῷον παντὶ ἀνθρώπῳ καὶ ὅλῳ πεζῷ
ἕπεται, ἄνθρωπος δ᾽ οὐ παντὶ πεζῷ. ὥστ᾽ ἂν ληφθῇ τὸ Α τῷ
ομὲν B ὅλῳ ὑπάρχειν, τῷ δὲ Γ΄ τινὶ μὴ ὑπάρχειν, ἡ μὲν κα-
θόλου πρότασις ἀληθής, ἡ δ᾽ ἐν μέρει ψευδής, τὸ δὲ συμ-
πέρασμα ἀληθές.
2 Φανερὸν δὲ καὶ ὅτι ἐξ ἀμφοτέρων ψευδῶν
ν 1 , » θέ. LÀ , ὃ D 1 ἢ
εσται τὸ συμπέερασμα ἀλη ες, εἴπερ EVOEXETAL TO Α και
yh
TQ B xoi τῷ I' ὅλῳ ὑπάρχειν, τὸ μέντοι B τινὶ τῷ Γ μὴ
ἕπεσθαι. ληφθέντος γὰρ τοῦ A τῷ μὲν Β μηδενὶ τῷ δὲ Γ τινὶ
L4 , e 4 4 > , ὃ ^ X. δὲ
ὑπάρχειν, αἱ μὲν προτάσεις ἀμφότεραι ψευδεῖς, τὸ δὲ
συμπέρασμα ἀληθές. ὁμοίως δὲ καὶ κατηγορικῆς οὔσης τῆς
καθόλου προτάσεως, τῆς δ᾽ ἐν μέρει στερητικῆς. ἐγχωρεῖ γὰρ
τὸ A τῷ μὲν B μηδενὶ τῷ δὲ Γ᾽ παντὶ ἕπεσθαι, καὶ τὸ B
ω
M ~ ^ e , ^ , , \ , ^ ,
o τινὶ τῷ I μὴ ὑπάρχειν, olov ζῷον ἐπιστήμῃ μὲν οὐδεμιᾷ av-
θρώπῳ δὲ παντὶ ἕπεται, ἡ δ᾽ ἐπιστήμη οὐ παντὶ ἀνθρώπῳ.
ἐὰν οὖν ληφθῇ τὸ A τῷ μὲν B ὅλῳ ὑπάρχειν, τῷ δὲ Γ᾽ τινὶ
c
) ἔπεσθ. i pe 1 ψευδεῖς, τὸ δὲ συμπέρασ͵
μὴ επεσῦαι, at μεν προτασεις EVOELS, Tti μπερασμα
ἀληθές.
Ἔσται δὲ καὶ ἐν τῷ ἐσχάτῳ σχήματι διὰ ψευδῶν 4
5 ἀληθές, καὶ ἀμφοτέρων ψευδῶν οὐσῶν ὅλων καὶ ἐπί τι ἑκα-
, M ^ x Lj , ’ ~ 4 ~ δ᾽ € , ~
τέρας, kai τῆς μὲν ἑτέρας ἀληθοῦς ὅλης τῆς δ᾽ ἑτέρας ψευδοῦς,
αἷς τινὶ τ οὔ (2, an recte? : + οὐχ ὑπάρχει m: + μὴ ὑπάρχειν D 20 οὐδενὶ
ABC 24 πρότασις- ἀληθής A 29 ἄνθρωπος] ὁ ἄνθρωπος C 35
ἔπεσθαι- οἷον τὸ ζῷον οὐδενὶ ἀνθρώπῳ, ζῷόν τινι ἐπιστήμῃ, ἄνθρωπός τινι
ἐπιστήμῃ οὐχ ὑπάρχει 7 bs ἀληθές νιν οὐσῶν Om. C xaid-8& A
οὐσῶν- xai nt
a b
3. 56*14-4. 56°41
Kal τῆς μὲν ἐπί τι ψευδοῦς τῆς δ᾽ ὅλης ἀληθοῦς, καὶ ává-
παλιν, καὶ ὁσαχῶς ἄλλως ἐγχωρεῖ μεταλαβεῖν τὰς προ-
PA $$ ^ 4, , ^ , x ^ ^
Tages. οὐδὲν yap κωλύει μήτε τὸ A μήτε τὸ B μηδενὶ τῷ
Γ ὑπάρχειν, τὸ μέντοι A τινὲ τῷ B ὑπάρχειν, οἷον οὔτ᾽ ἄν-
θρωπος οὔτε πεζὸν οὐδενὶ ἀψύχῳ ἕπεται, ἄνθρωπος μέντοι τινὶ
πεζῷ ὑπάρχει. ἐὰν οὖν ληφθῇ τὸ Α καὶ τὸ Β παντὶ τῷ Γ
ὑπάρχειν, αἱ μὲν προτάσεις ὅλαι ψευδεῖς, τὸ δὲ συμπέρασμα
ἀληθές. ὡσαύτως δὲ καὶ τῆς μὲν στερητικῆς τῆς δὲ κατα-
φατικῆς οὔσης. ἐγχωρεῖ γὰρ τὸ μὲν B μηδενὶ τῷ Γ΄ ὑπάρ-
M ^ , * AY ‘ ^ a LA /
xew, τὸ δὲ A παντί, kai τὸ A τινὶ τῷ B μὴ ὑπάρχειν,
οἷον τὸ μέλαν οὐδενὶ κύκνῳ, ζῷον δὲ παντί, καὶ τὸ ζῷον οὐ
παντὶ μέλανι. ὥστ᾽ ἂν ληφθῇ τὸ μὲν B παντὶ τῷ I’, τὸ δὲ
A μηδενί, τὸ A τινὲ τῷ B οὐχ ὑπάρξει: καὶ τὸ μὲν συμ-
2 > , Lj 4 L4 ^ * > > ,
πέρασμα ἀληθές, ai δὲ προτάσεις ψευδεῖς. καὶ εἰ ἐπί τι
. , , » 4 , » 2 or ‘
ἑκατέρα ψευδής, ἔσται τὸ συμπέρασμα ἀληθές. οὐδὲν yap
, 4 4A x A ‘4 ~ € , * *
κωλύει καὶ τὸ A καὶ τὸ B rwi τῷ D ὑπάρχειν, καὶ τὸ
A τινὶ τῷ B, οἷον τὸ λευκὸν καὶ τὸ καλὸν τινὲ ζῴῳ ὑπάρ-
* 4 ^ L] ~ 3k t A ~ M M ‘
χει, καὶ τὸ λευκὸν Twi καλῷ. ἐὰν οὖν τεθῇ τὸ A kai τὸ
B παντὶ τῷ D ὑπάρχειν, αἱ μὲν προτάσεις ἐπί τι ψευδεῖς,
M A , > , * ^ 4) ~
τὸ δὲ συμπέρασμα ἀληθές. καὶ στερητικῆς δὲ τῆς A D m-
θεμένης ὁμοίως. οὐδὲν γὰρ κωλύει τὸ μὲν Α τινὶ τῷ Γ μὴ
Li , A 4 b] [4 L4 M M ~ x M
ὑπάρχειν, τὸ δὲ B τινὶ ὑπάρχειν, kai τὸ A τῷ B μὴ παντὶ
ὑπάρχειν, οἷον τὸ λευκὸν τινὶ ζῴῳ οὐχ ὑπάρχει, τὸ δὲ κα-
λὸν τινὶ ὑπάρχει, καὶ τὸ λευκὸν οὐ παντὶ καλῷ. ὥστ᾽ àv
ληφθῇ τὸ μὲν A μηδενὶ τῷ D, τὸ δὲ B παντί, ἀμφότεραι
μὲν αἱ προτάσεις ἐπί τι ψευδεῖς, τὸ δὲ συμπέρασμα ἀλη-
θές.
Ὡσαύτως δὲ καὶ τῆς μὲν ὅλης ψευδοῦς τῆς δ᾽ ὅλης
ἀληθοῦς λαμβανομένης. ἐγχωρεῖ γὰρ καὶ τὸ Α καὶ τὸ Β
M ~ L4 a , M ^ * € ,
παντὶ TQ I ἕπεσθαι, τὸ μέντοι A τινὲ τῷ B μὴ ὑπάρχειν,
οἷον ζῷον καὶ λευκὸν mavri κύκνῳ ἕπεται, τὸ μέντοι ζῷον
, τε ΄ ^ L4 T σ΄ 4 »* ^
ov παντὶ ὑπάρχει λευκῷ. τεθέντων οὖν ὅρων τοιούτων, ἐὰν ληφθῇ
τὸ μὲν B ὅλῳ τῷ D ὑπάρχειν, τὸ δὲ A ὅλῳ μὴ ὑπάρχειν,
ἡ μὲν B D ὅλη ἔσται ἀληθής, ἡ δὲ A D ὅλη ψευδής, καὶ
τὸ συμπέρασμα ἀληθές. ὁμοίως δὲ καὶ εἰ τὸ μὲν BI ψεῦ-
δος, τὸ δὲ A I ἀληθές: οἱ γὰρ αὐτοὶ ὅροι πρὸς τὴν ἀπό-
by kai . . . ψευδοῦς om. B 9 τὸ) τῷ n 29 λευκὸν . . . καλὸν)
καλὸν... λευκὸν AB Acuxov-+ καὶ τὸ καλὸν ft οὐχ om. C! 37 οὖν
+ravc τούτων ACn 41 of yàp] xai of Cr οἱ Γ αὐτοὶ) τοιοῦτοι C*
30
35
ANAAYTIKQN IIPOTEPON B
5738e£w [μέλαν--κύκνος--ἄψυχον)]. ἀλλὰ καὶ εἰ ἀμφότεραι
λαμβάνοιντο καταφατικαί. οὐδὲν γὰρ κωλύει τὸ μὲν Β
* ~ Ld 4 * μὲ * Li , A 4
παντὶ TQ I" ἕπεσθαι, τὸ δὲ A ὅλῳ μὴ ὑπάρχειν, καὶ τὸ
A τινὲ τῷ B ὑπάρχειν, οἷον κύκνῳ παντὶ ζῷον, μέλαν
δ᾽ y M 4, -^ ‘ M rà € / * ΄ὔ σ > ^
ς δ᾽ οὐδενὶ κύκνῷ, Kal τὸ μέλαν ὑπάρχει τινὶ ζῴῳ. dor àv
ληφθῇ τὸ A "καὶ τὸ B παντὶ τῷ Γ ὑπάρχειν, ἡ μὲν B T
ὅλη ἀληθής, ἡ δὲ A I ὅλη ψευδής, καὶ τὸ συμπέρασμα
ἀληθές. ὁμοίως δὲ καὶ τῆς A I ληφθείσης ἀληθοῦς" διὰ
9 γὰρ τῶν αὐτῶν ὅρων ἡ ἀπόδειξις.
9 Πάλιν τῆς μὲν ὅλης ἀλη-
το θοῦς οὔσης, τῆς δ᾽ ἐπί τι ψευδοῦς. ἐγχωρεῖ γὰρ τὸ μὲν Β
παντὶ τῷ Γ ὑπάρχειν, τὸ δὲ A τινί, καὶ τὸ A rui τῷ B,
, ^ M > , ^ , , , ^ M]
olov δίπουν μὲν παντὶ ἀνθρώπῳ, καλὸν δ᾽ o) παντί, Kat τὸ
καλὸν τινὶ δίποδι ὑπάρχει. ἐὰν οὖν ληφθῇ καὶ τὸ Α καὶ
τὸ B ὅλῳ τῷ Γ᾽ ὑπάρχειν, ἡ μὲν B D ὅλη ἀληθής, ἡ δὲ
τις Γ ἐπί τι ψευδής, τὸ δὲ συμπέρασμα ἀληθές. ὁμοίως δὲ
καὶ τῆς μὲν A Γ ἀληθοῦς τῆς δὲ BI ἐπί τι ψευδοῦς λαμ-
βανομένης" μετατεθέντων γὰρ τῶν αὐτῶν ὅρων ἔσται ἡ ἀπό-
δειξις. καὶ τῆς μὲν στερητικῆς τῆς δὲ καταφατικῆς οὔσης.
» M Ἂς > ^ 4 * Ld ^ € , A x
ἐπεὶ yàp ἐγχωρεῖ τὸ μὲν B ὅλῳ τῷ D ὑπάρχειν, τὸ δὲ A
, ow Ld Y , * ^ ^ Σ᾿ 7
20 τινί, καὶ ὅταν οὕτως ἔχωσιν, od παντὶ τῷ B τὸ A, ἐὰν οὖν λη-
$05 τὸ μὲν B ὅλῳ τῷ I ὑπάρχειν, τὸ δὲ A μηδενί, ἡ
1 Y LA , t 3, Ὁ ον L4 > B Η \
μὲν στερητικὴ ἐπί τι ψευδής, ἡ δ᾽ ἑτέρα ὅλη ἀληθὴς καὶ τὸ
, , 3 b a Ld ^ * *
συμπέρασμα. πάλιν ἐπεὶ δέδεικται ὅτι τοῦ μὲν A μηδενὶ
ς , ^ ^ A » , ^ x ^ ^
ὑπάρχοντος TQ l', τοῦ δὲ B τινί, ἐγχωρεῖ τὸ A τινὶ τῷ B
as μὴ ὑπάρχειν, φανερὸν ὅτι καὶ τῆς μὲν A I' ὅλης ἀληθοῦς
οὔσης, τῆς δὲ Β Γ ἐπί τι ψευδοῦς, ἐγχωρεῖ τὸ συμπέρασμα
εἶναι ἀληθές. ἐὰν γὰρ ληφθῇ τὸ μὲν Α μηδενὶ τῷ Γ, τὸ δὲ
B παντί, ἡ μὲν AT ὅλη ἀληθής, ἡ δὲ BL ἐπίτι ψευδής.
Φανερὸν δὲ καὶ ἐπὶ τῶν ἐν μέρει συλλογισμῶν ὅτι πάν-
L4 ‘ - > , e ^ 3 \ σ ^
3o Tos ἔσται διὰ ψευδῶν ἀληθές. of yàp αὐτοὶ ὅροι ληπτέοι
καὶ ὅταν καθόλου ὦσιν αἱ προτάσεις, οἱ μὲν ἐν τοῖς κατη-
γορικοῖς κατηγορεκοί, οἱ δ᾽ ἐν τοῖς στερητικοῖς στερητικοί.
3$ * D 5 ee ' ER IET,
οὐδὲν yap διαφέρει μηδενὶ ὑπάρχοντος παντὶ λαβεῖν ὑπάρ-
57*1 μέλαν... ἄψυχον secl. Waitz: μέλαν... ἄνθρωπος I 4 ὅλως Β
4 κύκνῳ- μὲν ACT 13 τινὶ -Ε τῷ An 14 τὸ] τῷ 4 16 ἐπί τι
ψευδοῦς ἩΓ: ψευδοῦς ἐπί τι ABC? : ψευδοῦς C 17 αὐτῶν om. 2 20
οὖν CnI': om. AB 23 συμπέρασμα-: ἄληθές Cn: + ἔσται ἀληθές T
24 rob y B τινῇ παντί A? 29 δὲ] δὲ οὖν D: δὴ Tredennick 32
κατηγορικοί et στερητικοί om. ἈΠ
a b
4. 571-5. 57 2
b Ἂν € 4 , ^ e / M
xev, καὶ τινὶ ὑπάρχοντος καθόλου λαβεῖν ὑπάρχειν, πρὸς
τὴν τῶν ὅρων ἔκθεσιν" ὁμοίως δὲ καὶ ἐπὶ τῶν στερητικῶν. 35
Φανερὸν οὖν ὅτι ἂν μὲν ἦ τὸ συμπέρασμα ψεῦδος,
LANA we Oe t H ^ $. bi ΄ ^o» L4
ἀνάγκη, ἐξ ὧν 6 λόγος, ψευδῆ εἶναι ἢ πάντα 7j ἔνια, ὅταν
δ᾽ ἀληθές, οὐκ ἀνάγκη ἀληθὲς εἶναι οὔτε τὶ οὔτε πάντα, ἀλλ᾽
» A v > ^ ^ » ^ ^ a
ἔστι μηδενὸς ὄντος ἀληθοῦς τῶν ev τῷ συλλογισμῷ τὸ συμ-
, € , T > ,ὔ ἄς * , > 4 LÀ 3
πέρασμα ὁμοίως εἶναι ἀληθές- οὐ μὴν ἐξ ἀνάγκης. αἴτιον δ᾽ 4o
L4 L4 , LA [4 M χλλ Ld , Y > b
ὅτι ὅταν δύο ἔχῃ οὕτω πρὸς ἄλληλα ὥστε θατέρου ὄντος ἐξ 57
ἀνάγκης εἶναι θάτερον, τούτου μὴ ὄντος μὲν οὐδὲ θάτερον ἔσται,
ὄντος δ᾽ οὐκ ἀνάγκη εἶναι θάτερον: τοῦ δ᾽ αὐτοῦ ὄντος καὶ μὴ
L4 > ὁ 2 3 , A , , / LI * A^
ὄντος ἀδύνατον ἐξ ἀνάγκης εἶναι τὸ αὐτό" λέγω δ᾽ οἷον τοῦ
A ὄντος λευκοῦ τὸ DB εἶναι μέγα ἐξ ἀνάγκης, καὶ μὴ ὄντος ς
λευκοῦ τοῦ A τὸ B εἶναι μέγα ἐξ ἀνάγκης. ὅταν γὰρ Tovdi óv-
ZA ^ M > ^ , 4 ^ z
τος λευκοῦ, τοῦ A, Todt ἀνάγκη μέγα εἶναι, τὸ B, μεγάλου
δὲ τοῦ B ὄντος τὸ l' μὴ λευκόν, ἀνάγκη, εἰ τὸ A λευκόν,
M A , * .“ , L4 , x
TO Γ μὴ εἶναι λευκόν. καὶ ὅταν δύο ὄντων θατέρου ὄντος
ἀνάγκη θάτερον εἶναι, τούτου μὴ ὄντος ἀνάγκη τὸ πρῶτον μὴ 10
εἶναι. τοῦ δὴ Β μὴ ὄντος μεγάλου τὸ Α οὐχ οἷόν τε λευκὸν
4 ^ 1 A0» ~ 257 H , 7.
εἶναι. τοῦ δὲ A μὴ ὄντος λευκοῦ εἰ ἀνάγκη τὸ B μέγα εἶναι,
, H 3 , ^ of M » , * M
συμβαίνει ἐξ ἀνάγκης τοῦ B μεγάλου μὴ ὄντος αὐτὸ τὸ B
εἶναι μέγα: τοῦτο δ᾽ ἀδύνατον. εἰ γὰρ τὸ B μὴ ἔστι μέγα,
* > » 4 3 5 4 3 kd 3 0x [4
τὸ A οὐκ ἔσται λευκὸν ἐξ ἀνάγκης. el οὖν μὴ ὄντος τούτου Àev- τς
κοῦ τὸ B ἔσται μέγα, συμβαΐνει, εἰ τὸ B μὴ ἔστι μέγα,
εἶναι μέγα, ὡς διὰ τριῶν.
5 Τὸ δὲ κύκλῳ καὶ ἐξ ἀλλήλων δείκνυσθαί ἐστι τὸ διὰ
τοῦ συμπεράσματος καὶ τοῦ ἀνάπαλιν τῇ κατηγορίᾳ τὴν
ἑτέραν λαβόντα πρότασιν συμπεράνασθαι τὴν λοιπήν, ἣν 20
> , > , ^ * Ψ M ^ "
ἐλάμβανεν ἐν θατέρῳ συλλογισμῷ. οἷον εἰ ἔδει δεῖξαι ὅτι
τὸ A τῷ I παντὶ ὑπάρχει, ἔδειξε δὲ διὰ τοῦ B, πάλιν εἰ
δεικνύοι ὅτι τὸ A τῷ D ὑπάρχει, λαβὼν τὸ μὲν A τῷ I
ὑπάρχειν τὸ δὲ I' τῷ B [καὶ τὸ A τῷ B]: πρότερον δ᾽ ἀνά-
παλιν ἔλαβε τὸ B τῷ I ὑπάρχον. ἢ εἰ [ὅτι) τὸ B τῷ Γ᾽ δεῖ 25
δεῖξαι ὑπάρχον, εἰ λάβοι τὸ A κατὰ τοῦ I, ὃ ἦν συμπέ-
844 καὶ εἴ τινι ὑπῆρχεν m ὑπάρχειν om. n 36 ψευδές B 38
ἀληθῆ εἶναι r?D 39 τῷ λόγῳ nT ba τούτου- δὲ: μὲν οἵη. "ὶ
5 et 6 μέγα om. ABI 1 τὸ] olov τὸ Cn: τὸ δὲ P 8 424-5 CD
I0 ἀνάγκη" - ἦπ πρῶτον scripsi: à codd. 11 8é mt 12 εἶναι μέγας
13 μὴ μεγάλον n 17 ὡς διὰ τριῶν codd. et ut vid. P: διὰ τριῶν Γ:
secl. Maier 19 an τοῦξ secludendum vel 20 λαβεῖν legendum? 21
ἐν om. m 22 παντὶ ta y C 23 δεικνύει C 24 kai... B
om. n 25 ὑπάρχειν fecit A ὅτι seclusi
4985 N
ANAAYTIKQN IIPOTEPON B
ρασμα, τὸ δὲ B κατὰ τοῦ A ὑπάρχειν: πρότερον δ᾽ ἐλή-
φθη ἀνάπαλιν τὸ A κατὰ τοῦ B. ἄλλως δ᾽ οὐκ ἔστιν ἐξ ἀλ-
λήλων δεῖξαι. εἴτε γὰρ ἄλλο μέσον λήψεται, οὐ κύκλῳ:
οὐδὲν γὰρ λαμβάνεται τῶν αὐτῶν" εἴτε τούτων τι, ἀνάγκη
θάτερον μόνον: εἰ γὰρ ἄμφω, ταὐτὸν ἔσται συμπέρασμα,
32 δεῖ δ᾽ ἕτερον.
ο
3
!'E 4 * ^ M > , * >
3a v μὲν οὖν rots μὴ ἀντιστρέφουσιν ἐξ ἀναπο-
δείκτου τῆς ἑτέρας προτάσεως γίνεται 6 συλλογισμός" οὐ γὰρ
ἔστιν ἀποδεῖξαι διὰ τούτων τῶν ὅρων ὅτι τῷ μέσῳ τὸ τρίτον
as ὑπάρχει ἢ τῷ πρώτῳ τὸ μέσον. ἐν δὲ τοῖς ἀντιστρέφουσιν
ἔστι πάντα δεικνύναι δι’ ἀλλήλων, οἷον εἰ τὸ A καὶ τὸ B
καὶ τὸ Γ᾽ ἀντιστρέφουσιν ἀλλήλοις. δεδείχθω γὰρ τὸ A T
διὰ μέσου τοῦ B, καὶ πάλιν τὸ A B διά τε τοῦ συμπερά-
* A ^ , > , t ,
σματος καὶ διὰ τῆς B I προτάσεως ἀντιστραφείσης, ὡσαύ-
\ * A L4 ~ , * LJ
4o Tus δὲ καὶ τὸ Β Γ διά re τοῦ συμπεράσματος καὶ τῆς A B
58" προτάσεως ἀντεστραμμένης. δεῖ δὲ τήν τε Γ B καὶ τὴν BA
πρότασιν ἀποδεῖξαι: ταύταις γὰρ ἀναποδείκτοις κεχρήμεθα
μόναις. ἐὰν οὖν ληφθῇ τὸ Β παντὶ τῷ Γ ὑπάρχειν καὶ τὸ Γ
παντὶ τῷ A, συλλογισμὸς ἔσται τοῦ Β πρὸς τὸ A. πάλιν
ἐὰν ληφθῇ τὸ μὲν I παντὶ τῷ A, τὸ δὲ A παντὶ τῷ B,
M ~ A > , « , , , , a ,
παντὶ TQ B τὸ Γ ἀνάγκη ὑπάρχειν. ἐν ἀμφοτέροις δὴ ro-
^ - € , LÀ > ,
Tots τοῖς συλλογισμοῖς ἡ I A πρότασις εἴληπται ἀναπό-
tn
8eucros: ai yàp ἕτεραι δεδειγμέναι ἦσαν. ὥστ᾽ àv ταύτην
ἀποδείξωμεν, ἅπασαι ἔσονται δεδειγμέναι δι’ ἀλλήλων. ἐὰν
οὖν ληφθῇ τὸ Γ παντὶ τῷ Β καὶ τὸ Β παντὶ τῷ A ὑπάρ-
3 , , [i 4 > , ὔ
χειν, ἀμφότεραί τε αἱ προτάσεις ἀποδεδειγμέναι λαμβά-
a a ~ > L4 e , ^ T "
vovrat, καὶ τὸ I τῷ A ἀνάγκη ὑπάρχειν. φανερὸν οὖν ὅτι
, [4 ^ , , ΄ ^ » > , » ΄
ἐν μόνοις τοῖς ἀντιστρέφουσι κύκλῳ καὶ δι᾽ ἀλλήλων ἐνδέχε-
, ‘A 2 , > 4 ^ w t ,
ται γίνεσθαι τὰς ἀποδείξεις, ἐν δὲ τοῖς ἄλλοις ὡς πρότερον
is εἴπομεν. συμβαίνει δὲ καὶ ἐν τούτοις αὐτῷ τῷ δεικνυμένῳ
^ i] b » , M M M M ~ ^
χρῆσθαι πρὸς τὴν ἀπόδειξιν: τὸ μὲν yap I κατὰ τοῦ B καὶ
τὸ B κατὰ τοῦ A δείκνυται ληφθέντος τοῦ I’ κατὰ τοῦ A λέ-
M A A ^ ‘ , , -
γεσθαι, τὸ δὲ Γ κατὰ τοῦ A διὰ τούτων δείκνυται τῶν προ-
τάσεων, ὥστε τῷ συμπεράσματι χρώμεθα πρὸς τὴν ἀπό-
20 δειξιν.
᾽Επὶ δὲ τῶν στερητικῶν συλλογισμῶν ὧδε δείκνυται ἐξ
ἀλλήλων. ἔστω τὸ μὲν B παντὶ τῷ Γ᾽ ὑπάρχειν, τὸ δὲ A οὐ-
I
o
b40 re om. n 5841 ἔδει n! 6 τὸ y ἀνάγκη παντὶ τῷ B n: ἀνάγκη τὸ
y παντὶ τῷ B P 14 ὡς om. n 22 ὑπάρχον f.
b b
5. 57°27-6. 58°34
devi τῷ B- συμπέρασμα ὅτι τὸ A οὐδενὶ τῷ I. εἰ δὴ πάλιν
δεῖ συμπεράνασθαι ὅτι τὸ A οὐδενὶ τῷ B, ὃ πάλαι ἔλα-
Bev, ἔστω τὸ μὲν A μηδενὶ τῷ Γ, τὸ δὲ I' παντὶ τῷ B- οὕτω 25
^ 3 , € , ? 3 Ld 8 ^ ^
yap ἀνάπαλιν ἡ πρότασις. εἰ δ᾽ ὅτι τὸ Β τῷ I δεῖ συμπε-
, , 22» ε , > , M A B t ^ *, ‘
ράνασθαι, οὐκέθ᾽ ὁμοίως ἀντιστρεπτέον τὸ (ἡ γὰρ αὐτὴ
, ‘ ' ^ ‘ ^ M ^ t ,
πρότασις, ro B μηδενὶ τῷ A kai τὸ A μηδενὶ τῷ B ὑπάρ-
xew), ἀλλὰ ληπτέον, à τὸ A μηδενὶ ὑπάρχει, τὸ B παντὶ
Ui , L4 A ‘ ~ € [4 Ld T *
ὑπάρχειν. ἔστω TO A μηδενὶ τῷ I ὑπάρχειν, ὅπερ ἦν TO 3o
συμπέρασμα: ᾧ δὲ τὸ Α μηδενί, τὸ Β εἰλήφθω παντὶ
ὑπάρχειν. ἀνάγκη οὖν τὸ B παντὶ τῷ I ὑπάρχειν. wore
τριῶν ὄντων ἕκαστον συμπέρασμα γέγονε, καὶ τὸ κύκλῳ
ἀποδεικνύναι τοῦτ᾽ ἔστι, τὸ τὸ συμπέρασμα λαμβάνοντα καὶ
> ‘4 4 * , * M ,
ἀνάπαλιν τὴν ἑτέραν πρότασιν τὴν λοιπὴν συλλογίζεσθαι. 35
» * * Lal 2 , ^ M ' , ,
Emi δὲ τῶν ἐν μέρει συλλογισμῶν τὴν μὲν καθόλου πρό-
τασιν οὐκ ἔστιν ἀποδεῖξαι διὰ τῶν ἑτέρων, τὴν δὲ κατὰ μέ-
LÀ L4 4 > > L4 > ^ ‘ ,
pos ἔστιν. ὅτι μὲν οὖν οὐκ ἔστιν ἀποδεῖξαι τὴν καθόλου, φανε-
΄ A M k! , , M ^ , LE ^.
póv: τὸ μὲν yàp καθόλου δείκνυται διὰ τῶν καθόλου, τὸ δὲ
συμπέρασμα οὐκ ἔστι καθόλου, δεῖ δ᾽ ἐκ τοῦ συμπεράσμα- 4o
τος δεῖξαι καὶ τῆς ἑτέρας προτάσεως. ἔτι ὅλως οὐδὲ γίνεται
συλλογισμὸς ἀντιστραφείσης τῆς προτάσεως- ἐν μέρει γὰρ 58°
ἀμφότεραι γίνονται αἷ προτάσεις. τὴν δ᾽ ἐπὶ μέρους ἔστιν. δε-
δείχθω γὰρ τὸ Α κατὰ τινὸς τοῦ Γ διὰ τοῦ Β. ἐὰν οὖν λη-
$05 * B x ^ A 4 x , [4 M B A
ἢ τὸ B παντὶ τῷ A kai τὸ συμπέρασμα μένῃ, τὸ B τινὶ
^ € x ,ὔ A a ^ ^ * A
TQ I ὑπάρξει: γίνεται yap τὸ πρῶτον σχῆμα, kai τὸ Α͂ ς
, » A A Ld , * HI , ^
μέσον. εἰ δὲ στερητικὸς ὁ συλλογισμός, THY μὲν καθόλου mpó-
? L4 ^ , «^ * ᾿ς Y 2 X > » ,
τασιν οὐκ ἔστι δεῖξαι, δι᾿ ὃ Kai πρότερον ἐλέχθη" τὴν δ᾽ ἐν ué-
w yA € , > c M L4 > M ~
pet ἔστιν, ἐὰν ὁμοίως ἀντιστραφῇ τὸ A B ὥσπερ κἀπὶ τῶν ka-
θόλου, [οὐκ ἔστι, διὰ προσλήψεως δ᾽ ἔστιν,] οἷον ᾧ τὸ A τινὶ
M € , ‘ A € L4 LÀ A » ,
μὴ ὑπάρχει, τὸ B τινὲ ὑπάρχειν. ἄλλως yap od γίνεται 10
M M A 3 a M , , ,
συλλογισμὸς διὰ τὸ ἀποφατικὴν εἶναι τὴν ἐν μέρει mpó-
τασιν.
Mo δὲ ^ 8 , , ^ a * *
v δὲ τῷ δευτέρῳ σχήματι TO μὲν καταφατικὸν οὐκ
ἔστι δεῖξαι διὰ τούτου τοῦ τρόπου, τὸ δὲ στερητικὸν ἔστιν. τὸ μὲν
323 τῷ Cy: τῶν ABn τῷ CnI': τῶν AB 24 δέοι n TQ nl:
τῶν ABC 25 ἔσται ABC τῷ! ACnT': τῶν B 21-853 ...79 A
om. n! 30 τῷ P: τῶν codd. ὑπάρχον Tredennick 31 To B A
32 ὑπάρχον A® τῷ y παντὶ C 33 7a 34 τὸ τὸ C? : τοῦ τὸ DB : τὸ
AB Cn 41 οὐδὲ ὅλως C by προτάσεως ἑτέρας fecit A 2
ἐπιδεδείχθω n 5 ró! om. n 1 διὸ AB 8éorvom.C ἐὰν-
μὲν A2Cn?: + οὖν Bà 9 οὐκ... ἔστιν B*Cn?P* : om. ABnT— Som.
EL 10 μὴ ὑπάρχῃ 443
ANAAYTIKQN IIPOTEPON B
4 1 E , 4 t 1 > "
1500” κατηγορικὸν οὐ δείκνυται διὰ τὸ μὴ ἀμφοτέρας εἶναι
τὰς προτάσεις καταφατικάς" τὸ γὰρ συμπέρασμα στερητι-
κὄν ἐστι, τὸ δὲ κατηγορικὸν ἐξ ἀμφοτέρων ἐδείκνυτο κατα-
φατικῶν. τὸ δὲ στερητικὸν ὧδε δείκνυται. ὑπαρχέτω τὸ A
Α ^ ~ b , , 4 ΕΣ M
παντὶ TQ B, τῷ δὲ I μηδενί: συμπέρασμα τὸ B οὐδενὶ
20 TQ. Γ΄. ἐὰν οὖν ληφθῇ τὸ B παντὶ τῷ A ὑπάρχον, [τῷ δὲ I
, > 4 3 ι ~ * , a MJ
μηδενί) ἀνάγκη τὸ A μηδενὶ τῷ I ὑπάρχειν: γίνεται yap
^ 4, ^ , ^ , ^ * ^
τὸ δεύτερον σχῆμα: μέσον τὸ B. εἰ δὲ τὸ A B στερητικὸν
ἐλήφθη, θάτερον δὲ κατηγορικόν, τὸ πρῶτον ἔσται σχῆμα.
4 A M M ^ & ^ , x ^ σ , ,
τὸ μὲν yàp I παντὶ τῷ A, τὸ δὲ B οὐδενὶ τῷ I’, ὥστ᾽ ov-
25 devi τῷ A τὸ Β' οὐδ᾽ ἄρα τὸ A τῷ B. διὰ μὲν οὖν τοῦ
συμπεράσματος καὶ τῆς μιᾶς προτάσεως οὐ γίνεται συλ-
λογισμός, προσληφθείσης δ᾽ ἑτέρας ἔσται. εἰ δὲ μὴ καθό-
Aov 6 συλλογισμὸς, ἡ μὲν ἐν ὅλῳ πρότασις οὐ δείκνυται
διὰ τὴν αὐτὴν αἰτίαν ἥνπερ εἴπομεν καὶ πρότερον, ἡ δ᾽ ἐν μέ-
3o per δείκνυται, ὅταν jj τὸ καθόλου κατηγορικόν: ὑπαρχέτω
γὰρ τὸ A παντὶ τῷ Β, τῷ δὲ Γ μὴ παντί: συμπέρασμα B I.
ἐὰν οὖν ληφθῇ τὸ B παντὶ τῷ A, τῷ δὲ Γ᾽ οὐ παντί, τὸ A
^ ~ *, Li * 2, > > > x Ld a
τινὶ TQ Γ οὐχ ὑπάρξει: μέσον B. et δ᾽ ἐστὶν ἡ καθόλου στε-
ρητωκςή, οὐ δειχθήσεται ἡ A Γ᾿ πρότασις ἀντιστραφέντος τοῦ A B-
ἃς συμβαίνει γὰρ ἢ ἀμφοτέρας ἢ τὴν ἑτέραν πρότασιν γίνεσθαι
, , LÀ > > L4 , 2 , ig ,
ἀποφατικήν, ὥστ᾽ οὐκ ἔσται συλλογισμός. ἀλλ᾽ ὁμοίως
δειχθήσεται ὡς καὶ ἐπὶ τῶν καθόλου, ἐὰν ληφθῇ, ᾧ τὸ Β
τινὶ μὴ ὑπάρχει, τὸ A τινὶ ὑπάρχειν.
E 4 ^ ~ Li , "v A ΕΣ , €
πὶ δὲ τοῦ τρίτου σχήματος ὅταν μὲν ἀμφότεραι αἱ ἢ
4o προτάσεις καθόλου ληφθῶσιν, οὐκ ἐνδέχεται δεῖξαι δι᾽ ἀλλή-
λων: τὸ μὲν γὰρ καθόλου δείκνυται διὰ τῶν καθόλου, τὸ
590" δ᾽ ἐν τούτῳ συμπέρασμα ἀεὶ κατὰ μέρος, ὥστε φανερὸν ὅτι
LÀ ?, , , ~ ^ ra ~ , ^
ὅλως οὐκ ἐνδέχεται δεῖξαι διὰ τούτου τοῦ σχήματος τὴν
4 καθόλου πρότασιν.
3 'Eàv δ᾽ ἡ μὲν jj καθόλου ἡ δ᾽ ἐν μέρει,
E A LÀ M , ᾽ L4 LÀ ^ 7 > ,
ποτὲ μὲν ἔσται ποτὲ δ᾽ οὐκ ἔσται. ὅταν μὲν οὖν ἀμφότεραι
ς κατηγορικαὶ ληφθῶσι καὶ τὸ καθόλου γένηται πρὸς τῷ ἐλάτ-
τονι ἄκρῳ, ἔσται, ὅταν δὲ πρὸς θατέρῳ, οὐκ ἔσται. ὑπαρ-
, ^ A * ~ ^ A , ,
xérw yap τὸ A παντὶ τῷ I, τὸ δὲ B τινί: συμπέρασμα
brg-20 B*-I] B τῷ y μηδενί n 20-1 ra® . . . μηδενί om. ABIC! n
24 yàp om. B! 27 ἣν Aldina 28 συλλογισμὸς- ἦ ABC 30
καθόλου τὸ 43: καθόλου AIBC! 31 BD] τὸ By n 33 ὑπάρξει nT':
ὑπάρχει ABC 38 μὴ ὑπάρχῃ An 40 GAAjjAwe+ τὴν καθόλου
πρότασιν ΑΓ
b a
6. 58°15-7. 59'41
τὸ A B. ἐὰν οὖν ληφθῇ τὸ Γ παντὶ τῷ A ὑπάρχειν, τὸ μὲν
Γ δέδεικται τινὶ τῷ B ὑπάρχον, τὸ δὲ B τινὶ τῷ I οὐ δέ-
ὃ , > , > M D ^ ^ B M A B ^
εἰκται. καίτοι ἀνάγκη, εἰ τὸ I’ τινὶ τῷ B, καὶ τὸ B τινὶ
τῷ I ὑπάρχειν. ἀλλ’ οὐ ταὐτόν ἐστι τόδε τῷδε καὶ τόδε
^ L4 , > x eg > , * ^ a
τῷδε ὑπάρχειν: ἀλλὰ προσληπτέον, εἰ τόδε Tui τῷδε, Kal
θάτερον τινὶ τῶδε. τούτου δὲ ληφθέντος οὐκέτι γίνεται ἐκ τοῦ
συμπεράσματος καὶ τῆς ἑτέρας προτάσεως ὁ συλλογισμός.
εἰ δὲ τὸ B παντὶ τῷ I, τὸ δὲ A τινὶ τῷ I, ἔσται δεῖ-
fat τὸ A I, ὅταν ληφθῇ τὸ μὲν I' παντὶ τῷ B ὑπάρχειν,
τὸ δὲ Α τινί. εἰ γὰρ τὸ Γ παντὶ τῷ Β, τὸ δὲ Α τινὶ τῷ Β,
> ,ὔ ^ N ~ € 4 , i] M L4
ἀνάγκη τὸ A rui τῷ Γ᾽ ὑπάρχειν: μέσον τὸ B. καὶ ὅταν ἦ
ἡ μὲν κατηγορικὴ ἡ δὲ στερητική, καθόλου δ᾽ ἡ κατηγορική,
Ca [4 ἘΠῚ 4 ec 4 M ' * ^ ^
δειχθήσεται ἡ ἑτέρα. ὑπαρχέτω yap to B παντὶ τῷ D, τὸ
δὲ A τινὲ μὴ ὑπαρχέτω: συμπέρασμα ὅτι τὸ A τινὶ τῷ B
> Li L4 Y 7T ~ ^ M ~ e ,
οὐχ ὑπάρχει. ἐὰν οὖν προσληφθῇ τὸ Γ᾽ παντὶ τῷ B ὑπαρ-
2 , ^ A M ~ I hi Li 4 4 ‘ B
xew, ἀνάγκη τὸ τινὶ τῷ μὴ ὑπάρχειν: μέσον τὸ B.
ὅταν δ᾽ ἡ στερητικὴ καθόλου γένηται, οὐ δείκνυται ἡ ἑτέρα,
εἰ μὴ ὥσπερ ἐπὶ τῶν πρότερον, ἐὰν ληφθῇ, ᾧ τοῦτο τινὶ
μὴ ὑπάρχει, θάτερον τινὶ ὑπάρχειν, οἷον εἰ τὸ μὲν A μη-
dei τῷ I, τὸ δὲ B τινί: συμπέρασμα ὅτι τὸ A τινὶ τῷ B
, € , »* 7T — T τ M x t ,
οὐχ ὑπάρχει. ἐὰν οὖν ληφθῇ, ᾧ τὸ A τινὶ μὴ ὑπάρχει,
A ^ € 4 > , * ἣν ~ t , w
τὸ Γ τινὶ ὑπάρχειν, ἀνάγκη τὸ Γ τινὲ τῷ B ὑπάρχειν. dA-
λως δ᾽ οὐκ ἔστιν ἀντιστρέφοντα τὴν καθόλου πρότασιν δεῖξαι
τὴν érépav- οὐδαμῶς γὰρ ἔσται συλλογισμός.
[Φανερὸν οὖν ὅτι ἐν μὲν τῷ πρώτῳ σχήματι ἡ δι᾽’ ἀλ-
λήλων δεῖξις διά τε τοῦ τρίτου καὶ διὰ τοῦ πρώτου γίνεται σχή-
ματος. κατηγορικοῦ μὲν γὰρ ὄντος τοῦ συμπεράσματος διὰ
τοῦ πρώτου, στερητικοῦ δὲ διὰ τοῦ ἐσχάτου: λαμβάνεται
γάρ, ᾧ τοῦτο μηδενί, θάτερον παντὶ ὑπάρχειν. ἐν δὲ τῷ μέσῳ
καθόλου μὲν ὄντος τοῦ συλλογισμοῦ δι᾽ αὐτοῦ τε καὶ διὰ τοῦ
πρώτου σχήματος, ὅταν δ᾽ ἐν μέρει, δι’ αὐτοῦ τε καὶ τοῦ
ἐσχάτου. ἐν δὲ τῷ τρίτῳ OV αὐτοῦ πάντες. φανερὸν δὲ καὶ
ὅτι ἐν τῷ τρίτῳ καὶ τῷ μέσῳ οἱ μὴ δι᾿ αὐτῶν γινόμενοι
λλογισμοὶ ἢ οὐκ εἰσὶ l τὴν κύκλῳ δεῖξιν ἢ ἀτελεῖς.]
συλλογισμοὶ ἢ οὐκ εἰσὶ κατὰ τὴν κύκλῳ δεῖξιν ἢ ἀτελεῖς.
5938 ὑπάρχειν -᾿ τὸ δὲ a τινὶ τῶ BC 12 προσληπτέον ὅτι ef f IS rot
+pe AT 22 ὑπάρχειν) ὑπάρχον ἦν τὸ a τῷ B fecit A 26 μὴ
ὑπάρχῃ AlCn 27 ta*| τῶν B 28 μὴ 0m. 4! ὑπάρχῃ Cn 29 τὸ]
τούτῳ τὸ C τῷ hl: τῶν ABC 32-41 Φανερὸν, . . ἀτελεῖς
seclusi: habent codd. PP 38 σχήματος CnP :- καὶ διὰ τοῦ ἐσχάτου AB
40 rà! om. C
10
15
20
25
30
35
40
ANAAYTIKQN IIPOTEPQN B
b * 3 3 , , "ἢ 4 , M ,
59» To δ᾽ ἀντιστρέφειν ἐστὲ τὸ μετατιθέντα τὸ συμπέρασμα 8
ποιεῖν τὸν συλλογισμὸν ὅτι ἢ τὸ ἄκρον τῷ μέσῳ οὐχ ὑπάρ-
£e ἢ τοῦτο τῷ τελευταίῳ. ἀνάγκη γὰρ τοῦ συμπεράσματος
ἀντιστραφέντος καὶ τῆς ἑτέρας μενούσης προτάσεως ἀναιρεῖ-
5s σθαι τὴν Aovrjv: εἰ γὰρ ἔσται, καὶ τὸ συμπέρασμα ἔσται.
διαφέρει δὲ τὸ ἀντικειμένως ἢ ἐναντίως ἀντιστρέφειν τὸ συμ-
πέρασμα: οὐ γὰρ ὃ αὐτὸς γίνεται συλλογισμὸς ἑκατέρως
> , Lj A a~ > ¥ ^ ^ € , ,
ἀντιστραφέντος" δῆλον δὲ τοῦτ᾽ ἔσται διὰ τῶν ἑπομένων. λέγω
> ^ ^ Y * ^
δ᾽ ἀντικεῖσθαι μὲν τὸ παντὶ τῷ οὐ παντὶ καὶ τὸ τινὶ τῷ οὐ-
10 δενί, ἐναντίως δὲ τὸ παντὶ τῷ οὐδενὶ καὶ τὸ τινὲ τῷ οὐ τινὶ
X , » ^ ta * 4. ~ A 4
ὑπάρχειν. ἔστω yap δεδειγμένον τὸ A κατὰ τοῦ Γ διὰ μέ-
σου τοῦ B. εἰ δὴ τὸ A ληφθείη μηδενὶ τῷ Γ᾽ ὑπάρχειν, τῷ
δὲ B παντί, οὐδενὶ τῷ I ὑπάρξει τὸ B. καὶ εἰ τὸ μὲν A
μηδενὶ τῷ D', τὸ δὲ B παντὶ τῷ I, τὸ A οὐ παντὶ τῷ B
‘ Uu « ^ 3 , ΕΣ ^ » , M 06. 8 ^ ~
15 Kal οὐχ ἁπλῶς οὐδενί: οὐ yap ἐδείκνυτο TO καθόλου διὰ τοῦ
ἐσχάτου σχήματος. ὅλως δὲ τὴν πρὸς τῷ μείζονι ἄκρῳ
πρότασιν οὐκ ἔστιν ἀνασκευάσαι καθόλου διὰ τῆς ἀντιστρο-
$üs ἀεὶ γὰρ ἀναιρεῖται διὰ τοῦ τρίτου σχήματος: ἀνάγκη
γὰρ πρὸς τὸ ἔσχατον ἄκρον ἀμφοτέρας λαβεῖν τὰς προτά-
20 σεις. καὶ εἰ στερητικὸς 6 συλλογισμός, ὡσαύτως. δεδείχθω
‘ M x ~ I « p. ὃ A ~ B 3 ~ n A
yap τὸ A μηδενὶ τῷ l' ὑπάρχον διὰ τοῦ B. οὐκοῦν av λη-
φθῇ τὸ A τῷ Γ᾽ παντὶ ὑπάρχειν, τῷ δὲ B μηδενί, οὐδενὶ
τῷ Γ τὸ B ὑπάρξει. καὶ εἰ τὸ A καὶ τὸ B παντὶ τῷ T,
τὸ Α τινὶ τῷ Β' ἀλλ᾽ οὐδενὶ ὑπῆρχεν.
, ^ , , , > ^ M] , *
25 Ἐὰν δ᾽ ἀντικειμένως ἀντιστραφῇ τὸ συμπέρασμα, καὶ
οἱ συλλογισμοὶ ἀντικείμενοι καὶ οὐ καθόλου ἔσονται. γίνε-
ται γὰρ ἡ ἑτέρα πρότασις ἐν μέρει, ὥστε καὶ τὸ συμπέρα-
σμα ἔσται κατὰ μέρος. ἔστω γὰρ κατηγορικὸς ὁ συλλογι-
σμός, καὶ ἀντιστρεφέσθω οὕτως. οὐκοῦν εἰ τὸ Α οὐ παντὶ
3o TQ. D' τῷ δὲ B παντί, τὸ B οὐ παντὶ τῷ Γ΄’ καὶ εἰ τὸ μὲν
A μὴ παντὶ τῷ ΓΙ, τὸ δὲ B παντί, τὸ A οὐ παντὶ τῷ B.
€ , ^ * , A Lj , , M M
ὁμοίως δὲ καὶ εἰ στερητικὸς 6 συλλογισμός. εἰ yàp τὸ A
* ^ [4 , ^ b , M M ^ ,
τινὶ τῷ I ὑπάρχει, τῷ δὲ B μηδενί, τὸ B τινὶ τῷ I’ οὐχ
@ , , Li Ac yy ἧς ^ > ^ if A ^ D ,
ὕπαρξει, οὐχ ἁπλῶς οὐδενί: καὶ εἰ TO μὲν τῷ Twí,
3570 δὲ B παντί, ὥσπερ ev ἀρχῇ ἐλήφθη, τὸ A τινὶ τῷ B
ὑπάρξει.
bg ἀντιστρέφοντος A 6 ἀντιστραφεῖν B 8 dvrtarpéóovros C
15 οὐχὶ ABC ἁπλῶς nDP: ὅλως ABC 18 τρίτου] Y π 19 τὸ
ἄκρον τὸ ἔσχατον C 2ιτῷ CnP : τῶν 4 Β ὑπάρχειν C 23 rà!
CD: τῶν ABn 29 od oin. C: μὴ n 34 οὐχ) καὶ οὐχ nt”
8. 59^1-9. 60*29
E * δὲ ~ ? , =~ - ^ »
πὶ δὲ τῶν ἐν μέρει συλλογισμῶν ὅταν μὲν ἀντικει-
, > , * ta 3 ^ , ,
μένως ἀντιστρέφηται τὸ συμπέρασμα, ἀναιροῦνται ἀμφότε-
ραι αἱ προτάσεις, ὅταν δ᾽ ἐναντίως, οὐδετέρα. οὐ γὰρ ἔτι
, , , ^ ta > ^ » ,
συμβαίνει, καθάπερ ἐν τοῖς καθόλου, ἀναιρεῖν ἐλλείποντος 4o
~ , 4 x , , > , 292 μὲ
τοῦ συμπεράσματος κατὰ τὴν ἀντιστροφήν, ἀλλ᾽ οὐδ᾽ ὅλως
? ^ , A * ^ M ^ , ^ hal
ἀναιρεῖν. δεδείχθω yap τὸ A xarà twos τοῦ Γ΄. οὐκοῦν dv 608
ληφθῇ τὸ A μηδενὶ τῷ I ὑπάρχειν, τὸ δὲ B τινί, τὸ A
τῷ B τινὶ οὐχ ὑπάρξει: καὶ εἰ τὸ A μηδενὶ τῷ I, τῷ δὲ
Β παντί, οὐδενὶ τῷ Γ τὸ B. ὥστ᾽ ἀναιροῦνται ἀμφότεραι.
ἐὰν δ᾽ ἐναντίως ἀντιστραφῇ, οὐδετέρα. εἰ γὰρ τὸ Α τινὶ τῷ ς
I a € , ^ A B Ψ ^ B M ~ ?,
μὴ ὑπάρχει, τῷ δὲ παντί, τὸ τινὶ τῷ I οὐχ
Li , > > L4 > a Li , » ~ , ,
ὑπάρξει, ἀλλ’ οὔπω ἀναιρεῖται τὸ ἐξ ἀρχῆς: ἐνδέχεται
γὰρ τινὲ ὑπάρχειν καὶ τινὲ μὴ ὑπάρχειν. τῆς δὲ καθόλου,
~ Ld , * ^ , , * x b
τῆς A B, ὅλως οὐδὲ γίνεται συλλογισμός. εἰ yàp τὸ μὲν
A τιν τῷ Γ μὴ ὑπάρχει, τὸ δὲ B τινὶ ὑπάρχει, οὐδετέρα 1o
καθόλου τῶν προτάσεων. ὁμοίως δὲ καὶ εἰ στερητικὸς 6 συλ-
λογισμός: εἰ μὲν γὰρ ληφθείη τὸ A παντὶ τῷ Γ᾽ ὑπάρ-
2 “- > * > a , , , > ΄
χειν, ἀναιροῦνται ἀμφότεραι, εἰ δὲ τινί, οὐδετέρα. ἀπόδει-
£s δ᾽ ἡ αὐτή.
» 4 ~ ΄ , M ^ M c^ ,
9 Ev δὲ τῷ δευτέρῳ σχήματι τὴν μὲν πρὸς τῷ μείζονι τς
ἄκρῳ πρότασιν οὐκ ἔστιν ἀνελεῖν ἐναντίως, ὁποτερωσοῦν τῆς
Σ - , LER T a LÀ x , ?, ~
ἀντιστροφῆς γινομένης" det yap ἔσται τὸ συμπέρασμα ev τῷ
΄, > > ,
τρίτῳ σχήματι, καθόλου δ᾽ οὐκ ἦν ἐν τούτῳ συλλογισμός.
τὴν δ᾽ ἑτέραν ὁμοίως ἀναιρήσομεν τῇ ἀντιστροφῇ. λέγω δὲ
τὸ ὁμοίως, εἰ μὲν ἐναντίως ἀντιστρέφεται, ἐναντίως, εἰ δ᾽ 20
> , 5 , € , 4 ^ 4 ~
ἀντικειμένως, ἀντικειμένως. ὑπαρχέτω yap τὸ A παντὶ τῷ
~ M , , AJ ^
B, τῷ δὲ I' μηδενί: συμπέρασμα BI. ἐὰν οὖν ληφθῇ τὸ
B παντὶ τῷ I" ὑπάρχειν καὶ τὸ A B μένῃ, τὸ A παντὶ τῷ
I' ὑπάρξει: γίνεται γὰρ τὸ πρῶτον σχῆμα. εἰ δὲ τὸ B
παντὶ τῷ l', τὸ δὲ A μηδενὶ τῷ Γ, τὸ A οὐ παντὶ τῷ Β. 25
^ * » γι > , , > ~ ‘
σχῆμα τὸ ἔσχατον. ἐὰν δ᾽ ἀντικειμένως ἀντιστραφῇ τὸ B T,
ἡ μὲν A B ὁμοίως δειχθήσεται, ἡ δὲ A I ἀντικειμένως. εἰ
γὰρ τὸ B τινὶ τῷ I, τὸ δὲ A μηδενὶ τῷ I, τὸ A τινὶ τῷ
B οὐχ ὑπάρξει. πάλιν εἰ τὸ B τινὶ τῷ Γ, τὸ δὲ A παντὶ
bgo ἀφαιρεῖν ri 41 οὐδ᾽ om. s 6041 dvatpeiv+ οὐκ ἐνδέχεται ἡ
συζυγία τὸ a παντὶ τῷ B, τὸ B τινὶ ro y mn Tüv y n τινὶ ro BC
S5TÜÓv yn 6 ὑπάρχῃ π 9 οὐ(: οὐδεὶς n 1o ràv y ABCT
μὴ ὑπάρχῃ π 11 εἰ) ὅτε 22 ΒΓῚ τὸ βγπ 26 σχῆμα- δὲ π
28 167] τῶν n 29 et 30 Trav y f
ANAAYTIKQN IIPOTEPON B
3o TQ. B, τὸ A τινὶ τῷ Γ, ὥστ᾽ ἀντικείμενος γίνεται 6 συλλο-
, € [4 b , Αι , > , LÀ t
ywpós. ὁμοίως δὲ δειχθήσεται καὶ εἰ ἀνάπαλιν ἔχοιεν at
προτάσεις. εἰ δ᾽ ἐστὶν ἐπὶ μέρους ὁ συλλογισμός, ἐναντίως
μὲν ἀντιστρεφομένου τοῦ συμπεράσματος οὐδετέρα τῶν προ-
τάσεων ἀναιρεῖται, καθάπερ οὐδ᾽ ἐν τῷ πρώτῳ σχήματι,
Σ y δ᾽ 3 , , ^ ‘ ^ M
35 ἀντικειμένως ἀμφότεραι. κείσθω yap τὸ A τῷ μὲν B
M € , ^ 4 , , UA i. d
μηδενὶ ὑπάρχειν, τῷ δὲ D τινί: συμπέρασμα BI. ἐὰν οὖν
^ ‘ B ^ ^ € ra x ^ [4 /
τεθῇ τὸ B τινὲ τῷ Γ ὑπάρχειν καὶ τὸ A B μένῃ, ovumé-
» L4 * A ^ 3 € JF 2 » U
ρασμα ἔσται ὅτι τὸ A τινὶ τῷ I" οὐχ ὑπάρχει, ἀλλ᾽ οὐκ
* ~ *,
ἀνήρηται τὸ ἐξ ἀρχῆς" ἐνδέχεται yap τινὲ ὑπάρχειν καὶ μὴ
€ , , > * E. ^ M ‘ M ^ »
4o ὑπάρχειν. πάλιν εἰ τὸ B τινὶ τῷ Γ kai τὸ A τινὶ τῷ Γ, οὐκ
L4 , , , x , ^ * L4
ἔσται συλλογισμός: οὐδέτερον yàp καθόλου τῶν εἰλημμένων.
6 b ν΄ > , > ^ \ A B yA δ᾽ > , > 4
o> ὥστ᾽ οὐκ ἀναιρεῖται τὸ . ἐὰν δ᾽ ἀντικειμένως ἀντιστρέφη-
3 “- > / , AY ^ * ~ M
Tat, ἀναιροῦνται ἀμφότεραι. εἰ yap τὸ B παντὶ τῷ I, τὸ
δὲ A μηδενὶ τῷ B, οὐδενὶ τῷ I τὸ A> ἦν δὲ τινί. πάλιν
εἰ τὸ B παντὶ τῷ I, τὸ δὲ A τινὶ τῷ I, τινὶ τῷ B τὸ A.
« > b 9 * ὁδ ‘ > δ 86. ,
5*j αὐτὴ δ᾽ ἀπόδειξις καὶ ef τὸ καθόλου κατηγορικόν.
᾿Επὶ δὲ τοῦ τρίτου σχήματος ὅταν μὲν ἐναντίως ἀντι-
στρέφηται τὸ συμπέρασμα, οὐδετέρα τῶν προτάσεων ἀναιρεῖ-
ται κατ᾽ οὐδένα τῶν συλλογισμῶν, ὅταν δ᾽ ἀντικειμένως,
ἀμφότεραι καὶ ἐν ἅπασιν. δεδείχθω γὰρ τὸ Α τινὶ τῷ Β
το ὑπάρχον, μέσον δ᾽ εἰλήφθω τὸ I, ἔστωσαν δὲ καθόλου ai
, 3 ^ LAJ ^ ^ M ^ ^ t ,
προτάσεις. οὐκοῦν ἐὰν ληφθῇ τὸ A τινὶ τῷ B μὴ ὑπάρχειν,
* ^ 3 ^ > , x ~ *
τὸ δὲ B παντὶ τῷ I, οὐ γίνεται συλλογισμὸς τοῦ A καὶ
τοῦ Γ΄. οὐδ᾽ εἰ τὸ A τῷ μὲν B τινὶ μὴ ὑπάρχει, τῷ δὲ Γ
, > L4 ~ M ^ , € , ^
παντί, οὐκ ἔσται τοῦ B καὶ τοῦ I συλλογισμός. ὁμοίως δὲ
, ^ » ^ , € à ^ M ,
15 δειχθήσεται Kal εἰ μὴ καθόλου ai προτάσεις. ἢ yàp ἀμφο-
τέρας ἀνάγκη κατὰ μέρος εἶναι διὰ τῆς ἀντιστροφῆς, ἢ τὸ
Fé 4 ~ , , LÀ » Ld » 2
καθόλου πρὸς τῷ ἐλάττονι ἄκρῳ γίνεσθαι: οὕτω δ᾽ οὐκ ἣν
συλλογισμὸς οὔτ᾽ ἐν τῷ πρώτῳ σχήματι οὔτ᾽ ἐν τῷ μέσῳ.
ἐὰν δ᾽ ἀντικειμένως ἀντιστρέφηται, αἱ προτάσεις ἀναιροῦν-
, ^ M
2o Tat ἀμφότεραι. εἰ yàp τὸ A μηδενὶ τῷ B, τὸ δὲ B παντὶ
TQ D, τὸ A οὐδενὶ τῷ I" πάλιν εἰ τὸ A τῷ μὲν B μη-᾿
, ^ ^ €
sai, τῷ δὲ I παντί, τὸ B οὐδενὶ τῷ I. καὶ εἰ ἡ ἑτέρα
~ A *
μὴ καθόλου, ὡσαύτως. εἰ yàp τὸ A μηδενὶ τῷ B, τὸ δὲ B
a30 ἀντικείμενος Alu: ἀντικειμένως 4380 38 ὑπάρξει Cr’ bg τινὶ
τῷ B] ἔσται τινὶ τῶν B. n 5 κατηγορικὸν εἴη n 9 τῶν B Bn τὶ
τῷ ACI: τῶν Bn I3 τῷ) τῶν A μὲν om. I τινὶ] παντὶ ἢ
15 ἀμφοτέρας post 16 μέρος C I9 ἀντιστρέφηται fort. P, coni. Waitz:
ἀντιστρέφωνται ABC: ἀντιστρέφονται n
9. 60*30—10. 61°16
τινὶ TQ D, τὸ A τινὶ τῷ Γ᾽ οὐχ ὑπάρξει: εἰ δὲ τὸ A τῷ
μὲν Β μηδενί, τῷ δὲ Γ παντί, οὐδενὶ τῷ Γ τὸ Β.
Ὁμοίως
δὲ καὶ εἰ στερητικὸς 6 συλλογισμός. δεδείχθω γὰρ τὸ A
^ ^ * Ui tí » 3 M M 4
Tui τῷ B μὴ ὑπάρχον, ἔστω δὲ κατηγορικὸν μὲν τὸ B T,
> ‘ M A ig L4 ^ 3 ὃ € ,
ἀποφατικὸν δὲ τὸ A Γ' οὕτω yap ἐγίνετο 6 συλλογισμός.
^ 1 ~ ^
Grav μὲν οὖν τὸ ἐναντίον ληφθῇ τῷ συμπεράσματι, οὐκ ἔσται
συλλογισμός. εἰ γὰρ τὸ Α τινὶ τῷ Β, τὸ δὲ Β παντὶ τῷ
ογισμος. yap p D, TO !
, A ~ ‘ ^ 2 , M ^ ^
Γ᾽ οὐκ ἦν συλλογισμὸς τοῦ A kai τοῦ D. οὐδ᾽ εἰ τὸ A τινὶ τῷ
B, τῷ δὲ Γ μηδενί, οὐκ ἦν τοῦ B καὶ τοῦ Γ᾽ συλλογισμός.
e E ES n "
ὥστε οὐκ ἀναιροῦνται αἱ προτάσεις. Grav δὲ τὸ ἀντικείμενον,
2 ^ , a * M ~ M A ^ x
ἀναιροῦνται. ef yap τὸ A παντὶ τῷ B καὶ τὸ B τῷ I, τὸ
A παντὶ τῷ Γ΄ ἀλλ᾽ οὐδενὶ ὑπῆρχεν. πάλιν εἰ τὸ A παντὶ
τῷ B, τῷ δὲ Γ᾽ μηδενί, τὸ B οὐδενὶ τῷ I* ἀλλὰ παντὶ
€ ^ e€ Eg δὲ ὃ , 4 , ^ 00A. » t €
ὑπῆρχεν. ὁμοίως δὲ δείκνυται kai εἰ μὴ καθόλου εἰσὶν at
προτάσεις. γίνεται γὰρ τὸ A I καθόλου τε καὶ στερητικόν,
θάτερον δ᾽ ἐπὶ μέρους καὶ κατηγορικόν. εἰ μὲν οὖν τὸ A παντὶ
τῷ B, τὸ δὲ B τινὶ τῷ D, τὸ A rwi τῷ I ovupBaiver-
ἀλλ᾽ οὐδενὶ ὑπῆρχεν. πάλιν εἰ τὸ A παντὶ τῷ Β, τῷ δὲ D
μηδενί, τὸ B οὐδενὶ τῷ Γ΄ ἔκειτο δὲ τινί. εἰ δὲ τὸ A τινὶ
τῷ B καὶ τὸ B τινὶ τῷ D, οὐ γίνεται συλλογισμός: οὐδ᾽
εἰ τὸ A τινὶ τῷ B, τῷ δὲ Γ᾽ μηδενί, οὐδ᾽ οὕτως. ὥστ᾽ ἐκεί-
νως μὲν ἀναιροῦνται, οὕτω δ᾽ οὐκ ἀναιροῦνται ai προτάσεις.
Φανερὸν οὖν διὰ τῶν εἰρημένων πῶς ἀντιστρεφομένου
τοῦ συμπεράσματος ἐν ἑκάστῳ σχήματι γίνεται συλλογι-
σμός, καὶ πότ᾽ ἐναντίος τῇ προτάσει καὶ πότ᾽ ἀντικείμενος,
καὶ ὅτι ἐν μὲν τῷ πρώτῳ σχήματι διὰ τοῦ μέσου καὶ τοῦ
ἐσχάτου γίνονται οἱ συλλογισμοί, καὶ ἡ μὲν πρὸς τῷ ἐλάτ-
TOV, ἄκρῳ ἀεὶ διὰ τοῦ μέσου ἀναιρεῖται, ἡ δὲ πρὸς τῷ μεί-
ζονι διὰ τοῦ ἐσχάτου- ἐν δὲ τῷ δευτέρῳ διὰ τοῦ πρώτου καὶ
^ ~ L4 ^
TOU ἐσχάτου, ἡ μὲν πρὸς τῷ ἐλάττονι ἄκρῳ dei διὰ τοῦ
~ ‘ ^
πρώτου σχήματος, ἡ δὲ πρὸς τῷ μείζονι διὰ τοῦ ἐσχάτου"
ἐν δὲ τῷ τρίτῳ διὰ τοῦ πρώτου καὶ διὰ τοῦ μέσου, καὶ ἡ
^ ~ > L3 * ^
μὲν πρὸς τῷ μείζονι διὰ τοῦ πρώτου dei, ἡ δὲ πρὸς τῷ
ἐλάττονι διὰ τοῦ μέσου.
b24 τῷ ACT: τῶν Bn τὸ... IT om. An} 31 καὶ] κατὰ ΒΓ τῷ
ACT: τῶν Bn 32 καὶ] κατὰ ΒΓ 35 παντὶ) τινὶ Γ 39 καὶ om.
nn 6141 ἔκειτο δὲ τινί om. AB 2 τῷ bis et 3 11] τῶν n
7 ἐναντίος... ἀντικείμενος AnD’: ἐναντίως... ἀντικειμένως BC II
καὶ 4- διὰ n? 12 ἡ] καὶ ἡ B 14 xai? om. AC 16 διὰ] ἀεὶ διὰ n7
25
25
39
35
40
613
IO
ANAAYTIKQN IIPOTEPON B
Ti μὲν οὖν ἐστὶ τὸ ἀντιστρέφειν Kai πῶς ἐν ἑκάστῳ xx
, ‘ ; , , * € A M
σχήματι Kal τίς γίνεται συλλογισμός, φανερόν. ὁ δὲ διὰ
^ > , X , * LÀ L4 > ,
τοῦ ἀδυνάτου συλλογισμὸς δείκνυται μὲν ὅταν ἡ ἀντίφα-
2ο σις τεθῇ τοῦ συμπεράσματος καὶ προσληφθῇ ἄλλη πρότα-
σις, γίνεται δ᾽ ἐν ἅπασι τοῖς σχήμασιν: ὅμοιον γάρ ἐστι
τῇ ἀντιστροφῇ, πλὴν διαφέρει τοσοῦτον ὅτι ἀντιστρέφεται
μὲν γεγενημένου συλλογισμοῦ καὶ εἰλημμένων ἀμφοῖν τῶν
προτάσεων, ἀπάγεται δ᾽ εἰς ἀδύνατον οὐ προομολογηθέντος
^ 3 , # 3 A ^ μὰ σ 2 4
as τοῦ ἀντικειμένου πρότερον, ἀλλὰ φανεροῦ ὄντος ὅτι ἀληθές.
e > Ld e , L4 , > ^ ‘ € LENA ^
οἱ δ᾽ ὅροι ὁμοίως ἔχουσιν ἐν ἀμφοῖν, kai ἡ αὐτὴ λῆψις
> , > M ^ X L4 , , a
ἀμφοτέρων. olov εἰ τὸ A τῷ B παντὶ ὑπάρχει, μέσον δὲ
4 AJ € ^ A -^ ‘A τ hal x ^ € »
τὸ Γ, ἐὰν ὑποτεθῇ τὸ A 7) μὴ παντὶ ἢ μηδενὶ τῷ B ὑπάρ-
χειν, τῷ δὲ I παντί, ὅπερ ἦν ἀληθές, ἀνάγκη τὸ Γ' τῷ
^ M hal A ‘ € L4 ^ , * € σ
3o B ἢ μηδενὶ 7) μὴ παντὶ ὑπάρχειν. τοῦτο δ᾽ ἀδύνατον, ὥστε
^ A e f 3 b L4 4 > , € , 4
ψεῦδος τὸ ὑποτεθέν: ἀληθὲς dpa τὸ ἀντικείμενον. ὁμοίως δὲ
' », N ^ w 4 σ > > ^ ,
καὶ ἐπὶ τῶν ἄλλων σχημάτων: ὅσα γὰρ ἀντιστροφὴν δέχε-
ται, καὶ τὸν διὰ τοῦ ἀδυνάτου συλλογισμόν.
Τὰ μὲν οὖν ἄλλα προβλήματα πάντα δείκνυται διὰ
35 τοῦ ἀδυνάτου ἐν ἅπασι τοῖς σχήμασι, τὸ δὲ καθόλου κα-
τηγορικὸν ἐν μὲν τῷ μέσῳ καὶ τῷ τρίτῳ δείκνυται, ἐν δὲ
~ P4 , , € , ^ A ~ 4 *
τῷ πρώτῳ od δείκνυται. ὑποκείσθω yap τὸ A τῷ B μὴ παντὶ
- ὃ x € La * mu θ, ἄλλ , ¢
ἢ μηδενὶ ὑπάρχειν, καὶ προσειλήφθω ἢ πρότασις ὅπο-
- LJ ^ ^ L4 , ^ LÀ A x
τερωθενοῦν, eire τῷ A παντὶ ὑπάρχειν τὸ I etre τὸ B παντὶ
4o TO 4: οὕτω γὰρ ἂν εἴη τὸ πρῶτον σχῆμα. εἰ μὲν οὖν ὑπό-
κειται μὴ παντὶ ὑπάρχειν τὸ A τῷ B, οὐ γίνεται συλλο-
61> γισμὸς ὁποτερωθενοῦν τῆς προτάσεως λαμβανομένης, εἰ δὲ
, Ld * € B 4 05 λλι * X L4
μηδενί, ὅταν μὲν ἡ προσληφθῇ, συλλογισμὸς μὲν ἔσται
^ , , , * A , , M M
τοῦ ψεύδους, οὐ δείκνυται δὲ τὸ προκείμενον. εἰ yàp τὸ A
μηδενὶ τῷ B, τὸ δὲ. Β παντὶ τῷ 4, τὸ A οὐδενὶ τῷ 4.
ς τοῦτο δ᾽ ἔστω ἀδύνατον- ψεῦδος ἄρα τὸ μηδενὶ τῷ B τὸ Α
ὑπάρχειν. ἀλλ᾽ οὐκ εἰ τὸ μηδενὶ ψεῦδος, τὸ παντὶ ἀληθές.
ἐὰν δ᾽ ἡ I A προσληφθῇ, οὐ γίνεται συλλογισμός, οὐδ᾽
" L4 ^ A * ~ ^ (4 , σ M
ὅταν ὑποτεθῇ μὴ παντὶ τῷ Β τὸ A ὑπάρχειν. ὥστε φανερὸν
ὅτι τὸ παντὶ ὑπάρχειν οὐ δείκνυται ἐν τῷ πρώτῳ σχήματι
1o διὰ τοῦ ἀδυνάτου.
5. , + M * M M A M
to To δέ ye τινὶ καὶ τὸ μηδενὶ καὶ μὴ παντὶ
δείκνυται. ὑποκείσθω yap τὸ A μηδενὶ τῷ Β ὑπάρχειν, τὸ
423 yeyernpdvov+ τοῦ n 28 3i? om. 5 39 τῷ B παντὶ τὸ B
2 pe? om. C 5 ἔσται C 7 οὐδ᾽ codd.: an ὥσπερ οὐδ᾽ ?
II. 61717-6273
A , , ^ nn a ~ > ~~ > , A
δὲ Β εἰλήφθω παντὶ ἢ τινὶ τῷ I. οὐκοῦν ἀνάγκη τὸ A μη-
Ll , ^ » ,
Bevi ἣ μὴ παντὶ τῷ D ὑπάρχειν. τοῦτο δ᾽ ἀδύνατον---ἔστω
γὰρ ἀληθὲς καὶ φανερὸν ὅτι παντὶ ὑπάρχει τῷ I τὸ A—
ὥστ᾽ εἰ τοῦτο ψεῦδος, ἀνάγκη τὸ Α rwi τῷ B ὑπάρχειν. ἐὰν 15
δὲ πρὸς τῷ Α ληφθῇ ἡ ἑτέρα πρότασις, οὐκ ἔσται συλλο-
γισμός. οὐδ᾽ ὅταν τὸ ἐναντίον τῷ συμπεράσματι ὑποτεθῇ,
οἷον τὸ τινὶ μὴ ὑπάρχειν. φανερὸν οὖν ὅτι τὸ ἀντικείμενον ὗπο-
θετέον. 19
Πάλιν ὑποκείσθω τὸ A τινὶ τῷ B ὑπάρχειν, εἰλή- 19
φθω δὲ τὸ I παντὶ τῷ A. ἀνάγκη οὖν τὸ Γ twi τῷ B :o
€ L4 ^ , 3 , e ^ 4 € [4
ὑπάρχειν. τοῦτο δ᾽ ἔστω ἀδύνατον, wore ψεῦδος τὸ ὑποτεθέν.
LI ? L4 , i M M [4 7 t , ^ * ‘J
εἰ δ᾽ οὕτως, ἀληθὲς τὸ μηδενὶ ὑπάρχειν. ὁμοίως δὲ kai ef
στερητικὸν ἐλήφθη τὸ I' A. εἰ δ᾽ ἡ πρὸς τῷ B εἴληπται πρό-
τασις, οὐκ ἔσται συλλογισμός. ἐὰν δὲ τὸ ἐναντίον ὑποτεθῇ,
M b L4 A * > , > , ^ M
συλλογισμὸς μὲν ἔσται Kai τὸ ἀδύνατον, οὐ δείκνυται δὲ τὸ 25
4, L4 ra kl * ~ * e , :
προτεθέν. ὑποκείσθω yap παντὶ τῷ B τὸ A ὑπάρχειν, kai
τὸ Γ τῷ A εἰλήφθω παντί. οὐκοῦν ἀνάγκη τὸ I παντὶ τῷ
Β ὑπάρχειν. τοῦτο δ᾽ ἀδύνατον, ὥστε ψεῦδος τὸ παντὶ τῷ Β
M L4 # > 3 L4 > ^ » * ,
TO A ὑπάρχειν. ἀλλ᾽ οὔπω ye ἀναγκαῖον, εἰ μὴ παντί,
4 e 4 ε , hi * > 3 ^ , ©
μηδενὶ ὑπάρχειν. ὁμοίως δὲ καὶ εἰ πρὸς τῷ B ληφθείη ἡ 30
ἑτέρα πρότασις- συλλογισμὸς μὲν γὰρ ἔσται καὶ τὸ ἀδύ-
νατον, οὐκ ἀναιρεῖται δ᾽ ἡ ὑπόθεσις. ὥστε τὸ ἀντικείμενον
ὑποθετέον. 33
Πρὸς δὲ τὸ μὴ παντὶ δεῖξαι ὑπάρχον τῷ DB τὸ 33
A, ὑποθετέον παντὶ ὑπάρχειν: εἰ γὰρ τὸ A παντὶ τῷ B
καὶ τὸ l' παντὶ τῷ A, τὸ Γ παντὶ τῷ DB, ὥστ᾽ εἰ τοῦτο 35
ἀδύνατον, ψεῦδος τὸ ὑποτεθέν. ὁμοίως δὲ καὶ εἰ πρὸς τῷ Β
ἐλήφθη ἡ ἑτέρα πρότασις. καὶ εἰ στερητικὸν ἦν τὸ I' A, wo-
αὐτως- καὶ γὰρ οὕτω γίνεται συλλογισμός. ἐὰν δὲ πρὸς τῷ
B ἢ τὸ στερητικόν, οὐδὲν δείκνυται. ἐὰν δὲ μὴ παντὶ ἀλλὰ
4 € 4 tc ^ > , Ld » M , > "
τινὶ ὑπάρχειν ὑποτεθῇ, οὐ δείκνυται ὅτι οὐ παντὶ ἀλλ᾽ ὅτι 4o
οὐδενί. εἰ γὰρ τὸ A τινὶ τῷ B, τὸ δὲ I παντὶ τῷ A, τινὶ
τῷ Β τὸ Γ ὑπάρξει. εἰ οὖν τοῦτ᾽ ἀδύνατον, ψεῦδος τὸ τινὶ 625
ὑπάρχειν τῷ Β τὸ A, ὥστ᾽ ἀληθὲς τὸ μηδενί. τούτου δὲ
δειχθέντος προσαναιρεῖται τὸ ἀληθές: τὸ γὰρ Α τῷ Β τινὶ
br2 rüv yn 15 rà» Bn 1676 A 20 ràv B n 23 ya+ ἡ yàp
μείζων ἔσται οὕτως C: +% yàp μείζων ἔσται οὕτως (- ἡ δὲ ἐλάττων n?)
μερικὴ ἐν πρώτῳ σχήματι n 26 ὑπάρχειν 4ηΓ: om. BC 27 τῷ
nP:om. ABC 30 κἂν et Cn Anpeg C 34 παντὶ") τὸ παντὶ ἘΠ
35 0... Bom. πὶ 37 ay C 39 d om. C οὐδὲ n
ANAAYTIKQN IIPOTEPON B
' € ^ t LI $, L4 ^ » > t X M e Ld
μὲν ὑπῆρχε, τινὲ δ᾽ ody ὑπῆρχεν. ἔτι οὐδὲν παρὰ τὴν ὑπόθε-
, 4 3 L4 Lo M bal LÀ » >
sow συμβαίνει [τὸ] ἀδύνατον: ψεῦδος yap dv εἴη, εἴπερ ἐξ
ἀληθῶν μὴ ἔστι ψεῦδος συλλογίσασθαι: νῦν δ᾽ ἐστὶν ἀληθές"
€ Fd 4 * ‘ ~ L4 > 3 € , M L4 a
ὑπάρχει yàp TO A τινὶ τῷ B. ὥστ᾽ οὐχ ὑποθετέον τινὶ ὑπάρ-
» Ἂς , L4 , & a > M M € ie ~
yew, ἀλλὰ παντί. ὁμοίως δὲ καὶ ef Twi μὴ ὑπάρχον τῷ B
τὸ A δεικνύοιμεν: εἰ γὰρ ταὐτὸ τὸ τινὲ μὴ ὑπάρχειν καὶ
4 ^ € , € *, 1 > ^. > ,
το μὴ παντὶ ὑπάρχειν, ἡ αὐτὴ ἀμφοῖν ἀπόδειξις.
A T Ld > ' > , > M 4 5 ,ὔ
Φανερὸν οὖν ὅτι οὐ τὸ ἐναντίον ἀλλὰ τὸ ἀντικείμενον
ὑποθετέον ἐν ἅπασι τοῖς συλλογισμοῖς. οὕτω γὰρ τό τε ἀναγ-
καῖον ἔσται καὶ τὸ ἀξίωμα ἔνδοξον. εἰ γὰρ κατὰ παντὸς ἡ
΄ὔ΄ nn € > , L4 Ld Ls L4 5 ,
φάσις ἢ ἡ ἀπόφασις, δειχθέντος ὅτι οὐχ ἡ ἀπόφασις,
1s ἀνάγκη τὴν κατάφασιν ἀληθεύεσθαι. πάλιν εἰ μὴ τίθησιν
ἀληθεύεσθαι τὴν κατάφασιν, ἔνδοξον τὸ ἀξιῶσαι τὴν ἀπό-
φασιν. τὸ δ᾽ ἐναντίον οὐδετέρως ἁρμόττει ἀξιοῦν: οὔτε γὰρ
5 ^ 3 x 4 ^ A] M » , wy »
ἀναγκαῖον, εἰ TO μηδενὶ ψεῦδος, τὸ παντὶ ἀληθές, οὔτ᾽ &v-
δοξον ὡς εἰ θάτερον ψεῦδος, ὅτι θάτερον ἀληθές.
p 7)
Φ ^ T L4 > ^ td , ^ M LÀ
20 avepóv οὖν ὅτι ἐν TH πρώτῳ σχήματι τὰ μὲν ἄλλα
, , L4 ^ ^ > ,ὔ M M
προβλήματα πάντα δείκνυται διὰ τοῦ ἀδυνάτου, τὸ δὲ Ka-
θόλου καταφατικὸν οὐ δείκνυται. ἐν δὲ τῷ μέσῳ καὶ τῷ
ἐσχάτῳ καὶ τοῦτο δείκνυται. κείσθω γὰρ τὸ Α μὴ παντὶ
τῷ B ὑπάρχειν, εἰλήφθω δὲ τῷ I παντὶ ὑπάρχειν τὸ A.
Ὡςοὐκοῦν εἰ τῷ μὲν B μὴ παντί, τῷ δὲ D' παντί, οὐ παντὶ
^ ^ ~ > * , » ^ 1 Ld M
TQ DB τὸ I. τοῦτο δ᾽ ἀδύνατον: ἔστω yàp φανερὸν ὅτι παντὶ
TQ DB ὑπάρχει τὸ Γ΄, ὥστε ψεῦδος τὸ ὑποκείμενον. ἀληθὲς
ἄρα τὸ παντὶ ὑπάρχειν. ἐὰν δὲ τὸ ἐναντίον ὑποτεθῇ, συλ-
λογισμὸς μὲν ἔσται καὶ τὸ ἀδύνατον, οὐ μὴν δείκνυται τὸ
go προτεθέν. εἰ yàp τὸ A μηδενὶ τῷ B, τῷ δὲ I' παντί, οὐδενὶ
^ A ^ > 3 L4 Ld L3 4 4 [4 ,
τῷ Bro I. τοῦτο δ᾽ ἀδύνατον, ὥστε ψεῦδος τὸ μηδενὶ ὑπάρ-
a , ^ ^
yew. ἀλλ᾽ οὐκ εἰ τοῦτο ψεῦδος, τὸ παντὶ ἀληθές. ὅτι δὲ
τινὶ τῷ Β ὑπάρχει τὸ A, ὑποκείσθω τὸ A μηδενὶ τῷ B
€ 4 ~ M M € , > Á, T ^
ὑπάρχειν, τῷ δὲ IX παντὶ ὑπαρχέτω. ἀνάγκη οὖν τὸ I μη-
‘ ^ B "o , , ^ > , > , ^ A ' ^
ἃς 9ev( τῷ B. ὥστ᾽ εἰ τοῦτ᾽ ἀδύνατον, ἀνάγκη τὸ A τινὶ τῷ B
AJ 3 ^
ὑπάρχειν. ἐὰν δ᾽ ὑποτεθῇ Twi μὴ ὑπάρχειν, ταὐτ᾽ ἔσται
ἅπερ ἐπὶ τοῦ πρώτου σχήματος. πάλιν ὑποκείσθω τὸ A τινὶ
6244 οὐδὲν scripsi, fort. habet P: οὐδὲ n: οὐ ABC: δὲ οὐ I 576
seclusi, om. ut vid. P ψευδὴς B?n yàp om. AMBICT ἂν om. Bt
Ἱ )rápxevrót τῶνῃ geilin 12 ren: om. ABC 137] AB
14 5 om. AB 20 τῷ om. C 21 δείκνυνται C 27 ὑπάρχειν ni
32 óre Aldina 34 τῷ] τὸ Al 36 rate’ coni. Jenkinson: ταῦτ᾽
codd.: ταὐτὸν Γ
11. 6244-14. 62530
τῷ DB ina Ὁ δὲ I' μηδενὶ ὑ : lvd Ü
f pxew, τῷ δὲ μηδενὶ ὑπαρχέτω. ἀνάγκη οὖν
A 4 ~ x e , 3 * ‘ [4 ^ σ
τὰ Γ τινὶ τῷ Β μὴ ὑπάρχειν. ἀλλὰ παντὶ ὑπῆρχεν, ὥστε
ψεῦδο * [4 θέ 5 y» > » ^ B ‘ A t , L4
€ τὸ ὑποτεθέν: οὐδενὶ dpa τῷ τὸ ὑπάρξει. ὅτι 40
δ᾽ οὐ παντὶ τὸ Α τῷ Β, ὑποκείσθω παντὶ ὑπάρχειν, τῷ
δὲ I μηδενί. ἀνάγκη οὖν τὸ D μηδενὶ τῷ Β ὑπάρχειν. τοῦτο 62>
2
ὃ ἀδύνατον, ὥστ᾽ ἀληθὲς τὸ μὴ παντὶ ὑπάρχει. φανερὸν
οὖν ὅτι πάντες οἱ συλλογισμοὶ γίνονται διὰ τοῦ μέσου σχή-
ματος.
12 Ὁμοίως δὲ καὶ διὰ τοῦ ἐσχάτου. κείσθω γὰρ τὸ As
' ^ B ^ [4 , 4 δὲ I /. | L4 A * ^
τινὶ TQ D μὴ ὑπάρχειν, τὸ δὲ IX παντί: τὸ ἄρα A τινὶ τῷ
I » [ τ , 5. ^-^ iS 2 08 M ' *
οὐχ ὑπάρχει. εἰ ddv τοῦτ᾽ ἀδύνατον, ψεῦδος TO τινὶ μὴ
L4 , LA 3 > x M , ?* > t ^ i
ὑπάρχειν, ὥστ᾽ ἀληθὲς τὸ παντί. ἐὰν δ᾽ ὑποτεθῇ pndevi
e , ^ * L4 M M > 7 > £
ὑπάρχειν, συλλογισμὸς μὲν ἔσται kai τὸ ἀδύνατον, οὐ δεί-
κνυται δὲ τὸ προτεθέν: ἐὰν γὰρ τὸ ἐναντίον ὑποτεθῇ, ταὐτ᾽ τὸ
ἔσται ἅπερ ἐπὶ τῶν πρότερον. ἀλλὰ πρὸς τὸ τινὶ ὑπάρχειν
4 , € € , > x M * ^ ‘ Pj
αὕτη ληπτέα ἡ ὑπόθεσις. εἰ yàp τὸ A μηδενὶ τῷ B, τὸ δὲ
Γ τινὶ τῷ B, τὸ A οὐ παντὶ τῷ [Γ. εἰ οὖν τοῦτο ψεῦδος,
ἀληθὲς τὸ A τινὶ τῷ B ὑπάρχειν. ὅτι δ᾽ οὐδενὶ τῷ B ὑπάρ-
χει τὸ A, ὑποκείσθω τινὲ ὑπάρχειν, εἰλήφθω δὲ καὶ τὸ Dis
* ^ e JF , ~ > , ^ M M x /
παντὶ TQ B ὑπάρχον. οὐκοῦν ἀνάγκη τῷ I τινὲ τὸ A ὑπάρ-
3 3 35 X L4 ^ L4 08. * * ^ B € ,
xew. ἀλλ᾽ οὐδενὶ ὑπῆρχεν, ὥστε ψεῦδος τὸ τινὶ τῷ B ὑπάρ-
Y LA 3 L4 ^ XY ^ € , M 2
xev τὸ A. ἐὰν δ᾽ ὑποτεθῇ παντὶ τῷ B ὑπάρχειν τὸ A, οὐ
δείκνυται τὸ προτεθέν, ἀλλὰ πρὸς τὸ μὴ παντὶ ὑπάρχειν
LÀ , € * , ? M * i] ^ x. A]
αὕτη ληπτέα ἡ ὑπόθεσις. εἰ yàp τὸ A παντὶ τῷ D καὶ τὸ 20
Γ παντὶ τῷ B, τὸ A ὑπάρχει τινὶ τῷ Γ΄. τοῦτο δὲ οὐκ ἦν,
σ ^ A ' e , > > - 3 M X M
ὥστε ψεῦδος τὸ παντὶ ὑπάρχειν. εἰ δ᾽ οὕτως, ἀληθὲς τὸ μὴ
παντί. ἐὰν δ᾽ ὑποτεθῇ τινὶ ὑπάρχειν, ταὐτ᾽ ἔσται ἃ καὶ
ἐπὶ τῶν προειρημένων.
Φανερὸν οὖν ὅτι ἐν ἅπασι τοῖς διὰ τοῦ ἀδυνάτου συλ- 25
λογισμοῖς τὸ ἀντικείμενον ὑποθετέον. δῆλον δὲ καὶ ὅτι ἐν τῷ
μέσῳ σχήματι δείκνυταί πως τὸ καταφατικὸν καὶ ἐν τῷ
ἐσχάτῳ τὸ καθόλου.
14 Διαφέρει 8 ἡ εἰς τὸ ἀδύνατον ἀπόδειξις τῆς δεικτικῆς
^ , a ^ > ^ > , > * ΤΑ
τῷ τιθέναι ὃ βούλεται ἀναιρεῖν ἀπάγουσα εἰς ὁμολογούμε- 30
848 τῷ] τὸ Al: τῶν ΒΗΓ 39 τῶν Bn 40 ὅτι 4ΒΗΓ: ὅτε Aldina:
εἰς bio τὸϊ-Ἐ παντὶ C ταὐτ᾽ ἩΓ: ταῦτ᾽ ABC 12 τῶνβ Β
τῷ Bl I3 τῷ B A? BCTP*: τὸ B A: om. n 14 ὅτε Aldina
16 τῷ y τινὶ τὸ A*CnP : τὸ y τινὶ τῷ ABn? 17 τὸ om. AB 21
παντὶ ÁBCnDP*: τινὶ B*C? τὸ Á] ro y C: ó y n τῷ Γ]τὸ αΟ:
τῷ απ 23 ταῦτ᾽ ABC 29 δ᾽ ἡ] δὴ π
ANAAYTIKQN TIPOTEPQN B
vov ψεῦδος: ἡ δὲ δεικτικὴ ἄρχεται ἐξ ὁμολογουμένων θέσε-
cv. λαμβάνουσι μὲν οὖν ἀμφότεραι δύο προτάσεις
ὁμολογουμένας: ἀλλ᾽ ἡ μὲν ἐξ ὧν ὃ συλλογισμός, ἡ δὲ
μίαν μὲν τούτων, μίαν δὲ τὴν ἀντίφασιν τοῦ συμπεράσμα-
3g Tos. καὶ ἔνθα μὲν οὐκ ἀνάγκη γνώριμον εἶναι τὸ συμπέ-
» * os 7 t LÀ hal w LÀ ^
pacpa, οὐδὲ mpoUmoAaufdvew ὡς ἔστιν ἢ ov: ἔνθα δὲ
ἀνάγκη ὡς οὐκ ἔστιν. διαφέρει δ᾽ οὐδὲν φάσιν ἢ ἀπόφασιν
ῖ ‘ , , > € , v ‘ 3 ^
38 εἶναι τὸ συμπέρασμα, ἀλλ᾽ ὁμοίως ἔχει περὶ ἀμφοῖν.
38 “Ἅπαν
δὲ , ~ L4 ‘ ^ ^ > , ~ θή
€ τὸ δεικτικῶς περαινόμενον καὶ διὰ τοῦ ἀδυνάτοῦ δειχθήσε-
4o ται, καὶ τὸ διὰ τοῦ ἀδυνάτου δεικτικῶς διὰ τῶν αὐτῶν ὅρων
[οὐκ ἐν τοῖς αὐτοῖς δὲ σχήμασιν]. ὅταν μὲν γὰρ ὁ συλλο-
63. γισμὸς ἐν τῷ πρώτῳ σχήματι γένηται, τὸ ἀληθὲς ἔσται ἐν
Y 2 Y
~ , hel ^ > , * * ^ > ~ M
τῷ μέσῳ ἢ TQ ἐσχάτῳ, τὸ μὲν στερητικὸν ἐν TH μέσῳ, τὸ
δὲ κατηγορικὸν ἐν τῷ ἐσχάτῳ. ὅταν δ᾽ ἐν τῷ μέσῳ ὁ
iy ‘ - 4 > ~ , 2. % Z ~
συλλογισμός, τὸ ἀληθὲς ἐν τῷ πρώτῳ ἐπὶ πάντων τῶν
» 4 » > ^ > ΄ € , |
ςπροβλημάτων. ὅταν δ᾽ ἐν τῷ ἐσχάτῳ ὁ συλλογισμός, τὸ
ἀληθὲς ἐν τῷ πρώτῳ καὶ τῷ μέσῳ, τὰ μὲν καταφατικὰ
ἐν τῷ πρώτῳ, τὰ δὲ στερητικὰ ἐν τῷ μέσῳ. ἔστω γὰρ δεδει-
, 4 * hl A M - * ~ , ,
γμένον τὸ A μηδενὶ ἢ μὴ παντὶ τῷ B διὰ τοῦ πρώτου σχή-
, ~ € * t 56 7 * ^ B [4 , M A
ματος. οὐκοῦν ἡ μὲν ὑπόθεσις ἦν τινὶ τῷ B ὑπάρχειν τὸ A,
1070 δὲ Γ ἐλαμβάνετο τῷ μὲν A παντὶ ὑπάρχειν, τῷ δὲ B
> , L4 A » ἢ € M M * > ra
οὐδενί: οὕτω yap ἐγίνετο 6 συλλογισμὸς Kai τὸ ἀδύνατον.
τοῦτο δὲ τὸ μέσον σχῆμα, εἰ τὸ Γ τῷ μὲν Α παντὶ τῷ δὲ
* [4 , * » , , -΄ 9 M ^
B μηδενὶ ὑπάρχει. καὶ φανερὸν ἐκ τούτων ὅτι οὐδενὶ τῷ B
€ , a ig L * Li > A M L4 [4 ,
ὑπάρχει τὸ A. ὁμοίως δὲ καὶ ef μὴ παντὶ δέδεικται ὑπάρ-
t * ^ [4 , , , X [4 , M] *
15 Xov. ἡ μὲν yàp ὑπόθεσίς ἐστε παντὶ ὑπάρχειν, τὸ δὲ Γ
H , ~ Ν, td ~ M ΕΣ , M >
ἐλαμβάνετο τῷ μὲν A παντί, τῷ δὲ B οὐ παντί. καὶ εἰ
A Li ^ t , 4 * L4 ,
στερητικὸν λαμβάνοιτο τὸ Γ A, ὡσαύτως" kai yap οὕτω yi-
νεται τὸ μέσον σχῆμα. πάλιν δεδείχθω τινὶ ὑπάρχον τῷ
M] L4 4 T Li , M [4 , ^ ^
B τὸ A. ἡ μὲν οὖν ὑπόθεσις μηδενὶ ὑπάρχειν, τὸ δὲ B
, , ‘ ~ € 4 Li M a M hel M
go ἐλαμβάνετο παντὶ τῷ Γ᾽ ὑπάρχειν καὶ τὸ A 7j παντὶ ἢ τινὶ
^ ^ *
TQ I: οὕτω yap ἔσται τὸ ἀδύνατον. τοῦτο δὲ τὸ ἔσχατον
^ , ‘ * * ' ^ M M »
σχῆμα, εἰ τὸ A xai τὸ B παντὶ τῷ I. καὶ φανερὸν ἐκ
P a o >? z ^ * ^ [4 te € , 3
τούτων ὅτι ἀνάγκη τὸ A τινὶ τῷ B ὑπάρχειν. ὁμοίως δὲ
καὶ εἰ τινὶ τῷ Γ ληφθείη ὑπάρχον τὸ Β ἢ τὸ A.
b31 θέσεων) θέσεων ἀληθῶν A, fort. P : καὶ ἀληθῶν θέσεων I 37-8 ἀπό-
φασιν... τὸ fecit A 38 παρὰ n* 41 οὐκ... σχήμασιν Aldina:
om. codd. 6341 γίνεται n 3 δ] ἦ ὁ AT 4 ἀληθὲς -Ῥ ἔσται n
13 ὑπάρχῃ ἢ 14 ὑπάρχον-τὸα A: +roare pl 241] τὸ Aom.n
14. 62>31-63>19
Πάλιν ἐν τῷ μέσῳ σχήματι δεδείχθω τὸ A παντὶ τῷ
Β ὑπάρχον. οὐκοῦν ἡ μὲν ὑπόθεσις ἦν μὴ παντὶ τῷ Β τὸ
A ὑπάρχειν, εἴληπται δὲ τὸ A παντὶ τῷ Γ καὶ τὸ Γ᾽ παντὶ
τῷ Β' οὕτω γὰρ ἔσται τὸ ἀδύνατον. τοῦτο δὲ τὸ πρῶτον
~ ‘ ‘ ~ * * M ^ [4 ,
σχῆμα, τὸ A παντὶ τῷ Γ καὶ τὸ Γ᾽ παντὶ τῷ B. ὁμοίως
δὲ καὶ εἰ τινὶ δέδεικται ὑπάρχον: ἡ μὲν γὰρ ὑπόθεσις ἦν
M ^ ‘ [4 , ^ ^ M ~
μηδενὶ τῷ B τὸ A ὑπάρχειν, εἴληπται δὲ τὸ A παντὶ τῷ
Γ καὶ τὸ Γ rwi τῷ B. «i δὲ στερητικὸς ὁ συλλογισμός, ἡ
μὲν ὑπόθεσις τὸ Α τινὶ τῷ Β ὑπάρχειν, εἴληπται δὲ τὸ Α
μηδενὶ τῷ Γ καὶ τὸ Γ παντὶ τῷ B, wore γίνεται τὸ πρῶ-
~ ' , M , Ld , » J a
Tov σχῆμα. καὶ εἰ μὴ καθόλου ὁ συλλογισμός, ἀλλὰ τὸ
A τινὶ τῷ B δέδεικται μὴ ὑπάρχειν, ὡσαύτως. ὑπόθεσις
b ^4 M ~ ‘ -* , ww M M
μὲν yàp παντὶ τῷ B τὸ A ὑπάρχειν, εἴληπται δὲ τὸ A
^ ~ * M ‘ ^ L4 a ^ -
μηδενὶ τῷ D koi τὸ I τινὲ τῷ Β' οὕτω yap τὸ πρῶτον
σχῆμα.
2 ~ a ~
Πάλιν ἐν τῷ τρίτῳ σχήματι δεδείχθω τὸ A παντὶ τῷ
Β ὑπάρχειν. οὐκοῦν ἡ μὲν ὑπόθεσις ἦν μὴ παντὶ τῷ Β τὸ
A ὑπάρχειν, εἴληπται δὲ τὸ I' παντὶ τῷ B καὶ τὸ A παντὶ
τῷ I οὕτω γὰρ ἔσται τὸ ἀδύνατον. τοῦτο δὲ τὸ πρῶτον
~ L4 , 4 * 3 > % a L4 > d t *
σχῆμα. ὡσαύτως δὲ καὶ εἰ ἐπὶ τινὸς ἡ ἀπόδειξις" ἡ μὲν
A [4 , 4 ~ d L4 , μὰ 4 A
yap ὑπόθεσις μηδενὶ τῷ Β τὸ A ὑπάρχειν, εἴληπται δὲ τὸ
I τινὶ τῷ B καὶ τὸ A παντὶ τῷ Γ. εἰ δὲ στερητικὸς 6 συλ-
2 2 7)
^ LÀ
λογισμός, ὑπόθεσις μὲν τὸ A τινὶ τῷ B ὑπάρχειν, εἴλη-
ara, δὲ τὸ Γ τῷ μὲν A μηδενί, τῷ δὲ B παντί: τοῦτο δὲ
a 4, ~ [4 ,ὔ * ^ > * , e£ » la
τὸ μέσον σχῆμα. ὁμοίως δὲ καὶ ef μὴ καθόλου ἡ ἀπόδει-
£s. ὑπόθεσις μὲν γὰρ ἔσται παντὶ τῷ B τὸ A ὑπάρχειν,
εἴληπται δὲ τὸ I τῷ μὲν A μηδενί, τῷ δὲ B τινί: τοῦτο δὲ
τὸ μέσον σχῆμα.
Φανερὸν οὖν ὅτι διὰ τῶν αὐτῶν ὅρων καὶ δεικτικῶς ἔστι
δεικνύναι τῶν προβλημάτων ἕκαστον [καὶ διὰ τοῦ ἀδυνάτου].
ὁμοίως δ᾽ ἔσται καὶ δεικτικῶν ὄντων τῶν συλλογισμῶν εἰς
ἀδύνατον ἀπάγειν ἐν τοῖς εἰλημμένοις ὅροις, ὅταν ἡ ἀντικει-
μένη πρότασις τῷ συμπεράσματι ληφθῇ. γίνονται γὰρ οἱ
αὐτοὶ συλλογισμοὶ τοῖς διὰ τῆς ἀντιστροφῆς, ὥστ᾽ εὐθὺς
ἔχομεν καὶ τὰ σχήματα δι᾽ dv ἕκαστον ἔσται. δῆλον οὖν ὅτι
^ , ig > > , A ,
πᾶν πρόβλημα δείκνυται κατ᾽ ἀμφοτέρους τοὺς τρόπους,
420 τὸϊ] εἰ ron 23 ὑπάρχειν ΗΓ: om. ABC 48 010... τῷ] τῷ
... τὸ Al γὰρ] δὲ π 41 ὑπάρχον n j$vom.nI τὸ β τῷ 4!
bg δὴ B! I3 xai . . . ἀδυνάτον BnI': om. AC
25
40
63>
ANAAYTIKQN TIPOTEPQN B
, ~ > Ψ M ^ * , 3, ,
20 διά Te τοῦ ἀδυνάτου καὶ δεικτικῶς, Kal οὐκ ἐνδέχεται χω-
ρίζεσθαι τὸν ἕτερον.
> , M ἣν w , > , ὔ
Ev ποίῳ δὲ σχήματι ἔστιν ἐξ ἀντικειμένων προτάσεων
, ^ 5 a , L4 7o? la ,
συλλογίσασθαι καὶ ἐν ποίῳ οὐκ ἔστιν, ὧδ᾽ ἔσται φανερόν. λέγω
δ᾽ ἀντικειμένας εἶναι προτάσεις κατὰ μὲν τὴν λέξιν τέττα-
25 pas, οἷον τὸ παντὶ τῷ οὐδενί, καὶ τὸ παντὶ τῷ οὐ παντί, καὶ
M ^4 ~ , , M ‘ A ^ ᾿ , » > Φ' b
τὸ τινὶ τῷ οὐδενί, kai τὸ τινὶ τῷ οὐ Twi, Kar’ ἀλήθειαν δὲ
τρεῖς: τὸ γὰρ τινὲ τῷ οὐ τινὶ κατὰ τὴν λέξιν ἀντίκειται μό-
νον. τούτων δ᾽ ἐναντίας μὲν τὰς καθόλου, τὸ παντὶ τῷ μη-
* ^ ^
devi ὑπάρχειν, olov τὸ πᾶσαν ἐπιστήμην εἶναι σπουδαίαν τῷ
, 5 , ^ > » > ,
3o μηδεμίαν εἶναι σπουδαίαν, τὰς δ᾽ ἄλλας ἀντικειμένας.
Ἔν μὲν οὖν τῷ πρώτῳ σχήματι οὐκ ἔστιν ἐξ ἀντικει-
M
μένων προτάσεων συλλογισμός, οὔτε καταφατικὸς οὔτε ἀπο-
, x M Ld > , ^
φατικός, καταφατικὸς μὲν ὅτι ἀμφοτέρας δεῖ καταφατι-
κἂς εἶναι τὰς προτάσεις, αἱ δ᾽ ἀντικείμεναι φάσις καὶ
3 , x A 4 t M > , M > M
35 ἀπόφασις, στερητικὸς δὲ ὅτι αἱ μὲν ἀντικείμεναι TO αὐτὸ
τοῦ αὐτοῦ κατηγοροῦσι καὶ ἀπαρνοῦνται, τὸ δ᾽ ἐν τῷ πρώτῳ
μέσον οὐ λέγεται κατ᾽ ἀμφοῖν, ἀλλ᾽ ἐκείνου μὲν ἄλλο ἀπαρ-
^ 3 4 A Ld ^ T > 3 > ,
νεῖται, αὐτὸ δὲ ἄλλου κατηγορεῖται: αὗται δ᾽ οὐκ ἀντί-
κεινται.
> A ^ , , M , ^ > cA *
42 Ev δὲ τῷ μέσῳ σχήματι καὶ ex τῶν ἀντικειμένων Kal
ἐκ τῶν ἐναντίων ἐνδέχεται γίγνεσθαι συλλογισμόν. ἔστω γὰρ
64" ἀγαθὸν μὲν ἐφ᾽ οὗ A, ἐπιστήμη δὲ ἐφ᾽ οὗ B καὶ I. εἰ δὴ
^ * ^
πᾶσαν ἐπιστήμην σπουδαίαν ἔλαβε καὶ μηδεμίαν, τὸ A τῷ
M e , * - ? , L4 i ^ , ,
B παντὶ ὑπάρχει kai τῷ Γ᾽ οὐδενί, ὥστε τὸ B τῷ I' οὐδενί:
οὐδεμία ἄρα ἐπιστήμη ἐπιστήμη ἐστίν. ὁμοίως δὲ καὶ εἰ πᾶσαν
ς λαβὼν σπουδαίαν τὴν ἰατρικὴν μὴ σπουδαίαν ἔλαβε: τῷ
x » 4 t A ^ δὲ y , L4 L4 M > ,
μὲν yap B παντὶ τὸ A, τῷ δὲ I οὐδενί, ὥστε ἡ τὶς ἐπιστήμη
*, » , , A > ~ M I M d A ^ δὲ Β
οὐκ ἔσται ἐπιστήμη. καὶ εἰ τῷ μὲν I' παντὶ τὸ A, τῷ δὲ
, » b 4 b , 4 * δὲ I ? , M] δὲ
μηδενί, ἔστι δὲ τὸ μὲν B. ἐπιστήμη, τὸ δὲ I ἰατρική, τὸ δὲ
t , > , A > ; 4 e , * L4
4A ὑπόληψις: οὐδεμίαν yap ἐπιστήμην ὑπόληψιν λαβὼν et-
M ^ ,
1oAnde τινὰ εἶναι ὑπόληψιν. διαφέρει δὲ τοῦ πάλαι
^ ^ > Fe ^ ^ ^ ^
τῷ ἐπὶ τῶν ὅρων ἀντιστρέφεσθαι: πρότερον μὲν yàp πρὸς τῷ
Β ~ δὲ M ^ I 4 φ , 5 bal ἦ δὲ ‘ ES
, viv δὲ πρὸς τῷ Γ᾽ τὸ καταφατικόν. καὶ av 7 δὲ μὴ Ka
^ H M
θόλου ἡ ἑτέρα πρότασις, ὡσαύτως- ἀεὶ yàp TO μέσον ἐστὶν
b22-3 συλλογίσασθαι προτάσεων C 25 εἴ 26 τὸ] τῷ quater B 28
μὲν-Ἐ λέγομεν A τὸ] τῷ Β οὐδενὶ 9 30 μηδεμίαν 4- ἐπιστήμην n
34 φάσεις καὶ ἀποφάσεις A 38 αὐτὸ] τὸ αὐτὸ Β 6481 xai om. C
6 τὸ A] τω (sic) A 10 τινὰ -- ἐπιστήμην ABC — nói 4-1) γὰρ ἰατρικὴ
τὶς ἐπιστήμη ἐστίν, ἢ τις ἐλήφθη εἶναι ὑπόληψις n 12 δὲξ om. C
15
14. 6320-15. 6458
^ > A , 4 > ~ , M , b
6 ἀπὸ θατέρου μὲν ἀποφατικῶς λέγεται, κατὰ θατέρου δὲ
καταφατικῶς. ὥστ’ ἐνδέχεται τἀντικείμενα περαίνεσθαι,
^ , a. aoe , 5 > 28 - LÀ ‘ € ^
πλὴν οὐκ ἀεὶ οὐδὲ πάντως, ἀλλ᾽ ἐὰν οὕτως ἔχῃ τὰ ὑπὸ
4 , « > a ΕΣ 4 - L4 k] , * >
τὸ μέσον ὥστ᾽ ἢ ταὐτὰ εἶναι ἢ ὅλον πρὸς μέρος. ἄλλως ὃ
ἀδύνατον: οὐ γὰρ ἔσονται οὐδαμῶς ai προτάσεις οὔτ᾽ ἐναντίαι
οὔτ᾽ ἀντικείμεναι.
°K; δὲ ~ , L4 ‘ A ÀA
v δὲ τῷ τρίτῳ σχήματι καταφατικὸς μὲν συλλο-
γισμὸς οὐδέποτ᾽ ἔσται ἐξ ἀντικειμένων προτάσεων διὰ τὴν εἰ-
, ^
ρημένην αἰτίαν καὶ ἐπὶ τοῦ πρώτου σχήματος, ἀποφατικὸς
δ᾽ ἔσται, καὶ καθόλου καὶ μὴ καθόλου τῶν ὅρων ὄντων. ἔστω
γὰρ ἐπιστήμη ἐφ᾽ οὗ τὸ B xai I, ἰατρικὴ δ᾽ ἐφ᾽ od A. εἰ
οὖν λάβοι πᾶσαν ἰατρικὴν ἐπιστήμην καὶ μηδεμίαν ἰατρικὴν
ἐπιστήμην, τὸ B παντὶ τῷ A εἴληφε καὶ τὸ I οὐδενί, ὥστ᾽
ἔσται τις ἐπιστήμη οὐκ ἐπιστήμη. ὁμοίως δὲ καὶ ἂν μὴ καθό-
^ - , ? 4 , , ? i ,
λου ληφθῇ ἡ B A πρότασις: εἰ ydp ἐστί τις ἰατρικὴ ἐπι-
στήμη καὶ πάλιν μηδεμία ἰατρικὴ ἐπιστήμη, συμβαίνει ἐπι-
στήμην τινὰ μὴ εἶναι ἐπιστήμην. εἰσὶ δὲ καθόλου μὲν τῶν
ὅρων λαμβανομένων ἐναντίαι αἱ προτάσεις, ἐὰν δ᾽ ἐν μέρει
ἅτερος, ἀντικείμεναι.
a * E Ld H , * 4 ^ , ,
Δεῖ δὲ κατανοεῖν ὅτι ἐνδέχεται μὲν οὕτω τὰ αντικεί-
μενα λαμβάνειν ὥσπερ εἴπομεν πᾶσαν ἐπιστήμην σπου-
, 4 , ,ὔ -* A * ,
δαίαν εἶναι καὶ πάλιν μηδεμίαν, ἢ τινὰ μὴ σπουδαίαν"
ὅπερ οὐκ εἴωθε λανθάνειν. ἔστι δὲ δι’ ἄλλων ἐρωτημάτων συλ-
, , a « , ^ - > a ^ > M
λογίσασθαι θάτερον, ἢ ws ἐν rots Τοπικοῖς ἐλέχθη λαβεῖν. ἐπεὶ
δὲ τῶν καταφάσεων αἱ ἀντιθέσεις τρεῖς, éfaxyós συμβαί-
MJ ? , , ^ M hj , hod ‘
ve. τὰ ἀντικείμενα λαμβάνειν, ἢ παντὶ καὶ μηδενί, ἢ παντὶ
καὶ μὴ παντί, ἢ τινὶ καὶ μηδενί, καὶ τοῦτο ἀντιστρέψαι ἐπὶ
~ bd A A. ~ ^ A , ^ ~
τῶν ὅρων, olov τὸ A παντὶ τῷ B, τῷ δὲ Γ μηδενί, 7) τῷ
I παντί, τῷ δὲ B μηδενί, ἣ τῷ μὲν παντί, τῷ δὲ μὴ
, ^4 , ~ > , A ^ Ld Lj ,
παντί, kai πάλιν τοῦτο ἀντιστρέψαι κατὰ τοὺς ὄρους. ὁμοίως
δὲ καὶ ἐπὶ τοῦ τρίτου σχήματος. ὥστε φανερὸν ὁσαχῶς τε
4 ^
καὶ ἐν ποίοις σχήμασιν ἐνδέχεται διὰ τῶν ἀντικειμένων προ-
,
τάσεων γενέσθαι συλλογισμόν.
Φανερὸν δὲ καὶ ὅτι ἐκ ψευδῶν μὲν ἔστιν ἀληθὲς συλλο-
γίοσασθαι, καθάπερ εἴρηται πρότερον, ἐκ δὲ τῶν ἀντικειμέ-
aj] ταῦτα B. ἢ τὸ μὲν ὅλον τὸ δὲ μέρος Cu" 20uév-Fón 2123 δ᾽ ἔστι π
24 καὶ τ τὸ n 25-6 kai... ἐπιστήμην om. n! 26 τοῦ] τῷ B!
28 ap ful’ 32 θάτερος n 36 λανθάνειν- τοὺς προσδιαλεγομένους n
37 τοῖς om. A 38 καταφατικῶν n 39-40 72... μηδενί om. mil
b3 τοῦτον B!
4985 [0]
15
20
25
30
35
40
64>
ANAAYTIKQN IIPOTEPQN B
, LÀ | A 4 > , e t , ^
νων οὐκ ἔστιν: dei yàp ἐναντίος ὁ συλλογισμὸς γίνεται τῷ
F4 Ly 3 LÀ > , x 3 ᾽ὔ a > ^
10 πράγματι, otov εἰ ἔστιν ἀγαθόν, μὴ εἶναι ἀγαθόν, ἢ εἰ ζῷον,
^ ^ ὃ ^ ‘A , > ? ΐ x rr A *
μὴ ζῷον, διὰ τὸ ἐξ ἀντιφάσεως εἶναι τὸν συλλογισμὸν kai
τοὺς ὑποκειμένους ὅρους ἢ τοὺς αὐτοὺς εἶναι 7) τὸν μὲν ὅλον
4 * , ^ b 3 Ld Hi ^ ^ *, A
τὸν δὲ μέρος. δῆλον δὲ kai ὅτι ἐν τοῖς παραλογισμοῖς οὐδὲν
, ᾽ὔ ~ e a > 4 T > v
κωλύει γίνεσθαι τῆς ὑποθέσεως ἀντίφασιν, otov εἰ ἔστι περιτ-
15 τόν, μὴ εἶναι περιττόν. ἐκ γὰρ τῶν ἀντικειμένων προτάσεων
> , Lj , LAS 7 , , L4 ^
ἐναντίος ἦν ὁ συλλογισμός" ἐὰν οὖν λάβῃ τοιαύτας, ἔσται τῆς
L4 , » , ^ A ~ v L4 4 ? LÀ
ὑποθέσεως ἀντίφασις. δεῖ δὲ κατανοεῖν ὅτι οὕτω μὲν οὐκ ἔστιν
ἐναντία συμπεράνασθαι ἐξ ἑνὸς συλλογισμοῦ ὥστ᾽ εἶναι τὸ
td ki Ἂς nn > x > ^ *^ LÀ ~
συμπέρασμα τὸ μὴ ὃν ἀγαθὸν ἀγαθὸν ἢ ἄλλο τι τοιοῦτον,
LA * 3 A t , , ~ ~
20 ἐὰν μὴ εὐθὺς ἡ πρότασις τοιαύτη ληφθῃ (olov πᾶν ζῷον Aev-
M M * , M > L4 ~ > * a
κὸν εἶναι kai μὴ λευκόν, τὸν δ᾽ ἄνθρωπον ζῷον), ἀλλ᾽ ἢ mpoo-
λαβεῖν δεῖ τὴν ἀντίφασιν (οἷον ὅτι πᾶσα ἐπιστήμη ὑπόλη-
4 > € , 4 ^ ov t Ἵ ^ > /
ψις [καὶ οὐχ ὑπόληψις], εἶτα λαβεῖν ὅτι ἡ ἰατρικὴ ἐπιστήμη
ia * , , δ᾽ € A: 4 L4 LÀ a
μέν ἐστιν, οὐδεμία ὑπόληψις, ὥσπερ οἱ ἔλεγχοι γίνονται),
^ , ;* ^ σ , HJ , , > ,
25 ἢ ἐκ δύο συλλογισμῶν. dore δ᾽ εἶναι ἐναντία κατ᾽ ἀλή-
θειαν τὰ εἰλημμένα, οὐκ ἔστιν ἄλλον τρόπον ἢ τοῦτον, καθά-
περ εἴρηται πρότερον.
Τὸ δ᾽ ἐν ἀρχῇ αἰτεῖσθαι καὶ λαμβάνειν ἐστὶ μέν, ὡς
ἐν γένει λαβεῖν, ἐν τῷ μὴ ἀποδεικνύναι τὸ προκείμενον, τοῦτο
ki , ~ 4 * > L4 *
3e δὲ συμβαΐνει πολλαχῶς: καὶ yap εἰ ὅλως μὴ ovMo-
γίζεται, καὶ εἰ δι’ ἀγνωστοτέρων ἢ ὁμοίως ἀγνώστων, καὶ
εἰ διὰ τῶν ὑστέρων τὸ πρότερον: ἡ γὰρ ἀπόδειξις ἐκ πιστοτέ-
ρων τε καὶ προτέρων ἐστίν. τούτων μὲν οὖν οὐδέν ἐστι τὸ αἰτεῖ-
* , 2 ~ > 3 > ^ M * > e - ΄
σθαι τὸ ἐξ ἀρχῆς: ἀλλ᾽ ἐπεὶ τὰ μὲν δι’ αὑτῶν πέφυκε
35 γνωρίζεσθαι τὰ δὲ δι’ ἄλλων (αἱ μὲν γὰρ ἀρχαὶ δι’ αὖ-
~ A > € a ^ 3 iy > πῶ LÀ * 4 >
τῶν, τὰ δ᾽ ὑπὸ τὰς ἀρχὰς δι᾽ ἄλλων), ὅταν μὴ τὸ δι
αὑτοῦ γνωστὸν δι’ αὑτοῦ τις ἐπιχειρῇ δεικνύναι, τότ᾽ αἰτεῖται
A] , > ^ ^ > LÀ M LÀ ^ L4 > > ^ > ~
τὸ ἐξ ἀρχῆς. τοῦτο δ᾽ ἔστι μὲν οὕτω ποιεῖν ὥστ᾽ εὐθὺς ἀξιῶ-
σαι τὸ προκείμενον, ἐνδέχεται δὲ καὶ μεταβάντας ἐπ᾽
LÀ L4 ^ , > > , , ^ ,
4o ἄλλα ἄττα τῶν πεφυκότων δι᾽ ἐκείνου δείκνυσθαι διὰ τούτων
6 a 2 5 4, NH H , ^ T > i A 8 , 8 M ^
58 ἀποδεικνύναι τὸ ἐξ ἀρχῆς, οἷον εἰ τὸ εἰκνύοιτο διὰ τοῦ
B, τὸ δὲ B διὰ τοῦ Γ᾿, τὸ δὲ I πεφυκὸς εἴη δείκνυσθαι
bg ὁ ἐναντίος C 11 μὴ-Ἐ εἶναι n7 13 δήλου n? 16 τοιαύτας
Ἔ ἀντικειμένας ἢ 18 συμπεραίνεσθαι C 21 ἀλλ᾽ ἢ] ἀλλὰ C: ἄλλη Γ
προλαβεῖν ἩΓ 23 καὶ οὐχ ὑπόληψις om. Bln} 24 γίνονται ἀεὶ ἢ n?
25-6 τὰ εἰλημμένα κατ᾽ ἀλήθειαν C 30 ἐπισυμβαίνει ABC 33 τε om. A
34 αὐτῶν A Bn 35 αὐτῶν Bn 36 To μὴ" 37 αὑτοῦ CI: αὐτοῦ
ABn αὐτοῦ A Bn 40 ἄττα om. 7 ἐκείνων AB 6541 δεικνύοιτο
ἩΓῚ δεικνύοι τὸ C : δεικνύοι AB
τό
b, a
I5. 64^9-16. 65°34
διὰ τοῦ A+ συμβαίνει yàp αὐτὸ δι’ αὑτοῦ τὸ A δεικνύναι
a Ld f σ ~ ° E] ,
τοὺς οὕτω συλλογιζομένους. ὅπερ ποιοῦσιν of τὰς mapaAMj-
,
λους οἰόμενοι γράφειν. λανθάνουσι yap αὐτοὶ ἑαυτοὺς τοι-
~ Ld ^ ^ ~
abra λαμβάνοντες ἃ οὐχ οἷόν τε ἀποδεῖξαι μὴ οὐσῶν τῶν
P " ; ἌΡ ; ;
παραλλήλων. ὥστε συμβαδνει τοῖς οὕτω συλλογιζομένοις Exa-
, , Y bd of > L4 » ΕΣ e
στον εἶναι λέγειν, εἰ ἔστιν ἕκαστον: οὕτω δ᾽ ἅπαν ἔσται δι᾽ αὖ-
τοῦ γνωστόν: ὅπερ ἀδύνατον.
LI 7 3, , L4 L4 A L4 , ^
Ei οὖν τις ἀδήλου ὄντος ὅτι τὸ A ὑπάρχει τῷ TI,
- , b * L4 ^ > ^ ^ « , M
ὁμοίως δὲ xai ὅτι τῷ D, airoiro τῷ DB ὑπάρχειν τὸ A,
L4 ^ , ^ >? > ~ » ^ 3. > Ld , » Li
οὔπω δῆλον εἰ τὸ ἐν ἀρχῇ αἰτεῖται, ἀλλ᾽ ὅτι οὐκ ἀποδεί-
~ > ^ > ^ » LÀ M L4 , wv
κνυσι, δῆλον: οὐ yap ἀρχὴ ἀποδείξεως τὸ ὁμοίως ἄδηλον.
, , ^ A A] L4 L4 L4 , M ^
εἰ μέντοι τὸ B πρὸς τὸ l' οὕτως ἔχει wore ταὐτὸν εἶναι, ἢ
δῆλον ὅτι ἀντιστρέφουσιν, ἢ ἐνυπάρχει θάτερον θατέρῳ, τὸ ἐν
> ~ > ^ ^ A bal a Ll ^ € , »
ἀρχῇ αἰτεῖται. καὶ yap ἂν ὅτι τῷ B τὸ A ὑπάρχει δι
, z , * > , Li M ^ , > ,
ἐκείνων δεικνύοι, εἰ ἀντιστρέφοι (viv δὲ τοῦτο κωλύει, ἀλλ
οὐχ ὁ τρόπος). εἰ δὲ τοῦτο ποιοῖ, τὸ εἰρημένον ἂν ποιοῖ καὶ
> , . ~ e , * nn > M ^
ἀντιστρέφοι διὰ τριῶν. ὡσαύτως δὲ «dv εἰ τὸ B τῷ Γ
, € 4 Lj , M kJ ^ > ‘ Ld
λαμβάνοι ὑπάρχειν, ὁμοίως ἄδηλον ὃν καὶ εἰ τὸ A, οὔπω
τὸ ἐξ ἀρχῆς, ἀλλ᾽ οὐκ ἀποδείκνυσι. ἐὰν δὲ ταὐ-
^ 7 * " ^ ^ > L4 - ^ 2 ~
τὸν ἦ TO A καὶ B ἢ τῷ ἀντιστρέφειν ἢ τῷ ἔπεσθαι τῷ B
a ^ > 3 ~ , ^ ^ Α > * 37 34 * x
τὸ A, τὸ ἐξ ἀρχῆς αἰτεῖται διὰ τὴν αὐτὴν αἰτίαν: τὸ yap
> > ~ * ee LÀ L4 ^ Ld M , p - PA
ἐξ ἀρχῆς τί δύναται, εἴρηται ἡμῖν, ὅτι τὸ δι’ αὐτοῦ δεικνύναι
τὸ μὴ δι᾽ αὑτοῦ δῆλον.
> ^ > a > 3 - > -^ M > € -^ ,
Ei οὖν ἐστι τὸ ἐν ἀρχῇ αἰτεῖσθαι τὸ BV αὑτοῦ δεικνύναι
A M > € ~ ~ LJ > > A M Α , ΄
τὸ μὴ δι’ αὑτοῦ δῆλον, τοῦτο δ᾽ ἐστὶ τὸ μὴ δεικνύναι, ὅταν
€ , O27 u ^ , ‘ > T L ^
ὁμοίως ἀδήλων ὄντων τοῦ δεικνυμένου kai δι᾽ οὗ δείκνυσιν 7
τῷ ταὐτὰ τῷ αὐτῷ ἢ τῷ ταὐτὸν τοῖς αὐτοῖς ὑπάρχειν, ἐν
μὲν τῷ μέσῳ σχήματι καὶ τρίτῳ ἀμφοτέρως ἂν ἐνδέχοιτο
> ~ ^ ^ ^
τὸ ev ἀρχῇ αἰτεῖσθαι, ἐν δὲ κατηγορικῷ συλλογισμῷ ἔν
τε τῷ τρίτῳ καὶ τῷ πρώτῳ. ὅταν δ᾽ ἀποφατικῶς, ὅταν τὰ
αὐτὰ ἀπὸ τοῦ αὐτοῦ- καὶ οὐχ ὁμοίως ἀμφότεραι αἱ προτά-
[j [4 A M ^ 4 MJ M
σεις (ὡσαύτως δὲ kai ἐν TH μέσῳ), διὰ τὸ μὴ ἀντιστρέφειν
43 αὑτοῦ) αὐτοῦ An S αὐτοῦς (sic) n 8 εἰ fecit C αὐτοῦ An
I3 yáp-- ἐστιν n: +éora Γ 14 ἢ] € APC IS ἐνυπάρχει scripsi,
habet ut vid. P: ὑπάρχει codd. 18 ποιῇ C:om.T — ποιῇ APC 19
ἀντιστρέφῃ C? : ἀναστρέφοι 1 διὰ] ὡς διὰ (γι 20 δῆλον Β' α- τῷ
yCr 21 ἀρχῆς-Ἐ αἰτεῖται ACT 22 kaid- τὸ π 23 τὸ Á om. n!
24, 25, 26, 27 αὐτοῦ An 28 τοῦτ τε δείκνυται AT 20 αὐτῷ Ἢ
λαμβάνειν AC τῷ om. Cl, fecit n ὑπάρχειν -:- λαμβάνῃ nl 30 καὶ
Ἔτῷ ΟΓ 32 re om. B ὅταν δ᾽ ἀποφατικῶς] ἀποφατικῶς δὲ n?
33 xai om. n* 34 μὴ οἱ". πὶ
20
25
30
ANAAYTIKQN TIPOTEPQN B
^ " ^ 4 > x , LÀ 1
35 τοὺς ὅρους κατὰ τοὺς ἀποφατικοὺς συλλογισμούς. ἔστι δὲ
M > > ~ , ^ > A a > , 4 > 3 ,
τὸ ἐν ἀρχῇ αἰτεῖσθαι ἐν μὲν ταῖς ἀποδείξεσι τὰ κατ᾽ ἀλή-
L4 ν Li ^ ^ ^ a A ,
θειαν οὕτως ἔχοντα, ἐν δὲ τοῖς διαλεκτικοῖς τὰ κατὰ δόξαν.
4 A M ^ ^ , * ^ ^
Τὸ δὲ μὴ παρὰ τοῦτο συμβαίνειν τὸ ψεῦδος, 6 πολ-
λάκις ἐν τοῖς λόγοις εἰώθαμεν λέγειν, πρῶτον μέν ἐστιν ἐν
4o τοῖς εἰς τὸ ἀδύνατον συλλογισμοῖς, ὅταν πρὸς ἀντίφασιν F
65> τούτου ὃ ἐδείκνυτο τῇ εἰς τὸ ἀδύνατον. οὔτε γὰρ μὴ ἀντι-
,ὔ , ^ ^ A) A ~ > » L4 ^ P EN
φήσας ἐρεῖ τὸ οὐ παρὰ τοῦτο, ἀλλ᾽ ὅτι ψεῦδός τι ἐτέθη
^ » ^ ‘ ^ >
τῶν πρότερον, οὔτ᾽ ἐν TH δεικνυούσῃ" od yap τίθησι 6 avri-
> ^ ~ ^
φησιν. ἔτι δ᾽ Grav ἀναιρεθῇ τι δεικτικῶς διὰ τῶν A BI, οὐκ
ς ἔστιν εἰπεῖν ὡς οὐ παρὰ τὸ κείμενον γεγένηται 6 συλλογι-
σμός. τὸ γὰρ μὴ παρὰ τοῦτο γίνεσθαι τότε λέγομεν, ὅταν
3 L4 ra x * t ,
ἀναιρεθέντος τούτου μηδὲν ἧττον περαίνηται ὁ συλλογισμός,
ὅπερ οὐκ ἔστιν ἐν τοῖς δεικτικοῖς- ἀναιρεθείσης γὰρ τῆς θέσεως
οὐδ᾽ ὁ πρὸς ταύτην ἔσται συλλογισμός. φανερὸν οὖν ὅτι ἐν τοῖς
10 εἰς τὸ ἀδύνατον λέγεται τὸ μὴ παρὰ τοῦτο, καὶ ὅταν οὕτως
ἔχη πρὸς τὸ ἀδύνατον ἡ ἐξ ἀρχῆς ὑπόθεσις ὥστε καὶ οὔσης
καὶ μὴ οὔσης ταύτης οὐδὲν ἧττον συμβαίνειν τὸ ἀδύνατον.
ὋὉ μὲν οὖν φανερώτατος τρόπος ἐστὶ τοῦ μὴ παρὰ τὴν
θέσιν εἶναι τὸ ψεῦδος, ὅταν ἀπὸ τῆς ὑποθέσεως ἀσύναπτος
Σ * ^ I4 ^ M 3 , Lj , go
1s} ἀπὸ τῶν μέσων πρὸς τὸ ἀδύνατον ὁ συλλογισμός, ὅπερ
εἴρηται καὶ ἐν τοῖς Τοπικοῖς. τὸ γὰρ τὸ ἀναίτιον ὡς αἴτιον τιθέ-
ναι τοῦτό ἐστιν, οἷον εἰ βουλόμενος δεῖξαι ὅτι ἀσύμμετρος
ἡ διάμετρος, ἐπιχειροίη τὸν Ζήνωνος λόγον, ὡς
οὐκ ἔστι κινεῖσθαι, καὶ εἰς τοῦτο ἀπάγοι τὸ ἀδύνατον" οὐδα-
~ ἣν ΕΣ - , > x Li ^ Ld ^ >
20 μῶς yap οὐδαμῇ συνεχές ἐστι τὸ ψεῦδος τῇ dace τῇ ἐξ
, ^ L4 ^ , », A M LA ^ > ,
ἀρχῆς. ἄλλος δὲ τρόπος, εἰ συνεχὲς μὲν εἴη τὸ ἀδύνατον
τῇ ὑποθέσει, μὴ μέντοι δι᾽ ἐκείνην συμβαίνοι. τοῦτο γὰρ
ἐγχωρεῖ γενέσθαι καὶ ἐπὶ τὸ ἄνω καὶ ἐπὶ τὸ κάτω λαμ-
βάνοντι τὸ συνεχές, οἷον εἰ τὸ Α τῷ Β κεῖται ὑπάρ-
25 xov, τὸ δὲ B τῷ I, τὸ δὲ I τῷ A, τοῦτο δ᾽ εἴη ψεῦδος,
~ , > > ~
τὸ τὸ B τῷ A ὑπάρχειν. εἰ yap ἀφαιρεθέντος τοῦ A μηδὲν
L4 , M ^ ^ * ^ » ^ LA ‘
ἧττον ὑπάρχοι τὸ B τῷ D xai τὸ I τῷ A, οὐκ ἂν εἴη τὸ
^ X ^ , » LJ L4 , -^ , w Um M
ψεῦδος διὰ τὴν ἐξ ἀρχῆς ὑπόθεσιν. ἣ πάλιν εἴ τις ἐπὶ τὸ
ἄνω λαμβάνοι τὸ συνεχές, οἷον εἰ τὸ μὲν A τῷ B, τῷ δὲ
235 κατὰ om. C1 br γὰρ- ὁ A ἀντιφήσας ACnIP, fecit B : ἀντι-
φήσαντος Maier 2 ἐρεῖ] τις ἐρεῖ r? 3 ὃ ἀντίφησιν APC: ἀντίφασιν
Bn: ἀντίφησιν B*: ὁ ἀντιφήσων A: τὴν ἀντίφασιν C*: κατ᾽ ἀντίφασιν T
7 ἀντιφή ὴ
16 τοῖς om. AC τὸξ om. B 18 ἡ διάμετρος om. n Adyou+
δεικνύναι AL 19 anayn C: ἀπαγάγοι r?
17
16, 65735-18. 66724
Α τὸ E καὶ τῷ E τὸ Z, ψεῦδος δ᾽ εἴη τὸ ὑπάρχειν τῷ 30
A τὸ Z καὶ γὰρ οὕτως οὐδὲν ἂν ἧττον εἴη. τὸ ἀδύνατον
> 0 , ~ > 3 ^ e θέι ἀλλὰ ὃ - A AY
ἀναιρεθείσης τῆς ἐξ ἀρχῆς ὑποθέσεως. ἃ δεῖ πρὸς τοὺς
ἐξ ἀρχῆς ὅρους συνάπτειν τὸ ἀδύνατον: οὕτω γὰρ ἔσται διὰ
τὴν ὑπόθεσιν, οἷον ἐπὶ μὲν τὸ κάτω λαμβάνοντι τὸ συνεχὲς
πρὸς τὸν κατηγορούμενον τῶν ὅρων (εἰ γὰρ ἀδύνατον τὸ A 35
- L4 , » , ~ 2 , w M] ~
TQ 4 ὑπάρχειν, ἀφαιρεθέντος τοῦ A οὐκέτι ἔσται τὸ ψεῦδος)"
ye 4 * L4 > T ^ > M ^ M ,
ἐπὶ δὲ τὸ ἄνω, καθ᾽ ob κατηγορεῖται (εἰ yap τῷ B μὴ éy-
χωρεῖ τὸ Ζ ὑπάρχειν, ἀφαιρεθέντος τοῦ Β οὐκέτι ἔσται τὸ
ἀδύνατον). ὁμοίως δὲ καὶ στερητικῶν τῶν συλλογισμῶν
ὄντων. 40
Φανερὸν οὖν ὅτι τοῦ ἀδυνάτου μὴ πρὸς τοὺς ἐξ ἀρχῆς 662
L4 we * * b , ,^ A ΩΣ ^ Od
ὅρους ὄντος ov παρὰ τὴν θέσιν συμβαίνει τὸ ψεῦδος. ἢ οὐδ
L4 > 4 = a e , L4 ^ ^ M M 3 X
οὕτως dei διὰ τὴν ὑπόθεσιν ἔσται τὸ ψεῦδος; καὶ yàp εἰ μὴ
τῷ B ἀλλὰ τῷ K ἐτέθη τὸ A ὑπάρχειν, τὸ δὲ K τῷ D
4 ^ ^ ' - , 4 > , [4 , M *
καὶ τοῦτο TQ A, καὶ οὕτω μένει τὸ ἀδύνατον (ὁμοίως δὲ Kal 5
2% ^ L4 , * - " » > M * » M
ἐπὶ τὸ ἄνω λαμβάνοντι τοὺς ὄρους), ὥστ᾽ ἐπεὶ kai ὄντος Kat
μὴ ὄντος τούτου συμβαίνει τὸ ἀδύνατον, οὐκ ἂν εἴη παρὰ
A , »Ἁ a * L4 4 ν᾿ , ^ ~
τὴν θέσιν. ἢ τὸ μὴ ὄντος τούτου μηδὲν ἧττον γίνεσθαι τὸ ψεῦ-
, " , v > Δ , , ^
δος οὐχ οὕτω ληπτέον ὥστ᾽ ἄλλου τιθεμένου συμβαίνειν τὸ
> ‘ 3 ? J > , [4 M ~ ~
ἀδύνατον, ἀλλ᾽ Grav ἀφαιρεθέντος τούτου διὰ τῶν λοιπῶν το
προτάσεων ταὐτὸ περαίνηται ἀδύνατον, ἐπεὶ ταὐτό γε ψεῦ-
δος συμβαίνειν διὰ πλειόνων ὑποθέσεων οὐδὲν ἴσως ἄτοπον,
^ , 6 * > , , * t
olov τὰς παραλλήλους συμπίπτειν καὶ ef μείζων ἐστὶν ἡ
ἐντὸς τῆς ἐκτὸς καὶ εἰ τὸ τρίγωνον ἔχει πλείους ὀρθὰς
δυεῖν; 15
'O δὲ ψευδὴς λόγος γίνεται παρὰ τὸ πρῶτον ψεῦδος.
ἢ γὰρ ἐκ τῶν δύο προτάσεων ἣ ἐκ πλειόνων πᾶς ἐστι συλ-
λογισμός. εἰ μὲν οὖν ἐκ τῶν δύο, τούτων ἀνάγκη τὴν ἑτέραν
ἢ καὶ ἀμφοτέρας εἶναι ψευδεῖς: ἐξ ἀληθῶν γὰρ οὐκ ἦν ψευ-
4 , > δ᾽ > , f * t D ^ ^
dys συλλογισμός. εἰ δ᾽ ἐκ πλειόνων, olov τὸ μὲν Γ᾽ διὰ τῶν 20
A B, ταῦτα δὲ διὰ τῶν 4 E Z H, τούτων τι ἔσται τῶν
, , 08 x A ~ Lj λό * ^ A x B
ἐπάνω ψεῦδος, καὶ παρὰ τοῦτο 6 λόγος" τὸ yàp καὶ
,
δι’ ἐκείνων περαίνονται. ὥστε παρ᾽ ἐκείνων τι συμβαίνει τὸ
συμπέρασμα καὶ τὸ ψεῦδος.
b30 797] τὸ πὶ 34 τῷ κάτω Β 6622 ὄρους om. C! συμβαίνει)
λαμβάνει A 5 τούτῳ B 1 Toro C! συμβαίνοι B 13 rapaA-
λήλας din! συμπίπτειν fecit n 14 ἔχοι A Bn 16 πρῶτον om. B
17 ἔσται CI 19 ψευδεῖς) ψευδῆς A} 21 δὲ om. 460] 22 Adyos+
ψευδής n 23 περαίνεται C
25
3o
35
40
66>
Io
15
ANAAYTIKQN IIPOTEPON B
4 L: X A , ,
Πρὸς δὲ τὸ μὴ κατασυλλογίζεσθαι παρατηρητέον,
L4 w ~ » Σ ~ * , Ld Á.
ὅταν ἄνευ τῶν συμπερασμάτων ἐρωτᾷ τὸν λόγον, ὅπως μὴ
~ A > ^ L4 *,
δοθῇ δὶς ταὐτὸν ἐν ταῖς mporáceow, ἐπειδήπερ ἴσμεν ὅτι
» , M > oe , > > A *
ἄνευ μέσου συλλογισμὸς οὐ γίνεται, μέσον δ᾽ ἐστὶ τὸ mÀe-
ονάκις λεγόμενον. ὡς δὲ δεῖ πρὸς ἕκαστον συμπέρασμα τη-
ρεῖν τὸ μέσον, φανερὸν ἐκ τοῦ εἰδέναι ποῖον ἐν ἑκάστῳ σχή-
ματι δείκνυται. τοῦτο δ᾽ ἡμᾶς οὐ λήσεται διὰ τὸ εἰδέναι πῶς
ὑπέχομεν τὸν λόγον.
* ? L4 eA y >
Χρὴ δ᾽ ὅπερ φυλάττεσθαι παραγγέλλομεν ἀποκρινο-
> ~ ^ ^
μένους, αὐτοὺς ἐπιχειροῦντας πειρᾶσθαι λανθάνειν. τοῦτο δ᾽
ἔσται πρῶτον, ἐὰν τὰ συμπεράσματα μὴ προσυλλογίζων-
3 LI , 7. ~ > , M T LÀ A hJ
ται ἀλλ᾽ εἰλημμένων τῶν ἀναγκαίων ἄδηλα 7, ἔτι δὲ àv
4 D " , ^ 59 IJ " ” r3
μὴ τὰ σύνεγγυς ἐρωτᾷ, ἀλλ᾽ ὅτι μάλιστα ἄμεσα. οἷον
ἔστω δέον συμπεραίνεσθαι τὸ A κατὰ τοῦ Ζ' μέσα B Γ A E.
δεῖ οὖν ἐρωτᾶν εἰ τὸ A τῷ Β, καὶ πάλιν μὴ εἰ τὸ Β τῷ
I, ἀλλ᾽ εἰ τὸ 4 τῷ E, κάπειτα εἰ τὸ B τῷ I, καὶ οὕτω
^ rd ^ Li εν , , € , >? ^
τὰ λοιπά. κἂν δι’ ἑνὸς μέσου γίνηται ὁ συλλογισμός, ἀπὸ
^ , Ld » M * e Á, ^
τοῦ μέσου ἄρχεσθαι: μάλιστα yap ἂν οὕτω λανθάνοι τὸν
ἀποκρινόμενον.
E * δ᾽ » L4 * ^ , , ~ v Lg
πεὶ ἔχομεν πότε καὶ πῶς ἐχόντων τῶν ὅρων γί-
νεται συλλογισμός, φανερὸν καὶ πότ᾽ ἔσται καὶ πότ᾽ οὐκ
» yw 5, * A 7 ll > A
ἔσται ἔλεγχος. πάντων μὲν yap συγχωρουμένων, 3j ἐναλλὰξ
τιθεμένων τῶν ἀποκρίσεων, οἷον τῆς μὲν ἀποφατικῆς τῆς δὲ
καταφατικῆς, ἐγχωρεῖ γίνεσθαι ἔλεγχον. ἦν γὰρ συλλογι-
σμὸς καὶ οὕτω καὶ ἐκείνως ἐχόντων τῶν ὅρων, ὥστ᾽ εἰ τὸ
κείμενον ἐναντίον τῷ συμπεράσματι, ἀνάγκη γίνεσθαι ἔλεγ-
« 4 μὲ > 4 , > *
xov 6 yàp ἔλεγχος ἀντιφάσεως συλλογισμός. εἰ δὲ μη-
δὲν συγχωροῖτο, ἀδύνατον γενέσθαι ἔλεγχον: οὐ γὰρ ἦν
συλλυγισμὸς πάντων τῶν ὅρων στερητικῶν ὄντων, ὥστ᾽ οὐδ᾽
ἔλεγχος: εἰ μὲν γὰρ ἔλεγχος, ἀνάγκη συλλογισμὸν εἶναι,
^ , L4 2 > , LÀ € , M M]
συλλογισμοῦ δ᾽ ὄντος οὐκ ἀνάγκη ἔλεγχον. ὡσαύτως δὲ Kai
‘
εἰ μηδὲν τεθείη κατὰ τὴν ἀπόκρισιν ἐν ὅλῳ: 6 yap αὐτὸς
ἔσται διορισμὸς ἐλέγχου καὶ συλλογισμοῦ.
Σ t > 7 ἐν > ^ H ^ Ld
ὑμβαΐνει δ᾽ ἐνίοτε, καθάπερ ἐν τῇ θέσει τῶν ὅρων
3 , * ^ it € , δ M > ,
ἀπατώμεθα, καὶ κατὰ τὴν ὑπόληψιν γίνεσθαι τὴν ἀπάτην,
827 θέσεσιν n 31 δ᾽] dein 32 ὑπέχομεν codd. P : an ὑπέχωμενῦ
35 mpwrov-+ μὲν n προσσυλλογίζωνται D: προσυλλογίζονται t. 37 ἄμεσα
A BC?n et ut vid. P: τὰ μέσα BCT b8 κατηγορικῆς BC yap+
on 9 κείμενον nT: +9 AB: 4+ ἦν C :-E εἴη mm? I2 γίνεσθαι ABC
13 ὄντων om. nt
19
20
21
IB. 66?25-21. 67711
κι 3 hd , 4 , 4 , , [2 , x
olov εἰ ἐνδέχεται τὸ αὐτὸ πλείοσι πρώτοις ὑπάρχειν, Kal 20
᾿ A , ^ 4A ΜΝ * id , ^ A
τὸ μὲν λεληθέναι τινὰ καὶ οἴεσθαι μηδενὶ ὑπάρχειν, τὸ δὲ
, » » * ~ 3 ^ > € M L4 ,
εἰδέναι. ἔστω τὸ A τῷ B καὶ τῷ I καθ᾽ αὑτὰ ὑπάρ-
χον, καὶ ταῦτα παντὶ τῷ 4 ὡσαύτως. εἰ δὴ τῷ μὲν Β τὸ
A 4 LÀ € , M EJ ^ ^ b M
παντὶ οἴεται ὑπάρχειν, καὶ τοῦτο τῷ A, τῷ δὲ Γ τὸ A
μηδενί, καὶ τοῦτο τῷ A παντί, τοῦ αὐτοῦ κατὰ ταὐτὸν ἕξει 25
ἐπιστήμην καὶ ἄγνοιαν. πάλιν εἴ τις ἀπατηθείη περὶ τὰ ἐκ
τῆς αὐτῆς συστοιχίας, οἷον εἰ τὸ A ὑπάρχει τῷ B, τοῦτο δὲ
τῷ Γ᾽ καὶ τὸ Γ τῷ A, ὑπολαμβάνοι δὲ τὸ A παντὶ τῷ B
[4 , M , * ^ Ld iT » , ^
ὑπάρχειν καὶ πάλιν μηδενὶ τῷ lI" ἅμα yap εἴσεταί Te kai
1 € » t La T? e i , ^ Μ᾿ > ^ » ,
οὐχ ὑπολήψεται ὑπάρχειν. ἄρ᾽ οὖν οὐδὲν ἄλλο ἀξιοῖ ἐκ τού- 30
των ἢ ὃ ἐπίσταται, τοῦτο μὴ ὑπολαμβάνειν; ἐπίσταται γάρ
Ld A] ^ € , A ~ e ^ , 4
πως ὅτι τὸ A τῷ I ὑπάρχει διὰ τοῦ B, ὡς τῇ καθόλου τὸ
κατὰ μέρος, ὥστε ὅ πως ἐπίσταται, τοῦτο ὅλως ἀξιοῖ μὴ
ὑπολαμβάνειν: ὅπερ ἀδύνατον. 34
᾿Επὶ δὲ τοῦ πρότερον λεχθέν- 34
τος, εἰ μὴ ἐκ τῆς αὐτῆς συστοιχίας τὸ μέσον, καθ᾽ ἑκάτε- 35
ρον μὲν τῶν μέσων ἀμφοτέρας τὰς προτάσεις οὐκ ἐγχωρεῖ
ὑπολαμβάνειν, οἷον τὸ A τῷ μὲν B παντί, τῷ δὲ I' μη-
’ ES , > ? 1 ^. A , ‘ ^
devi, ταῦτα δ᾽ ἀμφότερα παντὶ τῷ 4. συμβαίνει yàp 3j
ε ^ * > , , , , A a ,
ἁπλῶς ἢ ἐπί τι ἐναντίαν λαμβάνεσθαι τὴν πρώτην mpóra-
* hi T ^ L4 ,ὔ M * ς ,
ow. εἰ yàp ᾧ TO B ὑπάρχει, παντὲ τὸ Α ὑπολαμβάνει 4o
ὑπάρχειν, τὸ δὲ B τῷ A οἶδε, καὶ ὅτι τῷ A τὸ A οἶδεν. 673
ὥστ᾽ εἰ πάλιν, ᾧ τὸ I’, μηδενὶ οἴεται τὸ A ὑπάρχειν, ᾧ τὸ
Β ^ ε JK * , » M A ε , 4 δὲ
τινι υπαρζει, TOUTW Οὐκ OLETAL TO vrapxeuw. TO €
* »f T- 4 , * M LÀ T M "^
παντὶ οἰόμενον ᾧ τὸ DB, πάλιν τινὶ μὴ οἴεσθαι ᾧ τὸ D, ἢ
: 1
Lj ~ *^ " , , , > ’
ἁπλῶς ἢ ἐπί τι ἐναντίον ἐστίν. 5
Οὕτω μὲν οὖν οὐκ ἐνδέχεται 5
Li ^ » € , bi M , a ^ » >
ὑπολαβεῖν, καθ᾽ ἑκάτερον δὲ τὴν μίαν ἢ κατὰ θάτερον ἀμ-
φ , δὲ Av p A A Ἂς ~ B i 4 B ^
orépas οὐδὲν κωλύει, olov τὸ παντὶ τῷ καὶ τὸ Β τῷ
4 καὶ A E A ὃ ' - I € , M € ,
i i πάλιν τὸ μηδενὶ τῷ lI. ὁμοία γὰρ ἡ τοιαύτη
ἀπάτη καὶ ὡς ἀπατώμεθα περὶ τὰς ἐν μέρει, οἷον εἰ ᾧ τὸ Β,
^ * € , ^ M ^ , X 4
παντὶ τὸ A ὑπάρχει, τὸ δὲ B τῷ I παντί, τὸ A παντὶ το
τῷ I ὑπάρξει. εἰ οὖν τις οἶδεν ὅτι τὸ A, ᾧ τὸ B, ὑπάρ-
b20 πρώτως C*T', fecit B 22 €otw+ yap Bn? αὑτὸ BL 23 τὸ]
τῷ Al 24 8-- παντὶ C τῷ... 25 μηδενί om. C 25 κατ᾽ αὐτὸν
Bar 32 διὰ τοῦ B om. mr τῇ) τῷπ 37 οἷον-Ἐ εἰ πὶ 38 τῷ
ὃ παντί n 39 πρώτην om. n! 6722 dom.nt Γ]γ παντὶ Ο: ΒΓ
on a fecit n 3 τοῦτο n! 6 καθ᾽ om. nt κατὰ θάτερον
καθεκάτερον AB: κατὰ τὸ ἕτερον n 9 τὰ Aldina: τὰς codd. ᾧ τὰ
ΒΗΓ: τῷ AC i170] τῷ Aln ὑπάρξει π
ANAAYTIKQN IIPOTEPON B
χει παντί, olde καὶ ὅτι τῷ I. ἀλλ᾽ οὐδὲν κωλύει ἀγνοεῖν
τὸ Γ ὅτι ἔστιν, οἷον εἰ τὸ μὲν A δύο ὀρθαί, τὸ δ᾽ ἐφ᾽’ ᾧ B
τρίγωνον, τὸ δ᾽ ἐφ᾽ à Γ᾿ αἰσθητὸν τρίγωνον. ὑπολάβοι γὰρ
L4 * H * I: ida - ^ , LÀ 8 , ,
15 dv τις μὴ εἶναι τὸ I, εἰδὼς ὅτι πᾶν τρίγωνον ἔχει δύο óp-
θάς, ὥσθ᾽ ἅμα εἴσεται καὶ ἀγνοήσει ταὐτόν. τὸ γὰρ εἰδέ-
^. L Ld , > - > € Li , > *
vat πᾶν τρίγωνον ὅτι δύο ὀρθαῖς οὐχ ἁπλοῦν ἐστιν, ἀλλὰ
* E! ~ * τὰ Μ > , A * A ,
τὸ μὲν τῷ τὴν καθόλου ἔχειν ἐπιστήμην, τὸ δὲ τὴν καθ
" [4 x -᾿ € ^ 06A (à Ay I Lg 8 [4 >
ἕκαστον. οὕτω μὲν οὖν ὡς τῇ καθόλου οἷδε τὸ IX ὅτι δύο dp-
, € M ~ > -" ? - > > L4 ^
20 Bai, ὡς δὲ τῇ καθ᾽ ἕκαστον οὐκ οἶδεν, ὥστ᾽ οὐχ ἕξει τὰς
> » L4 , A * L4 > ^ cA / Ld ε y.
ἐναντίας. ὁμοίως δὲ kai 6 ἐν τῷ Μένωνι λόγος, ὅτι ἡ uá-
θησις ἀνάμνησις. οὐδαμοῦ γὰρ συμβαίνει προεπίστασθαι τὸ
» «€ > ’ [4 ^ , ^ ΄ D ^
καθ᾽ ἕκαστον, ἀλλ᾽ dua τῇ ἐπαγωγῇ λαμβάνειν τὴν τῶν
κατὰ μέρος ἐπιστήμην ὥσπερ ἀναγνωρίζοντας. ἔνια γὰρ εὐ-
* LÀ Ld [4 ᾽ ^ 34 L4 L4 ,
25 θὺς ἴσμεν, olov ὅτι δύο ὀρθαῖς, ἐὰν ἴδωμεν ὅτι τρίγωνον.
« ,ὔ A AC M 23 ~ *
ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων.
^ x T H ~ LT > ) ~ > ,
Τῇ μὲν οὖν καθόλου θεωροῦμεν rà ἐν μέρει, τῇ δ᾽ oi-
H > ~
κείᾳ οὐκ ἴσμεν, ὥστ᾽ ἐνδέχεται καὶ ἀπατᾶσθαι περὶ αὐτά,
2 > > id 3 > » x 4 , > ~
πλὴν οὐκ ἐναντίως, ἀλλ᾽ ἔχειν μὲν τὴν καθόλου, ἀπατᾶ-
30 σθαι δὲ τὴν κατὰ μέρος. ὁμοίως οὖν καὶ ἐπὶ τῶν προειρημέ-
νων" οὐ γὰρ ἐναντία ἡ κατὰ τὸ μέσον ἀπάτη τῇ κατὰ τὸν
συλλογισμὸν ἐπιστήμῃ, οὐδ᾽ ἡ Kal? ἑκάτερον τῶν μέσων ὑπό-
ληψις. οὐδὲν δὲ κωλύει εἰδότα καὶ ὅτι τὸ A ὅλῳ τῷ B
«ε , X , ^ ^ > ^ M e , M
ὑπάρχει καὶ πάλιν τοῦτο τῷ l', οἰηθῆναι μὴ ὑπάρχειν τὸ
3s A τῷ I, οἷον ὅτι πᾶσα ἡμίονος ἄτοκος καὶ αὕτη ἡμίονος
v P4 4, > M 3—3 σ΄ M ~ 4
οἴεσθαι κύειν ταύτην: οὐ yàp ἐπίσταται ὅτι τὸ A τῷ Γ, μὴ
^ 4 ᾽ ε , ν ~ a X ᾽ i *
συνθεωρῶν τὸ Kal? ἑκάτερον. ὥστε δῆλον ὅτι καὶ ef τὸ μὲν
* * ^ > 2 L4 w Lj
olde τὸ δὲ μὴ oldev, ἀπατηθήσεται. ὅπερ ἔχουσιν ai xa-
θόλου πρὸς τὰς κατὰ μέρος ἐπιστήμας. οὐδὲν γὰρ τῶν αἰ-
^ Li , , » 9305 ^ ,
67> σθητῶν ἔξω τῆς αἰσθήσεως γενόμενον ἴσμεν, οὐδ᾽ àv ἠσθη-
μένοι τυγχάνωμεν, εἰ μὴ ὡς τῷ καθόλου καὶ τῷ ἔχειν τὴν
- > ^
οἰκείαν ἐπιστήμην, ἀλλ᾽ οὐχ ὡς τῷ ἐνεργεῖν. τὸ yap ἐπί-
, ^ ^ Li ^ , n ε ^ , ,
στασθαι λέγεται τριχῶς, ἢ ὡς TH καθόλου ἢ ὡς τῇ οἰκείᾳ
n t ^ > a σ * à 0» ^ ^ Ort
5 ἢ ὡς τῷ ἐνεργεῖν, ὥστε Kal TO ἠπατῆσθαι τοσαυταχῶς. οὐδὲν
^ * , A.
οὖν κωλύει Kal εἰδέναι καὶ ἠπατῆσθαι περὶ ταὐτό, πλὴν οὐκ
814 τὸ fecit B 4] o? AC 18 τῷ om. 5 rivACn:$v ἐν τῷ v?
τῷ δὲ n? 19 ὀρθαῖς n 24 ὥσπερ εἰ γνωρίζοντας n! εὐθὺς -
ἐδόντες n 25 οἷον om. C ἴδωμεν 4300: εἰδῶμεν AB 27 rà] τὸ n
29 μὲν om. B 30 τὴν scripsi: τῇ codd. 42 ἕτερον A 35 αὕτη ἡ A
37 ἑκάτερον- λῆμμα AT 38 καθόλου-! προτάσεις A bs τῷ CnP*:
τὸ 418 5 ὡς οἵη. τῷ] τὸ A! ἀπατᾶσθαι
21. 67*12-22. 67°39
$ ,ὔ σ ,ὔ X ^ > Lj e 32. ^
ἐναντίως. ὅπερ συμβαΐνει καὶ τῷ καθ᾽ ἑκατέραν εἰδότι τὴν
πρότασιν καὶ μὴ ἐπεσκεμμένῳ πρότερον. ὑπολαμβάνων γὰρ
κύειν τὴν ἡμίονον οὐκ ἔχει τὴν κατὰ τὸ ἐνεργεῖν ἐπιστήμην,
0.7 T A A t , > ’ > 4, ^ uU ,
οὐδ᾽ ad διὰ τὴν ὑπόληψιν ἐναντίαν ἀπάτην τῇ ἐπιστήμῃ: 10
συλλογισμὸς γὰρ ἡ ἐναντία ἀπάτη τῇ καθόλου.
Ὃ δ᾽ ὑπολαμβάνων τὸ ἀγαθῷ εἶναι κακῷ εἶναι, τὸ
3 A [4 , 3 ^ b ^ w X * A
αὐτὸ ὑπολήψεται ἀγαθῷ εἶναι καὶ κακῷ. ἔστω yap τὸ μὲν
3 ^ », 1? x x ^ 213 ,
ἀγαθῷ εἶναι ἐφ᾽ οὗ A, τὸ δὲ κακῷ εἶναι ἐφ᾽ οὗ B, πάλιν
δὲ τὸ ἀγαθῷ εἶναι ἐφ᾽ οὗ Γ. ἐπεὶ οὖν ταὐτὸν ὑπολαμβά- 15
νει τὸ B καὶ τὸ Γ, καὶ εἶναι τὸ Γ᾽ τὸ B ὑπολήψεται, καὶ
πάλιν τὸ B τὸ A εἶναι ὡσαύτως, ὥστε καὶ τὸ Γ τὸ A.
ὥσπερ yàp εἰ ἦν ἀληθές, καθ᾽ οὗ τὸ Γ, τὸ B, καὶ καθ᾽
οὗ τὸ Β, τὸ A, καὶ κατὰ τοῦ Γ τὸ A ἀληθὲς ἦν, οὕτω καὶ
»? ἊΝ ~ € 4 e , x M > 4 ~ , ~
ἐπὶ τοῦ ὑπολαμβάνειν. ὁμοίως δὲ καὶ ἐπὶ τοῦ εἶναι" ταὐτοῦ 20
γὰρ ὄντος τοῦ Γ καὶ Β, καὶ πάλιν τοῦ Β καὶ Α, καὶ τὸ Γ
τῷ A ταὐτὸν jv: ὥστε καὶ ἐπὶ τοῦ δοξάζειν ὁμοίως. ἄρ᾽ οὖν
:
^ » ^ ^ > 3 ^
τοῦτο μὲν ἀναγκαῖον, εἴ τις δώσει TO πρῶτον; ἀλλ᾽ ἴσως ἐκεῖνο
ψεῦδος, τὸ ὑπολαβεῖν τινὰ κακῷ εἶναι τὸ ἀγαθῷ εἶναι,
3 4 A LH ^ a 3 a ag?
εἰ μὴ κατὰ συμβεβηκός: πολλαχῶς yap ἐγχωρεῖ τοῦθ᾽ 25
- é , , * ^ /
ὑπολαμβάνειν. ἐπισκεπτέον δὲ τοῦτο βέλτιον.
σ 3 > , a » > , M N ,
22 Ὅταν δ᾽ ἀντιστρέφῃ τὰ ἄκρα, ἀνάγκη Kat τὸ μέσον
3 /, A Ld > ^ M a ~ x A^
ἀντιστρέφειν πρὸς ἄμφω. εἰ yap τὸ A κατὰ τοῦ Γ᾽ διὰ τοῦ
B ὑπάρχει, εἰ ἀντιστρέφει καὶ ὑπάρχει, ᾧ τὸ A, παντὶ
τὸ Γ, καὶ τὸ Β τῷ A ἀντιστρέψει καὶ ὑπάρξει, ᾧ τὸ A, 30
παντὶ τὸ B διὰ μέσου τοῦ I" καὶ τὸ Γ τῷ B ἀντιστρέψει
διὰ μέσου τοῦ A. καὶ ἐπὶ τοῦ μὴ ὑπάρχειν ὡσαύτως, οἷον
εἰ τὸ B τῷ Γ᾽ ὑπάρχει, τῷ δὲ B τὸ A οὐχ ὑπάρχει, οὐδὲ
τὸ A τῷ I οὐχ ὑπάρξει. εἰ δὴ τὸ B τῷ A ἀντιστρέφει,
hi a yas ~ A > Aj LÀ ^ M B ht L4 , m4
καὶ τὸ I τῷ A ἀντιστρέψει. ἔστω yap τὸ B μὴ ὑπάρχον 35
τῷ A: οὐδ᾽ ἄρα τὸ I" παντὶ yàp τῷ I τὸ B ὑπῆρχεν.
καὶ εἰ TQ B τὸ Γ ἀντιστρέφει, καὶ τὸ A ἀντιστρέψει: καθ᾽
οὗ γὰρ ἅπαντος τὸ Β, καὶ τὸ Γ. καί εἰ τὸ Γ «καὶ» πρὸς τὸ A
3 , ‘ X 3 , T ‘ ^
ἀντιστρέφει, καὶ τὸ B. ἀντιστρέψε. ᾧ yap τὸ B,
b8 μὴ om. nw 1I γάρ- ἐστιν 13 τὸ fecit C 18 rot om. ἢ
22T0a 1 dp' A 24 ὑπολαμβάνειν n τὸ] xai B 30 ἀντι-
στρέψει scripsi: ἀντιστρέφει codd. ὑπάρχει ABC 31 ἀντιστρέφει
ABC 35 ἀντιστρέψει ABCP : ἀντιστρέφει nt” 36 yàp om. "ἢ
37 τὸ βτῷ ABC wT xai . . , ἀντιστρέψει om. nl τὸ ABT: τῷ
ABC? ἀντιστρέψει Γ΄: ἀντιστρέφει ABC 38 dv παντὸς n καὶ
adieci 39 dvriarpé$e]- kai τὸ B coni. Jenkinson ἀντιστρέψει
scripsi: ἀντιστρέφει ABCn: ἀντιστρέφει πρὸς τὸ a f
ANAAYTIKQN TIPOTEPQN B
68476 I" ᾧ δὲ τὸ A, τὸ I οὐχ ὑπάρχει. καὶ μόνον τοῦτο
3 * ~ , Y ^ > Ld , L4 ,
ἀπὸ τοῦ συμπεράσματος ἄρχεται, rà δ᾽ ἄλλα ody ὁμοίως
3 καὶ ἐπὶ τοῦ κατηγορικοῦ συλλογισμοῦ.
3 IIdAw εἰ τὸ A καὶ
τὸ B ἀντιστρέφει, καὶ τὸ D' καὶ τὸ A ὡσαύτως, ἅπαντι δ᾽
> , ‘ ^ A e 5 b 4 M Ud Lud
ςἀνάγκη τὸ A ἣ τὸ I ὑπάρχειν, καὶ τὸ B καὶ A οὕτως ἕξει
e 4 , € τὰ » M ‘ T7 ‘ 4 b
ὥστε παντὶ θάτερον ὑπάρχειν. ἐπεὶ yap ᾧ τὸ A, τὸ B, xai
d τὸ D, τὸ A, παντὶ δὲ τὸ A ἣ τὸ Γ καὶ οὐχ ἅμα, φα-
A [d * 4 ^ 4 M M > LÀ
8vepóv ὅτι kai τὸ B ἢ τὸ 4 παντὶ Kai οὐχ ἅμα [olov...
ir γεγονέναι]: δύο yàp συλλογισμοὶ σύγκεινται. πάλιν εἰ παντὶ
a M ^ M A \ ^ ^ L4 * M € , » Ὁ
μὲν τὸ Α ἢ τὸ B καὶ τὸ Γ ἢ τὸ A, dpa δὲ μὴ ὑπάρχει, ei ἀντι-
στρέφει τὸ A καὶ τὸ D', καὶ τὸ B καὶ τὸ A ἀντιστρέφει. εἰ
M M M e , M T A c^ " M L4 ,
yap Twi μὴ ὑπάρχει τὸ B, ᾧ τὸ A, δῆλον ὅτι τὸ A ὑπάρχει.
, 4 ‘ 4 A > , , e L4 * ^
εἰ δὲ τὸ A, καὶ τὸ I ἀντιστρέφει γάρ. ὥστε ἅμα τὸ I kai
4 ^ 3 > Fa > > ‘ > ͵ » M
τό τὸ 4. τοῦτο δ᾽ ἀδύνατον. «otov εἰ τὸ ἀγένητον ἄφθαρτον καὶ
970 ἄφθαρτον ἀγένητον, ἀνάγκη τὸ γένομενον φθαρτὸν καὶ τὸ
10 φθαρτὸν γεγονέναι».
16 Ὅταν δὲ τὸ A ὅλῳ τῷ B καὶ τῷ TD
- , * A Ld ^ € /, * M
ὑπάρχῃ καὶ μηδενὸς ἄλλου κατηγορῆται, ὑπάρχῃ δὲ καὶ
τὸ B παντὶ τῷ l', ἀνάγκη τὸ A καὶ B ἀντιστρέφειν’ ἐπεὶ
M x , Li ΄ M ^ A
yàp κατὰ μόνων τῶν B Γ᾽ λέγεται τὸ A, κατηγορεῖται δὲ
^ 4 > A L4 ^ A - ^ e > T E:
2076 B xai αὐτὸ αὑτοῦ xai τοῦ D, φανερὸν ὅτι καθ᾽ ὧν τὸ A,
καὶ τὸ Β λεχθήσεται πάντων πλὴν αὐτοῦ τοῦ A. πάλιν ὅταν
τὸ A καὶ. τὸ B ὅλῳ τῷ I ὑπάρχῃ, ἀντιστρέφῃ δὲ τὸ D
~ > , A * ^ e , ? M A M
TQ B, ἀνάγκη τὸ A παντὶ τῷ B ὑπάρχειν: ἐπεὶ yàp παντὶ
τῷ Γ τὸ A, τὸ δὲ Γ τῷ B διὰ τὸ ἀντιστρέφειν, καὶ τὸ A
25 παντὶ τῷ Β.
25 Ὅταν δὲ δυοῖν ὄντοιν τὸ A τοῦ Β ai-
L4 7 L4 3 A M M ^ © Ü
ρετώτερον jj, ὄντων ἀντικειμένων, kai τὸ 4 τοῦ I’ ὡσαύτως,
εἰ αἱρετώτερα τὰ Α Γ τῶν Β 4, τὸ Α τοῦ 4 αἱρετώτερον.
Lj Jr ^ * ^ A ‘ ^ * ,
ὁμοίως yàp διωκτὸν τὸ A xai φευκτὸν τὸ B (ἀντικείμενα
γάρ), καὶ τὸ I τῷ 4 (καὶ γὰρ ταῦτα ἀντίκειται). εἰ οὖν
M ^ ε , © , b M ^ , € ,
3o TO A τῷ 4 ὁμοίως αἱρετόν, καὶ τὸ B τῷ Γ᾽ $evkróv: ἑκά-
6841 a, r0 y A? B*P : y, 76a ΑΒΟΉΓ 2 ópotas-- ὡς n 5 4] τὸ
én 8 xai οὐχ dua om. nT olov . . . γεγονέναι hic codd. P: post
τό ἀδύνατον Pacius 12 ὑπάρχῃ n 14 μὴ ὑπάρχῃ π 16 τὸ om. AB
οἷον. . . γεγονέναι hic Pacius: post 8 dua codd. P ἀγέννητον C 9
τῷ Β ἀγέννητον 16 bis τῷ γ ὑπάρχει n 18 καὶ τ τὸ n 23 τῷ)
καὶ τὸ ἢ 24 β-Ἰ παντὶ n 25 β-τ ὑπάρξει ABC τὸ] οἷον τὸ
CT, fecit n 28 yàp] τε yàp n 29 τῷ] καὶ τὸ π ἀντίκεινται n
30 y+ ὁμοίως ἢ
22. 68*1-23. 68620
τερον yap ἑκατέρῳ ὁμοίως, φευκτὸν διωκτῷ. ὥστε καὶ τὰ
ἄμφω τὰ A I τοῖς B A. ἐπεὶ δὲ μᾶλλον, οὐχ οἷόν τε
ὁμοίως" καὶ γὰρ ἂν τὰ Β A ὁμοίως ἦσαν. εἰ δὲ τὸ A τοῦ A
« , ‘ ^ B ^ T , a M LÀ
αἱρετώτερον, kai τὸ B τοῦ I ἧττον $evkróv: τὸ yàp &ar-
Tov τῷ ἐλάττονι ἀντίκειται. αἱρετώτερον δὲ TO μεῖζον dya- 35
θὸν καὶ ἔλαττον κακὸν ἢ τὸ ἔλαττον ἀγαθὸν καὶ μεῖζον
, * M L4 LÀ 4 t ^ ~
κακόν: καὶ τὸ ἅπαν dpa, τὸ B A, αἱρετώτερον τοῦ A I.
^ 9 s » a A L4 « , ^ * ' »
νῦν δ᾽ οὐκ ἔστιν. τὸ A dpa αἱρετώτερον τοῦ 4, καὶ ro Γ dpa
~ , » 3. LÀ ^ L4 » 5 ^ S 4
τοῦ B ἧττον φευκτόν. «i δὴ ἕλοιτο más ὁ ἐρῶν κατὰ τὸν
‘
ἔρωτα τὸ A τὸ οὕτως ἔχειν ὥστε χαρίζεσθαι, καὶ τὸ μὴ 40
χαρίζεσθαι τὸ ἐφ᾽ οὗ D, ἣ τὸ χαρίζεσθαι τὸ ἐφ᾽ οὗ A, καὶ
τὸ μὴ τοιοῦτον εἶναι οἷον χαρίζεσθαι τὸ ἐφ᾽ od B, δῆλον ὅτι 68>
τὸ Α τὸ τοιοῦτον εἶναι αἱρετώτερόν ἐστιν ἣ τὸ χαρίζεσθαι. τὸ
ἄρα φιλεῖσθαι τῆς συνουσίας αἱρετώτερον κατὰ τὸν ἔρωτα.
^ L4 € L4 > * ^ , - ^ ^ , A
μᾶλλον dpa 6 ἔρως ἐστὶ τῆς φιλίας ἢ τοῦ συνεῖναι. εἰ δὲ
μάλιστα τούτου, καὶ τέλος τοῦτο. τὸ ἄρα συνεῖναι 7) οὐκ ἔστιν ς
Ld ^ ~ a e M M t » > ,
ὅλως ἢ ToU φιλεῖσθαι ἕνεκεν: καὶ yap αἱ ἄλλαι ἐπιθυμίαι
καὶ τέχναι οὕτως.
PS 4 T v e 9 1 x > H
23 Πῶς μὲν οὖν ἔχουσιν of ὅροι κατὰ τὰς ἀντιστροφὰς
* 1 € ΄ ^ H $. ΄ σ > ,
καὶ τὸ aiperwrepor ἢ φευκτότεροι εἶναι, φανερόν: ὅτι δ᾽ οὐ
/ € M * > * ‘ *
μόνον of διαλεκτικοὶ Kal ἀποδεικτικοὶ συλλογισμοὶ διὰ το
τῶν προειρημένων γίνονται σχημάτων, ἀλλὰ καὶ οἱ ῥητορι-
koi καὶ ἁπλῶς ἡτισοῦν πίστις καὶ ἡ καθ᾽ ὁποιανοῦν μέθοδον,
^ nn » , L4 x , ^ ‘
νῦν dv εἴη λεκτέον. ἅπαντα yàp πιστεύομεν 3j διὰ συλλο-
Lj > , ~
γισμοῦ 7) e£ ἐπαγωγῆς.
> 4 M T > 4 e 3 HJ ^ AA
Ἐπαγωγὴ μὲν οὖν ἐστι καὶ 6 ἐξ ἐπαγωγῆς συλλογι- 15
σμὸς τὸ διὰ τοῦ ἑτέρου θάτερον ἄκρον τῷ μέσῳ συλλογίσα-
σθαι, οἷον εἰ τῶν A I μέσον τὸ B, διὰ τοῦ [' δεῖξαι τὸ A
τῷ B ὑπάρχον: οὕτω γὰρ ποιούμεθα τὰς ἐπαγωγάς. οἷον
L4
ἔστω τὸ A μακρόβιον, τὸ δ᾽ ἐφ᾽ à B τὸ χολὴν μὴ ἔχον,
ἐφ᾽ T δὲ I A θ᾽ " B f LÀ 6 ‘
ἐφ᾽ ᾧ δὲ Γ τὸ καθ᾽ ἕκαστον μακρόβιον, olov ἄνθρωπος Kai 20
531 τὰ om. "2 32 τοῖς] καὶ rà n! 338yC δὴ 35 τῷ) TON
37 τὸ BAom.C 38 δ᾽ om. C? 40 xai τὸ) τὸ δὲ ΗΓ 41 τὸ] 8e
τὸ om. ^ br rovn χαρίσασθαι n 2 χαρίσασθαι BC 3
κατὰ] ἐστὶ κατὰ nT” 4 ἐστὶ) ἐπὶ n 3 τῆς συνουσίας n 5 τοῦτο
ni xaitron 6 ἕνεκα m 7 οὔτω-Ἐ γίνονται a. y. B. ὃ ΑΔΓ:
+ylvovra n3 gra nl αἱρετώτεροι 7) φευκτότεροι Γ΄: φευκτότεροι
3j αἱρετώτεροι AB: φευκτότεροι καὶ αἱρετώτεροι C : αἱρετώτερον 3j φευκτότερον
fm 10 διαλεκτοὶ Al 13 πιστοῦμεν C 18 ὑπάρχειν Bekker:
om. C 19 r? om. n 20 rà καθ᾽ ἕκαστα μακρόβια m μακρόβιον
sec]. Consbruch, om. fort. P: ἄχολον Grote οἷον om. %
Ὁ
tn
30
35
40
Io
ANAAYTIKQN IIPOTEPON B
L4 A L4 ’ ~ 9 Ld L4 Ld A ~ A
ἵππος καὶ ἡμίονος. τῷ δὴ I' ὅλῳ ὑπάρχει τὸ A (πᾶν ydp
τὸ I” μακρόβιον): ἀλλὰ καὶ τὸ B, τὸ μὴ ἔχειν χολήν,
M e d c^ , + > 4, a ^ ‘ a
παντὶ ὑπάρχει τῷ I’. εἰ οὖν ἀντιστρέφει τὸ I' τῷ B καὶ μὴ
€ , M y > , A ^ e ra L4
ὑπερτείνει TO μέσον, ἀνάγκη τὸ A τῷ B ὑπάρχειν. δέδει-
κται γὰρ πρότερον ὅτι dv δύο ἄττα τῷ αὐτῷ ὑπάρχῃ καὶ
πρὸς θάτερον αὐτῶν ἀντιστρέφῃ τὸ ἄκρον, ὅτι τῷ ἀντιστρέ-
φοντι καὶ θάτερον ὑπάρξει τῶν κατηγορουμένων. δεῖ δὲ νοεῖν
A * > Li ^
τὸ Γ τὸ ἐξ ἁπάντων τῶν καθ᾽ ἕκαστον συγκείμενον: ἡ yàp
ἐπαγωγὴ διὰ πάντων.
"E δ᾽ ε ^ AA A ~ , M > ,
στι ὁ τοιοῦτος συλλογισμὸς τῆς πρώτης καὶ ἀμέ-
~ , ε
σου προτάσεως" ὧν μὲν γὰρ ἔστι μέσον, διὰ τοῦ μέσου ὁ
, T * A L4 ? ἣν ^ x ,
συλλογισμός, ὧν δὲ μὴ ἔστι, δι’ ἐπαγωγῆς. Kal τρόπον
τινὰ ἀντίκειται ἡ ἐπαγωγὴ τῷ συλλογισμῷ: 6 μὲν γὰρ διὰ
τοῦ μέσου τὸ ἄκρον τῷ τρίτῳ δείκνυσιν, ἡ δὲ διὰ τοῦ τρίτου
τὸ ἄκρον τῷ μέσῳ. φύσει μὲν οὖν πρότερος καὶ γνωριμώτε-
pos 6 διὰ τοῦ μέσου συλλογισμός, ἡμῖν δ᾽ ἐναργέστερος ὁ
διὰ τῆς ἐπαγωγῆς.
, > > * LZ ^ id ἣν L4 e ,
Ilapaderypa δ᾽ ἐστὶν ὅταν τῷ μέσῳ τὸ ἄκρον ὑπάρ-
χον δειχθῇ διὰ τοῦ ὁμοίου τῷ τρίτῳ. δεῖ δὲ καὶ τὸ μέσον
τῷ τρίτῳ καὶ τὸ πρῶτον τῷ ὁμοίῳ γνώριμον εἶναι ὑπάρχον.
T " A y a * a L4 , > ^
otov ἔστω τὸ A κακόν, τὸ δὲ B πρὸς ὁμόρους ἀναιρεῖσθαι
πόλεμον, ef d δὲ I τὸ ᾿Αθηναίους πρὸς Θηβαίους, τὸ δ᾽
ἐφ᾽ à 4 Θηβαίους πρὸς Φωκεῖς. ἐὰν οὖν βουλώμεθα δεῖξαι
Ld * , ^ LZ > L4 Ld M *
ὅτι τὸ Θηβαίοις πολεμεῖν κακόν ἐστι, ληπτέον ὅτι TO πρὸς
τοὺς ὁμόρους πολεμεῖν κακόν. τούτου δὲ πίστις ἐκ τῶν
€ , Ld , id AT ^ , * - M A
ὁμοίων, olov ὅτι Θηβαίοις ὁ πρὸς Φωκεῖς. ἐπεὶ οὖν τὸ πρὸς
τοὺς ὁμόρους κακόν, τὸ δὲ πρὸς Θηβαίους πρὸς ὁμόρους ἐστί,
φανερὸν ὅτι τὸ πρὸς Θηβαίους πολεμεῖν κακόν. ὅτι μὲν οὖν
^ ^ s
τὸ B τῷ Γ᾽ καὶ τῷ A ὑπάρχει, φανερόν (dud) ydp ἐστι
M ^ € , > ^ , ^ a Ly ~
πρὸς τοὺς ὁμόρους ἀναιρεῖσθαι πόλεμον), Kal ὅτι τὸ A τῷ
4 (Θηβαίοις γὰρ οὐ συνήνεγκεν ὁ πρὸς Φωκεῖς πόλεμος)" ὅτι
δὲ τὸ A τῷ B ὑπάρχει, διὰ τοῦ 4 δειχθήσεται. τὸν αὐ-
τὸν δὲ τρόπον κἂν εἰ διὰ πλειόνων τῶν ὁμοίων ἡ πίστις γε-
~ ,
vovro τοῦ μέσου πρὸς τὸ ἄκρον. φανερὸν οὖν ὅτι τὸ παράδει-
bar-2 πᾶν... μακρόβιον suspexit Tredennick 22 y Pacius: ἄχολον
A BCr? : ἄχολον y n 23 ἀντιστρέφῃ n 25 ἅττα ABC ὑπάρχει C
26 ἀντιστρέφει C 32 ἔστι-᾿ of vel ai πὶ 35 obv om. C καὶ γνωρι-
μώτερος om. nl 39-40 δεῖ... τρίτῳ oin. C 40 γνωριμώτερον nt”
6981 τὸ δ᾽ om. n 6rotsom.C κακόν... ὁμόρους om. nl 7 τὸ 0m. a?
10 ὁ om. C? I1 7G B r0 aC 12 καὶπ γίνοιτο AB 13 οὖν om. C
24
23. 6821-26. 6058
, * LÀ e ¥ 8 - L4 * - M H
γμά ἐστιν οὔτε ws μέρος πρὸς ὅλον οὔτε ws ὅλον πρὸς μέρος,
ἀλλ᾽ ὡς μέρος πρὸς μέρος, ὅταν ἄμφω μὲν jj ὑπὸ ταὐτό, τς
γνώριμον δὲ θάτερον. καὶ διαφέρει τῆς ἐπαγωγῆς, ὅτι ἡ
μὲν ἐξ ἁπάντων τῶν ἀτόμων τὸ ἄκρον ἐδείκνυεν ὑπάρχειν
~ , ‘ ‘ 3 L4 3 ^ * ,
τῷ μέσῳ kai πρὸς TO ἄκρον o) συνῆπτε τὸν συλλογισμόν,
τὸ δὲ καὶ συνάπτει καὶ οὐκ ἐξ ἁπάντων δείκνυσιν.
, * , , ᾿ σ ~ A , A ~ ~
25 ᾿Απαγωγὴ δ᾽ ἐστὶν ὅταν τῷ μὲν μέσῳ τὸ πρῶτον B$- 20
λον ἦ ὑπάρχον, τῷ δ᾽ ἐσχάτῳ τὸ μέσον ἄδηλον μέν, ὁμοίως
δὲ M - ^ -^ ^ LÀ hJ 97
€ πιστὸν ἢ μᾶλλον τοῦ συμπεράσματος: ἔτι dv ὀλίγα F
τὰ μέσα τοῦ ἐσχάτου καὶ τοῦ μέσου: πάντως γὰρ ἐγγύτερον
, ^ , , » ^ M id
εἶναι συμβαζψει τῆς ἐπιστήμης. οἷον ἔστω τὸ A τὸ διδακτόν,
vy? T , , 4 , € ‘ 7. > , Ld
ἐφ᾽ οὗ B ἐπιστήμη, τὸ Γ δικαιοσύνη. ἡ μὲν οὖν ἐπιστήμη ὅτι 25
διδακτόν, φανερόν: ἡ δ᾽ ἀρετὴ εἰ ἐπιστήμη, ἄδηλον. εἰ οὖν
ὁμοίως ἢ μᾶλλον πιστὸν τὸ BI τοῦ A D, ἀπαγωγή ἐστιν"
> ^ A ^ , , ὃ A ^ wr ,ὔ A A
ἐγγύτερον yap τοῦ ἐπίστασθαι διὰ τὸ προσειληφέναι τὴν A B
ἐπιστήμην, πρότερον οὐκ ἔχοντας. ἢ πάλιν εἰ ὀλίγα τὰ μέσα
~ * M e » , ~ 59. , , M
τῶν B I" kai yàp οὕτως ἐγγύτερον τοῦ εἰδέναι. olov εἰ τὸ 4 30
εἴη τετραγωνίζεσθαι, τὸ δ᾽ ἐφ᾽ ᾧ E εὐθύγραμμον, τὸ δ᾽
ἐφ᾽ à Z κύκλος: εἰ τοῦ E Ζ ἕν μόνον εἴη μέσον, τὸ μετὰ
μηνίσκων ἴσον γίνεσθαι εὐθυγράμμῳ τὸν κύκλον, ἐγγὺς ἂν
LJ ~ ᾽ ΄ - * ΄ , M B ^ A HERI
εἴη τοῦ εἰδέναι. ὅταν δὲ μήτε πιστότερον 7j τὸ Β Γ τοῦ 4 Γ μήτ
Y / 4 , , , > ra 3g? ΄ Ld x
ὀλίγα τὰ μέσα, οὐ λέγω ἀπαγωγήν. οὐδ᾽ ὅταν ἄμεσον ἡ τὸ 35
BI ἐπιστήμη γὰρ τὸ τοιοῦτον.
» > , M , , * KE ,
26 “Evoracis δ᾽ ἐστὶ πρότασις προτάσει ἐναντία. διαφέρει
δὲ τῆς προτάσεως, ὅτι τὴν μὲν ἔνστασιν ἐνδέχεται εἶναι ἐπὶ
μέρους, τὴν δὲ πρότασιν 1) ὅλως οὐκ ἐνδέχεται ἢ οὐκ ἐν τοῖς
, ^ , * * LÀ ~ 4
καθόλου συλλογισμοῖς. φέρεται δὲ ἡ ἔνστασις διχῶς καὶ 69b
διὰ δύο σχημάτων, διχῶς μὲν ὅτι ἢ καθόλου 7) ἐν μέρει
πᾶσα ἔνστασις, ἐκ δύο δὲ σχημάτων ὅτι ἀντικείμεναι φέ-
ρονται τῇ προτάσει, τὰ δ᾽ ἀντικείμενα ἐν τῷ πρώτῳ καὶ
τῷ τρίτῳ σχήματι περαίνονται μόνοις. ὅταν γὰρ ἀξιώσῃ ς
παντὶ ὑπάρχειν, ἐνιστάμεθα ἢ ὅτι οὐδενὶ ἢ ὅτι τινὶ οὐχ ὑπάρ-
χει" τούτων δὲ τὸ μὲν μηδενὶ ἐκ τοῦ πρώτου σχήματος, τὸ
δὲ τινὲ μὴ ἐκ τοῦ ἐσχάτου. οἷον ἔστω τὸ Α μίαν εἶναι ἐπιστή-
ars εἴ C 16 γνωριμώτερον n 21 δ᾽ om. n! 25 οὗ δὲς
7164-86 CT 28 προειληφέναι C τὴν AB scripsi: τὴν ay ABCn: τὴν
By πῆ: τῇ AT τὴν ΒΓ Pacius 31 τετράγωνον γνωρίζεσθαι n δ᾽.
om. C 32 ἐφ᾽ à om. B 34 δ) €» C 35 εἴη n: om. C
by δὲ fecit n xai] τε xai C 2 μὲν fecit n 3 ἐκ) διὰ CI 67
‘nT: om. ABd οὐδενὶ... οὐχ] τινὶ ἢ ὅτι οὐδενὶ μὴ C 8 ἔστιν d
Io
15
19
I9
20
25
30
35
ANAAYTIKQN IIPOTEPON B
, [» . M > , , ^ , 7 ~
μην, ἐφ᾽ à τὸ B ἐναντία. προτείναντος δὴ μίαν εἶναι τῶν
ἐναντίων ἐπιστήμην, T) ὅτι ὅλως οὐχ ἡ αὐτὴ τῶν ἀντικειμένων
ἐνίσταται, τὰ δ᾽ ἐναντία ἀντικείμενα, ὥστε γίνεται τὸ πρῶτον
σχῆμα, T ὅτι τοῦ γνωστοῦ καὶ ἀγνώστου οὐ pia: τοῦτο δὲ τὸ
τρίτον: κατὰ γὰρ τοῦ I’, τοῦ γνωστοῦ καὶ ἀγνώστου, τὸ μὲν
> 2 > , A ^ , *, ^ > uh: 4 ~
ἐναντία εἶναι ἀληθές, τὸ δὲ μίαν αὐτῶν ἐπιστήμην εἶναι ψεῦ-
~ ~ , ^
δος. πάλιν ἐπὶ τῆς στερητικῆς προτάσεως ὡσαύτως. ἀξιοῦν-
Ἂς 4 ~ H ^
Tos yap μὴ εἶναι μίαν τῶν ἐναντίων, 7j ὅτι πάντων τῶν ἀν-
^ , , Lu ^
τικειμένων ἢ OTL τινῶν ἐναντίων ἡ αὐτὴ λέγομεν, otov ὑγιεινοῦ
‘ 4 4 4 - ^
Kal νοσώδους: τὸ μὲν οὖν πάντων ἐκ τοῦ πρώτου, τὸ δὲ τινῶν
ἐκ τοῦ τρίτου σχήματος.
Ἁπλῶς γὰρ ἐν πᾶσι καθόλου μὲν
ἐνιστάμενον ἀνάγκη πρὸς τὸ καθόλου τῶν προτεινομένων τὴν
ἀντίφασιν εἰπεῖν, οἷον εἰ μὴ τὴν αὐτὴν ἀξιοῖ τῶν ἐναντίων,
πάντων εἰπόντα τῶν ἀντικειμένων μίαν. οὕτω δ᾽ ἀνάγκη τὸ
πρῶτον εἶναι σχῆμα: μέσον γὰρ γίνεται τὸ καθόλου πρὸς
M > > ^ , L4 la 4. Ld , , » T ,
τὸ ἐξ ἀρχῆς. ev μέρει δέ, πρὸς 6 ἐστι καθόλου καθ᾽ οὗ Aé-
γεται ἡ πρότασις, οἷον γνωστοῦ καὶ ἀγνώστου μὴ τὴν αὐτήν"
τὰ γὰρ ἐναντία καθόλου πρὸς ταῦτα. καὶ γίνεται τὸ τρίτον
σχῆμα: μέσον γὰρ τὸ ἐν μέρει λαμβανόμενον, οἷον τὸ γνω-
στὸν καὶ τὸ ἄγνωστον. ἐξ ὧν γὰρ ἔστι συλλογίσασθαι τούὐναν-
τίον, ἐκ τούτων καὶ τὰς ἐνστάσεις ἐπιχειροῦμεν λέγειν. διὸ
καὶ ἐκ μόνων τούτων τῶν σχημάτων φέρομεν: ἐν μόνοις γὰρ
οἱ ἀντικείμενοι συλλογισμοί: διὰ γὰρ τοῦ μέσου οὐκ ἦν κα-
΄- LÀ ^ μι A , , € x - ,
ταφατικῶς. ἔτι δὲ Kav λόγου δέοιτο πλείονος ἡ Sid τοῦ μέ-
, > X LÀ hi ^ € , *
cov σχήματος, olov εἰ μὴ δοίη τὸ A τῷ B ὑπάρχεν διὰ
i Ἂν, > ^ ᾽ ^ a ^ x » LÀ y
τὸ μὴ ἀκολουθεῖν αὐτῷ τὸ Γ. τοῦτο yàp δι’ ἄλλων mporá-
σεων δῆλον: οὐ δεῖ δὲ εἰς ἄλλα ἐκτρέπεσθαι τὴν ἔνστασιν,
, > *, LY ^ LÀ ^ L4 r4 , ^ M *
GAN εὐθὺς φανερὰν ἔχειν τὴν ἑτέραν πρότασιν. [διὸ Kal τὸ
σημεῖον ἐκ μόνου τούτου τοῦ σχήματος οὐκ ἔστιν.
E , A M * ^ LÀ > la f
πιοκεπτέον δὲ Kal περὶ τῶν ἄλλων ἐνστάσεων, olov
bg ὧν Β:ι οὗ τὸ οἵπ. 5 τῶν ἐναντίων μίαν εἶναι ἐπιστήμην C : τῶν
ἐναντίων μίαν ἐπιστήμην εἶναι Γ 10 ὅτι om. d I4 αὐτὸν n 15
ἀξιοῦνται A: ἀξιοῦντες Bd 16 yàpg--roó C rà om. Σ᾽, 17 Myo-
pe B I9 ἅπασι C 20 ἐνισταμένων ABdn τῷ προτεινομένῳ
ABdnT 25 γνωστὸν καὶ ἄγνωστον τοῦ μὴ n (μὴ om. n?) 28 τὸ om.
Cdn τὰ ἐναντία C 30 ἐκ om. d τῶν σχημάτων τούτων + τούτεστι
τοῦ πρώτου καὶ τοῦ τρίτου C 31 καταφατικός Cn 32 δέηται d
ἡ) εἰς 35 εἰς ἄλλα ἐκτρέπεσθαι om. πὶ Γ 36-7 διὸ... ἔστιν secl.
Susemihl, om. fort. P 38-7032 ᾿Επισκεπτέον .. . λαβεῖν codd. P : secl.
Cook Wilson
26. 69^9-27. 70°30
* ~ 3 ^5 L4 M ^c , M ~ M , 4
περὶ τῶν ἐκ τοῦ ἐναντίου Kai τοῦ ὁμοίου Kai τοῦ κατὰ δόξαν, καὶ
εἰ τὴν ἐν μέρει ἐκ τοῦ πρώτου ἢ τὴν στερητικὴν ἐκ τοῦ μέσου 705"
δυνατὸν λαβεῖν.
27 «Ἐνθύμημα δὲ ἐστὶ συλλογισμὸς ἐξ εἰκότων 7) σημείων,» εἰκὸς 10
* a ^ >
δὲ καὶ σημεῖον οὐ ταὐτόν ἐστιν, ἀλλὰ τὸ μὲν εἰκός ἐστι πρότασις 3
L4 ^ ‘A e 3." Nj AY w v , * ^
ἔνδοξος" 6 yap ὡς ἐπὶ τὸ πολὺ ἴσασιν οὕτω γινόμενον ἢ μὴ
γινόμενον 7) ὃν ἢ μὴ ὄν, τοῦτ᾽ ἐστὶν εἰκός, οἷον τὸ μισεῖν τοὺς 5
φθονοῦντας ἢ τὸ φιλεῖ: τοὺς ἐρωμένους. σημεῖον δὲ βούλεται
εἶναι πρότασις ἀποδεικτικὴ ἢ ἀναγκαία ἢ ἔνδοξος: οὗ γὰρ
ὄντος ἔστιν ἢ οὗ γενομένου πρότερον 7) ὕστερον γέγονε τὸ
πρᾶγμα, τοῦτο σημεῖόν ἐστι τοῦ γεγονέναι 7 εἶναι. [ἐνθύμημα 9
... σημείων] λαμβάνεται δὲ τὸ σημεῖον τριχῶς, ὁσαχῶς 11
καὶ τὸ μέσον ἐν τοῖς σχήμασιν: ἢ γὰρ ὡς ἐν τῷ πρώτῳ
ἢ ὡς ἐν τῷ μέσῳ ἢ ὡς ἐν τῷ τρίτῳ, οἷον τὸ μὲν δεῖξαι κύου-
σαν διὰ τὸ γάλα ἔχειν ἐκ τοῦ πρώτου σχήματος" μέσον
yàp τὸ γάλα ἔχειν. ἐφ᾽ ᾧ τὸ A κύειν, τὸ B γάλα ἔχειν, 15
X , al a I A δ᾽ Ed € t o ^ Il M ^
γυνὴ ἐφ᾽ ᾧ D. τὸ δ᾽ ὅτι οἱ σοφοὶ σπουδαῖοι, [Πιττακὸς yap
σπουδαῖος, διὰ τοῦ ἐσχάτου. ἐφ᾽ ᾧ A τὸ σπουδαῖον, ἐφ᾽ ᾧ
B οἱ σοφοί, ἐφ᾽’ ᾧ I Πιττακός. ἀληθὲς δὴ καὶ τὸ A καὶ
^ A^ ^ a ^ ^ * H M M 3 ,
τὸ B τοῦ Γ κατηγορῆσαι" πλὴν τὸ μὲν οὐ λέγουσι διὰ τὸ εἰδέ-
^ x , * A , Ld » ἐς ^ ~
vat, τὸ δὲ λαμβάνουσιν. τὸ δὲ κύειν, ὅτι ὠχρά, διὰ τοῦ 20
μέσον σχήματος βούλεται εἶναι: ἐπεὶ γὰρ ἕπεται ταῖς κυού-
‘ , , > ^ * * , ^ LÀ
gas τὸ ὠχρόν, ἀκολουθεῖ δὲ καὶ ταύτῃ, δεδεῖχθαι οἴονται
- , X , ^ ,»1? T * M] * 31} - ‘
ὅτι κύει. τὸ ὠχρὸν ἐφ᾽ οὗ τὸ A, τὸ κύειν ἐφ᾽ ob B, γυνὴ
ἐφ᾽ od T. 24
3 ^ ^ T € [4 ^ , ^ ,
Ἐὰν μὲν οὖν ἡ μία λεχθῇ πρότασις, σημεῖον yive- 24
, 7. Xx M € L4 , ^ ,
Tat μόνον, ἐὰν δὲ xai ἡ ἑτέρα προσληφθῇ, συλλογισμός, 25
οἷον ὅτι Πιττακὸς ἐλευθέριος: οἱ γὰρ φιλότιμοι ἐλευθέριοι,
Πιττακὸς δὲ φιλότιμος. ἢ πάλιν ὅτι οἱ σοφοὶ ἀγαθοί: Πιτ-
^ δ 3 , > A * a " M T ,
τακὸς yàp ἀγαθός, ἀλλὰ καὶ σοφός. οὕτω μὲν οὖν γίνονται
, A € * M ^ , * ΝΜ
συλλογισμοί, πλὴν ὁ μὲν διὰ τοῦ πρώτου σχήματος ἄλυ-
bal 2 x ^ , , > « \ ^ ^ , ,
Tos, dv ἀληθὴς ἦ (καθόλου γάρ ἐστιν), ὁ δὲ διὰ τοῦ ἐσχάτου 30
b39 περὶ τῶν] καὶ περὶ τοῦ CI: ἐπὶ τῶν ni ἐκ om. C karà-- τὴν ἡ
1032 λαμβάνειν δυνατύν n Io ᾿Ενθύμημα.... σημείων ex ll. 10-11 trans-
tuli δὲ Cr: μὲν οὖν ABd συλλογισμὸς - ἀτελὴς Ct 040
καὶ C: +éxn 4 οὕτω om. 7 ἢ CDnI'P*: om. AB ἀναγκαία
secl. Maier 9 robro om. dn ἐνθύμημα ... σημείων hic
codd. IP: ante 1. 3 collocavi 14 πρώτου] an 15 τὸ a τὸ κύειν, τὸ B
τὸ γάλα ἔχειν, γύνη δὲ ἐφ᾽ à r0 y C 17 4] τὸ a C 18 76 B ACdn
L]royC 23 ro? om. Cn B, γυνὴ] τὸ B, yv C 24 Dre yC
ἡ plalypivC! λεχθείη α 25 xai fecit 5 26 ἐλεύθερος d ἐλεύθεροι ἀ
ANAAYTIKON IIPOTEPON B
λύσιμος, κἂν ἀληθὲς 4 τὸ συμπέρασμα, διὰ τὸ μὴ εἶναι
καθόλου μηδὲ πρὸς τὸ πρᾶγμα τὸν συλλογισμόν: οὐ γὰρ
εἰ Πιττακὸς σπουδαῖος, διὰ τοῦτο καὶ τοὺς ἄλλους ἀνάγκη
σοφούς. 6 δὲ διὰ τοῦ μέσου σχήματος ἀεὶ καὶ πάντως λύ-
35 σιμος: οὐδέποτε γὰρ γίνεται συλλογισμὸς οὕτως ἐχόντων
70”
5
I5
~ Ld > A , t , > Ld J ^ Vi ^ L4
τῶν ὅρων: ot yap εἰ ἡ κύουσα ὠχρά, ὠχρὰ δὲ xai ἥδε,
, 3 , , ax θὲ * ἣν 3 " € , ^
κύειν ἀνάγκη ταύτην. ἀληθὲς μὲν οὖν ἐν ἅπασιν ὑπάρξει τοῖς
>
σημείοις, διαφορὰς δ᾽ ἔχουσι τὰς εἰρημένας.
Ἢ δὴ e 8 , ki ^ ^ A M ,
ἡ οὕτω διαιρετέον τὸ σημεῖον, τούτων δὲ τὸ μέσον
ὔ ^
τεκμήριον ληπτέον (τὸ yàp τεκμήριον τὸ εἰδέναι ποιοῦν φα-
σὶν εἶναι, τοιοῦτο δὲ μάλιστα τὸ μέσον), 7 τὰ μὲν ἐκ τῶν
ἄκρων σημεῖον λεκτέον, τὰ δ᾽ ἐκ τοῦ μέσου τεκμήριον. ἐνδο-
# A ^ , 3 1 ^ ^ ~ L4 ,
£órarov yàp xai μάλιστα ἀληθὲς τὸ διὰ τοῦ πρώτου σχή-
ματος.
Τὸ δὲ φυσιογνωμονεῖν δυνατόν ἐστιν, εἴ τις δίδωσιν ἅμα
μεταβάλλεν τὸ σῶμα καὶ τὴν ψυχὴν ὅσα φυσικά ἐστι
παθήματα' μαθὼν γὰρ ἴσως μουσικὴν μεταβέβληκέ τι τὴν
’ > > > ~ , € -^ 3 M ~ * La > »
ψυχήν, ἀλλ᾽ οὐ τῶν φύσει ἡμῖν ἐστὶ τοῦτο τὸ πάθος, ἀλλ
οἷον ὀργαὶ καὶ ἐπιθυμίαι τῶν φύσει κινήσεων. εἰ δὴ τοῦτό τε
ὃ 0 , M ^ ea ~ RA M δ d θ À ,
οθείη καὶ ἕν ἑνὸς σημεῖον εἶναι, καὶ δυναίμεθα λαμβάνειν
τὸ ἴδιον ἑκάστου γένους πάθος καὶ σημεῖον, δυνησόμεθα φυ-
σιογνωμονεῖν. εἰ γάρ ἐστιν ἰδίᾳ τινὶ γένει ὑπάρχον ard,
' ς
, ^ 3 i > * ^
πάθος, olov τοῖς λέουσιν ἀνδρεία, ἀνάγκη καὶ σημεῖον εἶναί
Tv συμπάσχειν γὰρ ἀλλήλοις ὑπόκειται. καὶ ἔστω τοῦτο τὸ
tA A > Ζ » "^ b L4 € , Li
μεγάλα τὰ ἀκρωτήρια ἔχειν: ὃ xai ἄλλοις ὑπάρχειν yé-
νεσι μὴ ὅλοις ἐνδέχεται. τὸ γὰρ σημεῖον οὕτως ἴδιόν ἐστιν,
- e / p] ΄ » 10. ' » 4 ἴδ
ὅτι ὅλου γένους ἴδιόν ἐστι [πάθος], καὶ οὐ μόνου ἴδιον,
ὥσπερ εἰώθαμεν λέγειν. ὑπάρξει δὴ καὶ ἐν ἄλλῳ γένει
τοῦτο, καὶ ἔσται ἀνδρεῖος [6] ἄνθρωπος καὶ ἄλλο τι ζῷον.
ἔξει ἄρα τὸ σημεῖον: ἕν γὰρ ἑνὸς ἦν. εἰ τοίνυν ταῦτ᾽ ἐστί,
M , LJ ^ L4 * X , ~
. καὶ δυνησόμεθα τοιαῦτα σημεῖα συλλέξαι ἐπὶ τούτων τῶν
25
, ^ , ^ , L4 LÀ LÀ , L4
ζῴων ἃ μόνον ἕν πάθος ἔχει τι ἴδιον, ἕκαστον δ᾽ ἔχει on-
μεῖον, ἐπείπερ ἕν ἔχειν ἀνάγκη, δυνησόμεθα φυσιογνωμο-
- » * , LJ LÀ L4 ^ ΄, e , > ^
νεῖν. εἰ δὲ δύο ἔχει ἴδια ὅλον τὸ γένος, olov 6 λέων ἀνδρεῖον
431 ἀληθὴς n! 33 ἀνάγκη δῃῖε διὰ 5 34 εἶναι σοφούς d br Ἢ δὴ ἤδη
An: εἰ 85 fecit C: ἣ εἰ δὴ d 2 λεκτέον nT” 4onpetaC τὸ CT
5 καὶ δ ὁ τὸ οἴῃ. B 8 ἐστὶ φυσικὰ C 9 ἴσως-Ἐτις C 10 τὸ]
τι ἃ 12 δυνάμεθα Β λαβεῖν d 13 καὶ] τε καὶ "Ξὀ ὀ δυνησόμεθα καὶ
φυσιογνωμονεῖν C 15 καὶ -- τὸ πὶ 19 πάθος seclusi, om. fort. P:
τὸ πάθος (πὶ 20 €vom.C 21 τοῦτο CnI': ταὐτὸ 48Βά ὁ seclusi
24 ἅ-ἰ kai C 25 ἐπεὶ γὰρ d évom. nr
27. 70°31->38
καὶ μεταδοτικόν, πῶς γνωσόμεθα πότερον ποτέρου σημεῖον
τῶν ἰδίᾳ ἀκολουθούντων είων; ἢ εἰ ἄλλῳ τινὶ μὴ ὅλ
: σημείων; ἢ : μὴ ὅλῳ
M x > T M Ld € 4 Ld A * LA :
ἄμφω, kai ἐν οἷς μὴ ὅλοις ἑκάτερον, ὅταν τὸ μὲν ἔχη τὸ
δὲ μή: εἰ γὰρ ἀνδρεῖος μὲν ἐλευθέριος δὲ μή, ἔχει δὲ τῶν 30
δύο τοδί, δῆλον ὅτι καὶ ἐπὶ τοῦ λέοντος τοῦτο σημεῖον τῆς
ἀνδρείας. 32
w * ^ ^ ~ » ~ 4^ ,
Ἔστι δὴ τὸ φυσιογνωμονεῖν τῷ ἐν τῷ πρώτῳ σχή- 32
ματι τὸ μέσον τῷ μὲν πρώτῳ ἄκρῳ ἀντιστρέφειν, τοῦ δὲ τρί-
του ὑπερτείνειν καὶ μὴ ἀντιστρέφειν, οἷον ἀνδρεία τὸ Α, τὰ
ἀκρωτήρια μεγάλα ἐφ᾽ οὗ B, τὸ δὲ I' λέων. ᾧ δὴ τὸ Ty ἃς
τὸ Β παντί, ἀλλὰ καὶ ἄλλοις. ᾧ δὲ τὸ Β, τὸ Α παντὶ
M » l4 5 > > LÀ > y Τὴ *, μὴ «
καὶ οὐ πλείοσιν, ἀλλ᾽ ἀντιστρέφει: εἰ δὲ μή, οὐκ ἔσται ἕν
ἑνὸς σημεῖον.
b28 ἄλλῳ τινὶ μὴ ὅλῳ Cn: τε ἄλλῳ μὴ ὅλῳ τινὶ ABd Zoe... μὴ
oim, Bt 31-2 τοῦτο... ἀνδρείας] σημεῖον τοῦτο ἀνδρίας ἐστίν C 32
τῷ] τῶν AB: τὸ Ci? 43 τὸ μὲν πρῶτον τῷ ἄκρῳ n! 34 ἀνδρία C
τὰ] τὸς 16 τὸ fecitB ἄλλας 4 Seéfecitn τῷ α ηξ
ANAAYTIKON YZTEPOQN A.
71* Πᾶσα διδασκαλία xai πᾶσα μάθησις διανοητικὴ ἐκ mpoü-
παρχούσης γίνεται γνώσεως. φανερὸν δὲ τοῦτο θεωροῦσιν ἐπὶ
πασῶν: ai τε γὰρ μαθηματικαὶ τῶν ἐπιστημῶν διὰ τούτου
τοῦ τρόπου παραγίνονται καὶ τῶν ἄλλων ἑκάστη τεχνῶν.
LÀ ~
5 ὁμοίως δὲ Kal περὶ τοὺς λόγους oi τε διὰ συλλογισμῶν Kai
Hi , , ^
οἱ δι’ ἐπαγωγῆς: ἀμφότεροι yàp διὰ προγινωσκομένων ποι-
~ ‘ διῶ αλί ε * A ΄ « ^ LA
οὔνται τὴν διδασκαλίαν, of μὲν λαμβάνοντες ὡς παρὰ ξυνιέν-
* b z M , M ~ ^ M »
των, of δὲ δεικνύντες τὸ καθόλου διὰ τοῦ δῆλον εἶναι τὸ καθ
ἕκαστον. ὡς δ᾽ αὔτως καὶ οἱ ῥητορικοὶ συμπείθουσιν- 7) γὰρ
10 διὰ παραδειγμάτων, ὅ ἐστιν ἐπαγωγή, ἢ δι’ ἐνθυμημάτων,
ὅπερ ἐστὶ συλλογισμός. διχῶς δ᾽ ἀναγκαῖον προγινώσκειν"
τὰ μὲν γάρ, ὅτι ἔστι, προὐὔὐπολαμβάνειν ἀναγκαῖον, τὰ δέ,
τί τὸ λεγόμενόν ἐστι, ξυνιέναι δεῖ, τὰ δ᾽ dud«o, οἷον ὅτι
* LÀ - ~ - > ^ > r4 - L4 4 ^ ,
μὲν ἅπαν 7j φῆσαι ἢ ἀποφῆσαι ἀληθές, ὅτι ἔστι, τὸ δὲ τρί-
L4 N. , M x L4 w 4 ,
15 γωνον, ὅτι τοδὶ σημαίνει, THY δὲ μονάδα ἄμφω, Kai τί ση-
μαίνει καὶ ὅτι ἔστιν. οὐ γὰρ ὁμοίως τούτων ἕκαστον δῆλον
1 ἡμῖν.
LÀ * , x x , , ^ A
17 Ἔστι δὲ γνωρίζειν τὰ μὲν πρότερον γνωρίσαντα, τῶν δὲ
καὶ ἅμα λαμβάνοντα τὴν γνῶσιν, οἷον ὅσα τυγχάνει ὄντα
ὑπὸ τὸ καθόλου οὗ ἔχει τὴν γνῶσιν. ὅτι μὲν γὰρ πᾶν τρί-
μὴ A 3 ^ LÀ E a x , ᾿ * ^
20 ywrov ἔχει δυσὶν ὀρθαῖς ἴσας, προήδει" ὅτι δὲ τόδε τὸ ἐν TH
ἡμικυκλίῳ τρίγωνόν ἐστιν, ἅμα ἐπαγόμενος ἐγνώρισεν. (ἐνίων
γὰρ τοῦτον τὸν τρόπον ἡ μάθησίς ἐστι, καὶ οὐ διὰ τοῦ μέσου
τὸ ἔσχατον γνωρίζεται, ὅσα ἤδη τῶν Kal? ἕκαστα τυγχά-
ver ὄντα καὶ μὴ καθ᾽ ὑποκειμένου τινός.) πρὶν δ᾽ ἐπαχθῆναι
^ ^ * , , LÀ “ Ἐπ - A
257) λαβεῖν συλλογισμὸν τρόπον μέν τινα ἴσως φατέον ἐπίστα-
, > LÀ » ^ A ^ L4 > LÀ € ~
σθαι, τρόπον δ᾽ ἄλλον ov. ὃ yap μὴ ἤδει εἰ ἔστιν ἁπλῶς,
τοῦτο πῶς ye. ὅτι δύο ὀρθὰς ἔχει ἁπλῶς; ἀλλὰ δῆλον ὡς
egy A , , σ rà > , € ^ 2 ,
di μὲν ἐπίσταται, ὅτι καθόλου ἐπίσταται, ἁπλῶς δ᾽ οὐκ
ΕΑΝ , * , * > ^ , > , L4
ἐπίσταται. εἰ δὲ μή, τὸ ἐν τῷ Μένωνι ἀπόρημα συμβήσεται"
Ἂ M ὃ A 0 L4 hd ^ t& > M E] , " ,
307) yàp οὐδὲν μαθήσεται ἢ d οἶδεν. οὐ yap δή, ws γέ τινες
> ~ , 2, rT > - A LÀ
ἐγχειροῦσι λύειν, λεκτέον. dp’ οἶδας ἅπασαν δυάδα ὅτι
7144 περιγίνονται C 5 διὰ - τῶν n 6 γὰρ om. 5 ὃ τοῦ] τὸ
Cd 9 ὡσαύτως δὲ C: ὡσαύτως B τι ὅς 13 συνιέναι C
δεῖ] δὴ n! 14 ἅπαν μὲν Β 17 πρότερα C γνωρίσαντα scripsi :
γνωρίζοντα codd. 19 οὗ scripsi, habent PT: ὧν codd. ἅπαν d
28 ὅτι- τὸ Cn
I. 711-2. 71533
> , - ν , * , ’, , ^ *, L4 ?
dpria ἢ οὔ; φήσαντος δὲ προήνεγκάν twa δυάδα Tv οὐκ der
- > 293 > , , M Ἵ , » , ~
εἶναι, ὥστ᾽ οὐδ᾽ apriav. λύουσι yàp οὐ φάσκοντες εἰδέναι πᾶ-
, , rd ^ > } « ΝΜ Ld , ,
σαν δυάδα apriav οὖσαν, add’ ἣν ἴσασιν ὅτι δυάς. καίτοι
ἴσασι μὲν οὗπερ τὴν ἀπόδειξιν ἔχουσι καὶ οὗ ἔλαβον, ἔλα- 71>
> » 4 A T * Qa a , -^ ov > ,
Bov δ᾽ οὐχὶ παντὸς οὗ ἂν εἰδῶσιν ὅτι τρίγωνον ἢ ὅτι ἀριθμός,
t ~ ~
GAN ἁπλῶς κατὰ παντὸς ἀριθμοῦ Kai τριγώνου: οὐδεμία
M la , Li Ld ^ M tà > 6
yàp πρότασις λαμβάνεται τοιαύτη, ὅτι dv σὺ οἶδας ἀριθ-
^ , » >?
μὸν ἢ ὃ σὺ οἶδας εὐθύγραμμον, ἀλλὰ κατὰ παντός. ἀλλ᾽ ς
, p , a L4 L4 LA > , LÀ
οὐδέν (οἶμαι) κωλύει, ὃ μανθάνει, ἔστιν ὡς ἐπίστασθαι, ἔστι
? e 2 - L4 ^ ΕΣ ᾽ , ^ , > ,
δ᾽ ὡς dyvoeiv: ἄτοπον yàp οὐκ εἰ οἶδέ πως ὃ μανθάνει, ἀλλ
᾽ δέ Lu T ^ A €
εἰ ὡδί, olov # μανθάνει Kai ws.
2 ᾿Επίστασθαι δὲ οἰόμεθ᾽ ἕκαστον ἁπλῶς, ἀλλὰ μὴ TOv
,
σοφιστικὸν τρόπον τὸν κατὰ συμβεβηκός, ὅταν THY τ᾽ αἰτίαν το
οἰώμεθα γινώσκειν δι’ ἣν τὸ πρᾶγμά ἐστιν, ὅτι ἐκείνου αἰτία
> , * εἶ » ¥ a > L4 v ^ , a
ἐστί, kai μὴ ἐνδέχεσθαι τοῦτ᾽ ἄλλως ἔχειν. δῆλον τοίνυν ὅτι
τοιοῦτόν τι τὸ ἐπίστασθαί ἐστι: καὶ γὰρ οἱ μὴ ἐπιστάμενοι καὶ
οἱ ἐπιστάμενοι οἱ μὲν οἴονται αὐτοὶ οὕτως ἔχειν, οἱ δ᾽ ἐπιστά-
μενοι καὶ ἔχουσιν, ὥστε οὗ ἁπλῶς ἔστιν ἐπιστήμη, τοῦτ᾽ ἀδύνατον 15
ἄλλως ἔχειν. 16
, i lod 3 cw L4 a > , ,
Εἰ μὲν οὖν kai ἕτερος ἔστι τοῦ ἐπίστασθαι τρόπος, 16
L4 d ^ a 3 * , > H » , > ,
ὕστερον ἐροῦμεν, φαμὲν δὲ καὶ δι᾽ ἀποδείξεως εἰδέναι. ἀπό-
ὃ δὲ , ÀA x , , , X δὲ
εἰξιν δὲ λέγω συλλογισμὸν ἐπιστημονικόν: ἐπιστημονικὸν δὲ
λέγω καθ᾽ ὃν τῷ ἔχειν αὐτὸν ἐπιστάμεθα. εἰ τοίνυν ἐστὶ τὸ ἐπί-
> 3
στασθαι otov ἔθεμεν, ἀνάγκη kai τὴν ἀποδεικτικὴν ἐπιστήμην ἐξ 20
ἀληθῶν τ᾽ εἶναι καὶ πρώτων καὶ ἀμέσων καὶ γνωριμωτέρων
καὶ προτέρων καὶ αἰτίων τοῦ συμπεράσματος" οὕτω γὰρ ἔσον-
ται καὶ αἱ ἀρχαὶ οἰκεῖαι τοῦ δεικνυμένου. συλλογισμὸς μὲν
A L4 ^ we L4 > “ὃ δ᾽ > L4 ΕἸ A
yap ἔσται kai ἄνευ τούτων, ἀπόδειξις δ᾽ οὐκ ἔσται: οὐ yàp
, *, , > ~ M T ^ LJ a *, v * A
ποιήσει ἐπιστήμην. ἀληθῆ μὲν οὖν δεῖ εἶναι, ὅτι οὐκ ἔστι τὸ μὴ 25
ὃν ἐπίστασθαι, οἷον ὅτι ἡ διάμετρος σύμμετρος. ἐκ πρώτων
, a
δ᾽ ἀναποδείκτων, ὅτι οὐκ ἐπιστήσεται μὴ ἔχων ἀπόδειξιν αὐ-
^ 4 x , , T > , v A A
τῶν: τὸ γὰρ ἐπίστασθαι ὧν ἀπόδειξις ἔστι μὴ κατὰ συμβε-
, A v M
βηκός, τὸ ἔχειν ἀπόδειξίν ἐστιν. αἴτιά Te Kal γνωριμώτερα
^ * , Ld
δεῖ εἶναι kai πρότερα, αἴτια μὲν ὅτι τότε ἐπιστάμεθα ὅταν 3o
᾿ ~
τὴν αἰτίαν εἰδῶμεν, kal πρότερα, εἴπερ αἴτια, Kal mpoyt-
νωσκόμενα οὐ μόνον τὸν ἕτερον τρόπον τῷ ξυνιέναι, ἀλλὰ καὶ
^ > , a M , > > M ‘ L4 ~
τῷ εἰδέναι ὅτι ἔστιν. πρότερα δ᾽ ἐστὶ Kai γνωριμώτερα διχῶς"
b6 μανθάνειν ἔστι μὲν ὡς n 10 T om. dP* 11 οἰόμεθα τ: 13 τι
om. C 14 αὐτὸ C 20 ἐθέμεθα Cn? 21 xai? om. C 24 yàp
ἔστι Cd 25 Set εἶναι fecit. A? 30 Set... πρότερα fecit B
ANAAYTIKQN YETEPQN A
οὐ yap ταὐτὸν πρότερον TH φύσει kai πρὸς ἡμᾶς πρότερον,
72* οὐδὲ γνωριμώτερον καὶ ἡμῖν γνωριμώτερον. λέγω δὲ πρὸς
ἡμᾶς μὲν πρότερα καὶ γνωριμώτερα τὰ ἐγγύτερον τῆς al-
σθήσεως, ἁπλῶς δὲ πρότερα καὶ γνωριμώτερα τὰ πορρώτε-
ον. ἔστι δὲ πορρωτάτω μὲν τὰ καθόλου μάλιστα, ἐγγυτάτω
2
‘A Ἂν > Ld * > Li a 55 > , > 4
5 δὲ rà καθ᾽ éxacra- καὶ ἀντίκειται ταῦτ᾽ ἀλλήλοις. ἐκ πρώ-
των δ᾽ ἐστὶ τὸ ἐξ ἀρχῶν οἰκείων: ταὐτὸ γὰρ λέγω πρῶτον
,
xai ἀρχήν. ἀρχὴ δ᾽ ἐστὶν ἀποδείξεως πρότασις ἄμεσος,
LÀ δὲ LJ L4 » , > » M >
ἄμεσος δὲ ἧς μὴ ἔστιν ἄλλη προτέρα. πρότασις δ᾽ ἐστὶν ἀπο-
, A L4 , ^ » K * * €
φάνσεως τὸ ἕτερον μόριον, ἕν καθ᾽ ἑνός, διαλεκτικὴ μὲν ἡ
“- €
10 ὁμοίως λαμβάνουσα ὁποτερονοῦν, ἀποδεικτικὴ δὲ ἡ wpt-
σμένως θάτερον, ὅτι ἀληθές. ἀπόφανσις δὲ ἀντιφάσεως ὅπο-
~ , 3, , a 3 7, *, L4 *
τερονοῦν μόριον, ἀντίφασις δὲ ἀντίθεσις ἧς οὐκ ἔστι μεταξὺ
» ig ΄, , 5 > Ld ^ M M ^ ^ ΄
καθ᾽ αὑτήν, μόριον δ᾽ ἀντιφάσεως τὸ μὲν τὶ κατὰ τινὸς κατά-
^ * +? A % , ,
14 φασις, τὸ δὲ τὶ ἀπὸ τινὸς ἀπόφασις.
, L4 > >
14 Auécov δ᾽ ap-
15 χῆς συλλογιστικῆς θέσιν μὲν λέγω ἣν μὴ ἔστι δεῖξαι, μηδ᾽
ἀνάγκη ἔχειν τὸν μαθησόμενόν rv ἣν δ᾽ ἀνάγκη ἔχειν τὸν
ὁτιοῦν μαθησόμενον, ἀξίωμα: ἔστι γὰρ ἔνια τοιαῦτα" τοῦτο
4 , ? 9» t - , vs » ’ ,
yap μάλιστ᾽ ἐπὶ τοῖς τοιούτοις εἰώθαμεν ὄνομα λέγειν. θέσεως
δ᾽ ἡ μὲν ὁποτερονοῦν τῶν μορίων τῆς ἀντιφάσεως λαμβά-
Hd t
20 vouca, olov λέγω τὸ elvai τι ἢ TO μὴ elvat τι, ὑπόθεσις, ἡ
δ᾽ ἄνευ τούτου ὄρισμός. 6 γὰρ ὁρισμὸς θέσις μέν ἐστι" τίθε-
ται γὰρ 6 ἀριθμητικὸς μονάδα τὸ ἀδιαίρετον εἶναι κατὰ τὸ
ποσόν: ὑπόθεσις δ᾽ οὐκ ἔστι" τὸ γὰρ τί ἐστι μονὰς καὶ τὸ εἶ-
ναι μονάδα οὐ ταὐτόν.
> M * a dé M > , M ^ ^
25 ᾿Επεὶ δὲ δεῖ πιστεύειν τε καὶ εἰδέναι τὸ πρᾶγμα τῷ
~ LÀ ^ ^ ~ > , LÀ ᾽
τοιοῦτον ἔχειν συλλογισμὸν ὃν καλοῦμεν ἀπόδειξιν, ἔστι ὃ
ha ~ δὶ H ἐξ T e λλι , > , A "d
οὗτος τῷ ταδὶ εἶναι ἐξ ὧν ὃ συλλογισμός, ἀνάγκη μὴ μόνον
^ 4 ~ n FQ * LA > ‘A ^ ^
Tpoywackew τὰ πρῶτα, ἢ πάντα ἢ ἔνια, ἀλλὰ Kal μᾶλ-
*,* 4A » ^ e ‘ L4 > , ^ [4 ,
λον: αἰεὶ yàp δι’ ὃ ὑπάρχει ἕκαστον, exeivw μᾶλλον ὑπάρ-
30 χει, οἷον δι’ ὃ φιλοῦμεν, ἐκεῖνο φίλον μᾶλλον. ὥστ᾽ εἴπερ
^ "
ἴσμεν διὰ τὰ πρῶτα καὶ πιστεύομεν, κἀκεῖνα ἴσμεν τε καὶ
, ~ - > > ~ 5 MJ L4 , tó
πιστεύομεν μᾶλλον, ὅτι δι’ ἐκεῖνα καὶ τὰ ὕστερα. οὐχ οἷόν
72*6 ταὐτὸ δέ ἐστι πρῶτον καὶ ἀρχή C I1ó τ P ἀντιθέσεως d
12 ἔστι Er C 13 μόρια C τό τὸν- ὁτιοῦν 5 τι om. n* 17 ἔνια
ταῦτα C 18 ὄνομα om. C 19 ároóávaeus ABCA 20 τοῦ
om. C 21 μέν om. C 27 τάδ᾽ ABCd 29 ἐκείνῳ scripsi, habent
PCT: ἐκεῖνο codd. 30 εἴπερ) εἰπεῖν A 31 ἐκεῖνα C 32 μᾶλλον)
καὶ μᾶλλον 2 ὕστερον ÁBd
b b
2. 7134-3. 72 25
, ^
Te δὲ πιστεύειν μᾶλλον ὧν οἷδεν à μὴ τυγχάνει μήτε εἰδὼς
Nn ὃ , a > 3, 7 is , ,
μήτε βέλτιον διακείμενος ἢ εἰ ἐτύγχανεν εἰδώς. συμβήσεται
A EJ ^
δὲ τοῦτο, ei μή τις προγνώσεται τῶν OU ἀπόδειξιν πιστευὸν-
των" μᾶλλον γὰρ ἀνάγκη πιστεύειν ταῖς ἀρχαῖς ἢ πάσαις
ἢ τισὶ τοῦ συμπεράσματος. τὸν δὲ μέλλοντα ἕξειν τὴν ἐπι-
rd ‘ 3 Σ ,ὔ > , ^ M > A ^
στήμην τὴν δι’ ἀποδείξεως od μόνον δεῖ τὰς ἀρχὰς μᾶλλον
, A ^ ^ , ~
γνωρίζειν καὶ μᾶλλον αὐταῖς πιστεύειν ἢ TQ δεικνυμένῳ,
3 M > L4 t i ~ , 4 ,
ἀλλὰ μηδ᾽ ἄλλο αὐτῷ πιστότερον εἶναι μηδὲ γνωριμώτερον
^ > ^ > ^
τῶν ἀντικειμένων ταῖς ἀρχαῖς ἐξ ὧν ἔσται συλλογισμὸς ὁ
^ , ^ ~
τῆς ἐναντίας ἀπάτης, εἴπερ δεῖ τὸν ἐπιστάμενον ἁπλῶς ἀμετά-
πειστον εἶναι.
᾿Ἑνίοις μὲν οὖν διὰ τὸ δεῖν τὰ πρῶτα ἐπίστασθαι οὐ δοκεῖ
ἐπιστήμη εἶναι, τοῖς δ᾽ εἶναι μέν, πάντων μέντοι ἀπόδειξις
- , , wey > A “Μ᾿ > a e * ^
εἶναι: ὧν οὐδέτερον οὔτ᾽ ἀληθὲς οὔτ᾽ ἀναγκαῖον. οἱ μὲν yap
τ , M a » LÀ Ὁ 3 » > ^
ὑποθέμενοι μὴ εἶναι ὅλως ἐπίστασθαι, οὗτοι εἰς ἄπειρον ἀξιοῦ-
σιν ἀνάγεσθαι ὡς οὐκ ἂν ἐπισταμένους τὰ ὕστερα διὰ τὰ
πρότερα, ὧν μὴ ἔστι πρῶτα, ὀρθῶς λέγοντες: ἀδύνατον γὰρ
τὰ ἄπειρα διελθεῖν. εἴ τε ἵσταται καὶ εἰσὶν ἀρχαΐ, ταύτας
ἀγνώστους εἶναι ἀποδείξεώς γε μὴ οὔσης αὐτῶν, ὅπερ φασὶν
εἶναι τὸ ἐπίστασθαι μόνον: εἰ δὲ μὴ ἔστι τὰ πρῶτα εἰδέναι,
οὐδὲ τὰ ἐκ τούτων εἶναι ἐπίστασθαι ἁπλῶς οὐδὲ κυρίως, ἀλλ᾽
2 e L4 , , ^ L4 e ^ ^ x a ,
ἐξ ὑποθέσεως, εἰ ἐκεῖνα ἔστιν. οἱ δὲ περὶ μὲν τοῦ ἐπίστασθαι
Lj ^ > 3 L * , 3 * s,
ὁμολογοῦσι: δι᾽ ἀποδείξεως yap εἶναι μόνον: ἀλλὰ πάντων
> , 3 Hi , > ; ^ , ^
εἶναι ἀπόδειξιν οὐδὲν κωλύειν: ἐνδέχεσθαι yap κύκλῳ yive-
σθαι τὴν ἀπόδειξιν καὶ ἐξ ἀλλήλων.
ς ^ , L4
Ἡμεῖς δέ φαμεν οὔτε
^ E , > ^4 3 M A ~ , H
πᾶσαν ἐπιστήμην ἀποδεικτικὴν εἶναι, ἀλλὰ THY τῶν ἀμέσων
ἀναπόδεικτον (καὶ τοῦθ᾽ ὅτι ἀναγκαῖον, φανερόν: εἰ γὰρ
3 , A , , X à τ ? Ls £. > »
ἀνάγκη μὲν ἐπίστασθαι τὰ πρότερα καὶ ἐξ ὧν ἡ ἀπόδειξις,
ἵσταται δέ ποτε τὰ ἄμεσα, ταῦτ᾽ ἀναπόδεικτα ἀνάγκη εἶναι)---
^ , » νι τὶ L4 L] > , > ὔ > ^
ταῦτά τ᾽ οὖν οὕτω Aeyouev, kai οὐ μόνον ἐπιστήμην ἀλλὰ
M > ^ 2 ἅ Ld
kal ἀρχὴν ἐπιστήμης elvai τινά φαμεν, fj τοὺς ὅρους γνω-
ρίζομεν. κύκλῳ τε ὅτι ἀδύνατον ἀποδείκνυσθαι ἁπλῶς, δῆ-
~
433 πιστεύομεν A τυγχάνῃ Ald 35 δι om. B ὃς ἐπίστασθαι
τὰ πρῶτα 6 ἐπιστήμην" ἀποδείξεις ABCn 8 ὅλως πῆ : ἄλλως
ABCédn IO ἔσται C τ δὲ ΟΤ ἵστανται C 14 ἐπίστασθαι
εἶναι Β 15 εἰ om, d! 17 ἐνδέχεται Cd 18 οὐ Bt 20 ava-
ποδείκτων d 22 more τὰ ἄμεσα A BdP: ποτε τὰ μέσα n: τὰ ἄμεσά more C
23 τ᾽ om. A 24 τινά ABCPS: τί dn 25 re ὅτι] δὲ ὅτι C?n*P : τὸ τί
AB: θ᾽ ὅτι ΒΞ: τὸ ὅτι dt
35
72»
IO
18
20
25
ANAAYTIKON YZTEPON A
w 5 , ^ * > , Η
λον, εἴπερ ἐκ προτέρων δεῖ τὴν ἀπόδειξιν εἶναι καὶ γνωριμω-
τέρων- ἀδύνατον γάρ ἐστι τὰ αὐτὰ τῶν αὐτῶν ἅμα πρότερα
καὶ ὕστερα εἶναι, εἰ μὴ τὸν ἕτερον τρόπον, οἷον τὰ μὲν πρὸς
ἡμᾶς τὰ δ᾽ ἁπλῶς, ὅνπερ τρόπον ἡ ἐπαγωγὴ ποιεῖ γνώρι-
, > L4 , n LÀ A € ^ » , ^ €
3o μον. εἰ δ᾽ οὕτως, οὐκ ἂν εἴη TO ἁπλῶς εἰδέναι καλῶς dpt-
, ? A f ^ > € ~ t « , 3 ,
σμένον, ἀλλὰ διττόν: ἢ οὐχ ἁπλῶς ἡ ἑτέρα ἀπόδειξις, ywo-
> ~ ^ ^
μένη γ᾽ ἐκ τῶν ἡμῖν γνωριμωτέρων. συμβαίνει δὲ τοῖς λέγουσι
, ι > , 4 ΕΣ , * LJ > L4 > »
κύκλῳ τὴν ἀπόδειξιν εἶναι οὐ μόνον τὸ νῦν εἰρημένον, ἀλλ
γι » , ^ c ^» » , ^5» L4 M ,
οὐδὲν ἄλλο λέγειν ἣ ὅτι τοῦτ᾽ ἔστιν εἰ τοῦτ᾽ ἔστιν: οὕτω δὲ πάντα
cs ^ ^ LI L4 ^ , ~ Ld
35 ῥάδιον δεῖξαι. δῆλον δ᾽ ὅτι τοῦτο συμβαίνει τριῶν ὅρων τε-
, M X ^ Ἂν ~ ^ > lA WI > f
θέντων. τὸ μὲν yap διὰ πολλῶν ἢ δ᾽ ὀλίγων ἀνακάμπτειν
, * * , > 53 7 > na ~ σ ^ ^
φάναι οὐδὲν διαφέρει, δ᾽ ὀλίγων OV ἢ δυοῖν. Grav yàp τοῦ
A ὄντος ἐξ ἀνάγκης ἡ τὸ B, τούτου δὲ τὸ I, τοῦ A ὄντος
v M ᾽ν A ^ L4 2 / a , >
ἔσται τὸ Γ. εἰ δὴ τοῦ A ὄντος ἀνάγκη τὸ B εἶναι, τούτου ὃ
73° ὄντος τὸ A (τοῦτο γὰρ ἦν τὸ κύκλῳ), κείσθω τὸ A ἐφ᾽ οὗ
τὸ Γ. τὸ οὖν τοῦ Β ὄντος τὸ Α εἶναι λέγειν ἐστὶ τὸ Γ εἶναι λέ-
yew, τοῦτο δ᾽ ὅτι τοῦ Α ὄντος τὸ Γ ἔστι: τὸ δὲ Γ τῷ Α τὸ
᾽ , e , LÀ A 7 y
αὐτό. dore συμβαίνει λέγειν τοὺς κύκλῳ φάσκοντας εἶναι
M 3 , $ * e M Ld ^ » M LÀ
5 τὴν ἀπόδειξιν οὐδὲν ἕτερον πλὴν ὅτι τοῦ A ὄντος τὸ A ἔστιν.
d a L4 ^ ce
6 οὕτω δὲ πάντα δεῖξαι ῥάδιον.
6 Od μὴν ἀλλ᾽ οὐδὲ τοῦτο δυνατόν,
M 3.* , ^ - > , v L4 * LÀ €
πλὴν ἐπὶ τούτων ὅσα ἀλλήλοις ἕπεται, ὥσπερ τὰ ἴδια. ἑνὸς
x * LA » μὲ , , > > , Ld
μὲν οὖν κειμένου δέδεικται ὅτι οὐδέποτ᾽ ἀνάγκη τι εἶναι ére-
, > €* ὔ Ld » - $-.* LÀ , - ,
pov (λέγω δ᾽ évós, ὅτι οὔτε ὅρου ἑνὸς οὔτε θέσεως μιᾶς τεθεί-
2 , * /, P a M > , u 7
το ans), ἐκ δύο δὲ θέσεων πρώτων καὶ ἐλαχίστων ἐνδέχεται,
LÀ x , ye x T , A ^ ^ ~
εἴπερ kai συλλογίσασθαι. ἐὰν μὲν οὖν τό τε A τῷ B καὶ τῷ
Γ ἕπηται, καὶ ταῦτ᾽ ἀλλήλοις καὶ τῷ A, οὕτω μὲν ἐνδέ-
3 3 , , /, M ? , » : ^
χεται ἐξ ἀλλήλων δεικνύναι πάντα τὰ αἰτηθέντα ἐν τῷ
πρώτῳ σχήματι, ὡς δέδεικται ἐν τοῖς περὶ συλλογισμοῦ.
/ X e. Ld > ^ L4 , hal , ,
15 δέδεικται δὲ kal ὅτι ἐν τοῖς ἄλλοις σχήμασιν ἢ od γίνεται
^ ^ » n ^ Li A * * >
συλλογισμὸς ἢ οὐ περὶ τῶν ληφθέντων. τὰ δὲ μὴ ἀντικατη-
, ὃ ~ L4 ^ ^ Xr L4 > 3 ^ la WA
yopovpeva οὐδαμῶς ἔστι δεῖξαι κύκλῳ, ὥστ᾽ ἐπειδὴ ὀλίγα τοι-
αῦτα ἐν ταῖς ἀποδείξεσι, φανερὸν ὅτι κενόν τε καὶ ἀδύνα-
bag ποιήσει ἡ 31 γινομένη γ᾽ scripsi: γινομένη ἡ BCdn: γινομένη A:
ἡ γινομένη PS 33 τὸ] τὸν Β 34 e] ἢ d! 34-5 padiov
πάντα C 37 δι om. C 38 τὸ Bom. d! 7331 τὸ 411) ἀνάγκη
τὸ a εἶναι ἢ 2 τοῦ om. A τοῦ dt τὸ- τὸ AB*C2dn? εἶναι om.
AB Mdn! λέγειν om. B 3701] τοῦ &! ἔστι om. n 4 λέγειν
post 5 ἕτερον C 8 τι εἶναι] εἶναι τὸ n I2 καὶ τῷ Aom, ΟΣ
15 ὅτι καὶ B 17 ἐπεὶ d τοιαῦτα ὀλίγα C 18 τι ἃ
3. 72°26-4. 73°12
tov τὸ λέγειν ἐξ ἀλλήλων εἶναι τὴν ἀπόδειξιν καὶ διὰ τοῦτο
, » , 3 ,
πάντων ἐνδέχεσθαι εἶναι ἀπόδειξιν. 20
4 "Ἐπεὶ 9' ἀδύνατον ἄλλως ἔχειν οὗ ἔστιν ἐπιστήμη ἁπλῶς,
ἀναγκαῖον ἂν εἴη τὸ ἐπιστητὸν τὸ κατὰ τὴν ἀποδεικτικὴν ἐπι-
, , * , > a a LÀ ^ " > ,
oTnpny: ἀποδεικτικὴ δ᾽ ἐστὶν ἣν ἔχομεν TH ἔχειν ἀπόδειξιν.
> 3 , L4 , > € > , ,
ἐξ ἀναγκαίων dpa συλλογισμός ἐστιν ἡ ἀπόδειξις. ληπτέον
dpa ἐκ τίνων καὶ ποίων αἱ ἀποδείξεις εἰσίν. πρῶτον δὲ διορί- 25
σωμεν τί λέγομεν τὸ κατὰ παντὸς καὶ τί τὸ καθ᾽ αὑτὸ καὶ
τί τὸ καθόλου.
^ T M > 4
4 EJ
Kara παντὸς μὲν οὖν τοῦτο λέγω ὃ dv jj μὴ ἐπὶ τινὸς
* M ΕἾ ΄ M * * ' ^ , * , M
μὲν τινὸς δὲ μή, μηδὲ ποτὲ μὲν ποτὲ δὲ μή, olov εἰ κατὰ
A > , ~ > > * , > > ^ L4
παντὸς ἀνθρώπου ζῷον, et ἀληθὲς τόνδ᾽ εἰπεῖν ἄνθρωπον, 3o
, x M ~ M 3 ^ , * , M > 3
ἀληθὲς kai ζῷον, kai ef viv θάτερον, καὶ θάτερον, καὶ εἰ ἐν
πάσῃ γραμμῇ στιγμή, ὡσαύτως. σημεῖον δέ: καὶ γὰρ τὰς
ἐνστάσεις οὕτω φέρομεν ὡς κατὰ παντὸς ἐρωτώμενοι, ἢ εἰ ἐπί
τινι μή, ἢ εἴ ποτε μή. 34
5 € M > Ed t , ?
Kal? αὑτὰ δ᾽ ὅσα ὑπάρχει τε ἐν 34
τῷ τί ἐστιν, οἷον τριγώνῳ γραμμὴ καὶ γραμμῇ στιγμή (ἡ 35
γὰρ οὐσία αὐτῶν ἐκ τούτων ἐστί, καὶ ἐν τῷ λόγῳ τῷ λέγοντι
τί ἐστιν ἐνυπάρχει), καὶ ὅσοις τῶν ὑπαρχόντων αὐτοῖς αὐτὰ
ἐν τῷ λόγῳ ἐνυπάρχουσι τῷ τί ἐστι δηλοῦντι, οἷον τὸ εὐθὺ
ὑπάρχει γραμμῇ καὶ τὸ περιφερές, καὶ τὸ περιττὸν καὶ
ἄρτιον ἀριθμῷ, καὶ τὸ πρῶτον καὶ σύνθετον, καὶ ἰσόπλευ- 4o
pov καὶ érepóumkes: καὶ πᾶσι τούτοις ἐνυπάρχουσιν ἐν τῷ 73
, ^ , , , L4 * A LÀ , ,
λόγῳ τῷ τί ἐστι λέγοντι ἔνθα μὲν γραμμὴ ἔνθα δ᾽ api-
, € , * * $ —4 ^ La M ^n e , p
Ünós. ὁμοίως δὲ Kai ἐπὶ τῶν ἄλλων rà τοιαῦθ᾽ ἑκάστοις Ka
e A , Ld 4 , € 4 ,
αὑτὰ λέγω, ὅσα δὲ μηδετέρως ὑπάρχει, συμβεβηκότα,
A A - i] ~ , LJ ^ 4 > €
οἷον τὸ μουσικὸν ἢ λευκὸν τῷ ζῴῳ. ἔτι ὃ μὴ καθ᾽ ὑποκει- 5
, , L4 , . A , μὴ , ^
μένου λέγεται ἄλλου τινός, otov τὸ βαδίζον ἕτερόν τι ὃν Ba-
, » ^ M M x L4 € » > , à o0€Y7 ,
δίζον ἐστὶ καὶ τὸ λευκὸν «λευκόν», ἡ δ᾽ οὐσία, καὶ ὅσα τόδε τι
onpaiver, οὐχ ἕτερόν τι ὄντα ἐστὶν ὅπερ ἐστίν. τὰ μὲν δὴ μὴ Kad”
^ a , L4
ὑποκειμένου Kal” αὑτὰ λέγω, rà δὲ καθ᾽ ὑποκειμένου συμ-
3» μὲ » L4 , M M > L4 A € ,
βεβηκότα. ἔτι δ᾽ ἄλλον τρόπον τὸ μὲν δι᾽ αὑτὸ ὑπάρχον το
« , u e , * 4 ‘A > € M , Ly >
ἑκάστῳ καθ᾽ αὑτό, τὸ δὲ μὴ δι’ αὑτὸ συμβεβηκός, οἷον εἰ
‘
βαδίζοντος ἤστραψε, συμβεβηκός: οὐ yap διὰ τὸ βαδίζειν
a19 τὸ om. d 20 ἐνδέχεται A BCd 20 pe! om. d 31 καὶ3]
πρὸς dt 33 ἐρωτωμένον A Bldn* εἰ om. d! 35 οἷον- ἐν n
37 ἐνυπάρχειν n) ὑπαρχόντων coni. Bonitz, fort. habet Τ᾽ : ἐνυπαρχόντων
codd. P* 38 ὑπάρχουσι C bg ὑπάρχῃ Ald 6 τὸ βαδίζειν B
1 79 om. ABCd λευκόν adieci 8 μὴ om. n!
ANAAYTIKQN YETEPQN A
ἤστραψεν, ἀλλὰ συνέβη, φαμέν, τοῦτο. εἰ δὲ δι’ αὑτό,
καθ᾽ αὑτό, olov εἴ τι σφαττόμενον ἀπέθανε, καὶ κατὰ τὴν
i5 σφαγήν, ὅτι διὰ τὸ σφάττεσθαι, ἀλλ’ οὐ συνέβη σφαττό-
μενον ἀποθανεῖν. τὰ ἄρα λεγόμενα ἐπὶ τῶν ἁπλῶς ἐπιστη-
τῶν καθ᾽ αὑτὰ οὕτως ὡς ἐνυπάρχειν τοῖς κατηγορουμένοις
^" > , , e , L4 > M] 3 > , > M
ἢ ἐνυπάρχεσθαι δι’ αὑτά τέ ἐστι kai ἐξ ἀνάγκης. ov yap
ἐνδέχεται μὴ ὑπάρχειν ἢ ἁπλῶς ἢ τὰ ἀντικείμενα, οἷον
^ ^ A F 3 > ^ M 4
20 γραμμῇ τὸ εὐθὺ ἢ TO καμπύλον καὶ ἀριθμῷ τὸ περιττὸν
ἢ τὸ ἄρτιον. ἔστι γὰρ τὸ ἐναντίον 1) στέρησις ἢ ἀντίφασις ἐν τῷ
αὐτῷ γένει, οἷον ἄρτιον τὸ μὴ περιττὸν ἐν ἀριθμοῖς fj ἕπεται.
v 3 , 5 , , - Ls 4 > , ^ A >
ὥστ᾽ εἰ ἀνάγκη φάναι ἢ ἀποφάναι, ἀνάγκη καὶ τὰ καθ
αὑτὰ ὑπάρχειν.
A * T ^ * * 3 qx δ , s
25 Τὸ μὲν οὖν κατὰ παντὸς καὶ καθ᾽ αὑτὸ διωρίσθω τὸν
y» ^ / A , ^ hd ^ L4
τρόπον τοῦτον: καθόλου δὲ λέγω ὃ ἂν κατὰ παντός τε
[4 , x > € A Y s ων 2 , * w Ld L4
ὑπάρχῃ kai καθ᾽ αὑτὸ καὶ fj αὐτό. φανερὸν dpa ὅτι ὅσα
καθόλου, ἐξ ἀνάγκης ὑπάρχει τοῖς πράγμασιν. τὸ καθ᾽
αὑτὸ δὲ καὶ jj αὐτὸ ταὐτόν, οἷον καθ᾽ αὑτὴν τῇ γραμμῇ
3e ὑπάρχει στιγμὴ καὶ τὸ εὐθύ (καὶ yap jj γραμμή), καὶ τῷ
τριγώνῳ % τρίγωνον δύο ὀρθαί (καὶ γὰρ καθ᾽ αὑτὸ τὸ τρί-
ριγώνῳ fj τρίγ ρ γὰρ p
, 3 ^ LÀ A 4 A t δὰ ra L4
y«vov δύο ὀρθαῖς ἴσον). τὸ καθόλου δὲ ὑπάρχει τότε, ὅταν
^ *
ἐπὶ τοῦ τυχόντος kai πρώτου δεικνύηται. οἷον τὸ δύο ὀρθὰς
ἔχειν οὔτε τῷ σχήματί ἐστι καθόλου (καίτοι ἔστι δεῖξαι
X ἃ σ , > A *w > , » ^ 7
35 κατὰ σχήματος ὅτι δύο ὀρθὰς ἔχει, ἀλλ᾽ od τοῦ τυχόντος
σχήματος, οὐδὲ χρῆται τῷ τυχόντι σχήματι δεικνύς" τὸ
γὰρ τετράγωνον σχῆμα μέν, οὐκ ἔχει δὲ δύο ὀρθαῖς ἴσας)---
A , > * w * x hi L4 , ^ LJ 3 »
TO δ᾽ ἰσοσκελὲς ἔχει μὲν τὸ τυχὸν δύο ὀρθαῖς ἴσας, ἀλλ
οὐ πρῶτον, ἀλλὰ τὸ τρίγωνον πρότερον. ὃ τοίνυν τὸ τυχὸν
~ * , » A μὰ ^ € L3 M , ,
4o πρῶτον δείκνυται δύο ὀρθὰς ἔχον ἢ ὁτιοῦν ἄλλο, τούτῳ πρώτῳ
a € , 00A + t ? 55 θ᾽ yx 4 06A
74* ὑπάρχει καθόλου, Kal ἡ ἀπόδειξις Kal? αὑτὸ τούτου καθόλου
> , ^ > Ld , A > 2 L4 , > t ^95
ἐστί, τῶν δ᾽ ἄλλων τρόπον τινὰ οὐ καθ᾽ αὑτό, οὐδὲ τοῦ ἰσοσκε-
λοῦς οὐκ ἔστι καθόλου ἀλλ᾽ ἐπὶ πλέον.
^ A , L4 , ^
Get δὲ μὴ λανθάνειν ὅτι πολλάκις συμβαίνει διαμαρ-
M t ^
s Tdvew καὶ μὴ ὑπάρχειν τὸ δεικνύμενον πρῶτον καθόλου, f$
δοκεῖ δείκνυσθαι καθόλου πρῶτον. ἀπατώμεθα δὲ ταύτην τὴν
> r4 v b] *: T ~ 3 , a 4 3
ἀπάτην, ὅταν ἢ μηδὲν ἢ λαβεῖν ἀνώτερον παρὰ τὸ καθ
br3 αὐτὸ A} (qui sic in sqq. saepius) B I4 kai om. # τὴν om, PS
26 λέγω ὅταν f . 29 αὑτὴν] αὑτῇ BC! τῇ γραμμῇ A BC*d?nT : τὴν
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b a
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ἕκαστον [ἢ rà καθ᾽ ἕκαστα), ἢ ἦ μέν, ἀλλ᾽ ἀνώνυμον ἡ ἐπὶ
"4 LÀ , . a , ^ [4 » ὕὔ LÀ
διαφόροις εἴδει πράγμασιν, ἢ τυγχάνῃ ὃν ws ἐν μέρει ὅλον
41 Φ , ^ 4 > * [d £p Li € » F
ἐφ᾽ ᾧ δείκνυται: τοῖς yap ἐν μέρει ὑπάρξει μὲν ἡ ἀπόδει- 10
ξις, καὶ ἔσται κατὰ παντός, ἀλλ᾽ ὅμως οὐκ ἔσται τούτου πρώ-
, t » , , a , P4 Lj 3. £
Tov καθόλου ἡ ἀπόδειξις. λέγω δὲ rovrov πρώτου, fj τοῦτο, ἀπό-
δειξιν, ὅταν ἦ πρώτου καθόλου. εἰ οὖν τις δείξειεν ὅτι αἱ dp-
Bai οὐ συμπίπτουσι, δόξειεν ἂν τούτου εἶναι ἡ ἀπόδειξις διὰ τὸ
LU 4 ~ ~ » ~ 3 » , » A σ ε M
ἐπὶ πασῶν εἶναι τῶν ὀρθῶν. οὐκ ἔστι δέ, εἴπερ μὴ ὅτι ὡδὲ τς
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ἴσαι γίνεται τοῦτο, ἀλλ᾽ 4 ὁπωσοῦν ἴσαι. καὶ εἰ τρίγωνον μὴ
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ἦν ἄλλο 7 ἰσοσκελές, ἡ ἰσοσκελὲς dv ἐδόκει ὑπάρχειν. Kai
τὸ ἀνάλογον ὅτι καὶ ἐναλλάξ, ἧ ἀριθμοὶ καὶ fj γραμμαὶ καὶ
ἢ στερεὰ καὶ ἧ χρόνοι, ὥσπερ ἐδείκνυτό ποτε χωρίς, ἐνδε-
, , A 4 Lj > N ἢ, ^ 3 A
χόμενόν ye xarà πάντων μιᾷ ἀποδείξει δειχθῆναι: ἀλλὰ 20
διὰ τὸ μὴ εἶναι ὠνομασμένον τι ταῦτα πάντα ἕν, ἀριθμοί
μήκη χρόνοι στερεά, καὶ εἴδει διαφέρειν ἀλλήλων, χωρὶς
3 [2 ~ 4 , * , 4 T M
ἐλαμβάνετο. viv δὲ καθόλου δείκνυται. οὐ yap f$ γραμμαὶ
ἢ 5 ἀριθμοὶ ὑπῆρχεν, ἀλλ᾽ ἡ τοδί, ὃ καθόλου ὑποτίθενται
e ta A Lj 29> L4 4, , o a ,
ὑπάρχειν. διὰ τοῦτο οὐδ᾽ dv τις δείξῃ καθ᾽ ἕκαστον τὸ Tplyw- 25
> Ld n “- μα € , ov , > a LÀ bd a
vov ἀποδείξει ἢ μιᾷ ἢ ἑτέρᾳ ὅτι δύο ὀρθὰς ἔχει ἕκαστον, TO
> ff. b M 4 ^ * A > , L4
ἰσόπλευρον χῶρὶς Kai τὸ σκαληνὲς kai τὸ ἰσοσκελές, οὔπω
οἷδε τὸ τρίγωνον ὅτι δύο ὀρθαῖς, εἰ μὴ τὸν σοφιστικὸν τρό-
% M 3 μὰ , > > Y LÀ ^ “-
πον, οὐδὲ καθ᾽ ὅλου τριγώνου, οὐδ᾽ εἰ μηδὲν ἔστι παρὰ ταῦτα
τρίγωνον ἕτερον. οὐ yap fj τρίγωνον οἶδεν, οὐδὲ πᾶν τρίγωνον, 3o
ἀλλ᾽ ἢ κατ᾽ ἀριθμόν: κατ᾽ εἶδος δ᾽ οὐ πᾶν, καὶ εἰ μηδὲν
ν a > 5 32
ἔστιν ὃ οὐκ older.
Ilór! οὖν οὐκ οἷδε καθόλου, καὶ πότ᾽ οἶδεν 32
[4 ^ ^ A σ > > Li τ "d 4 >
ἁπλῶς; δῆλον δὴ ὅτι εἰ ταὐτὸν ἣν τριγώνῳ εἶναι Kai ἰσο-
, -* € ὔ ^ ^ * M x > * LI , Ld
πλεύρῳ ἢ ἑκάστῳ ἢ πᾶσιν. εἰ δὲ μὴ ταὐτὸν ἀλλ᾽ ἕτερον,
er > D 3 y , , D E
ὑπάρχει δ᾽ ἧ τρίγωνον, οὐκ οἷδεν. πότερον δ᾽ ἧ τρίγωνον 7 35
ἢ ἰσοσκελὲς ὑπάρχει; καὶ πότε κατὰ τοῦθ᾽ ὑπάρχει πρῶ-
τον; καὶ καθόλου τίνος ἡ ἀπόδειξις; δῆλον ὅτι ὅταν ἀφαι-
ρουμένων ὑπάρχῃ πρώτῳ. οἷον τῷ ἰσοσκελεῖ χαλκῷ τριγώνῳ
48 3... ἕκαστα om. C et fort. PT 9 fom. nt τυγχάνει AL BCI
10 ὧν πὶ 12 πρώτου om. n! $54 15 ὅρων πὶ 16 γένονται
e ἢ] ἢ AB 17 f ἰσοσκελὲς om, d! 18 xai! nT : om. ABCd
19 χρόνος ἢ domep+ καὶ ACd! 21 πάντα ταῦτα A Bd 22 χρό-
νος ABCad διαφέρει d 24 ὑποτίθεται nl 25 οὐδ᾽ δ᾽ πὶ 26
ἀποδείξει om. B 27 σκαληνὸν A*BCd 29 καθόλου τριγώνου n:
καθόλου τρίγωνον ABC ἐὰν d 30 οὐδὲ γὰργ οὐδ᾽ εἰ πᾶν ἢ 319d
33 τρίγωνον B! 35 πότε n? 36 ἡ ACdP* : om. Bn 37 ἀφαιρου-
péva C 38 ὑπάρξῃ ABCd τὸ
ANAAYTIKQN YETEPQN A
ὑπάρξουσι δύο ὀρθαί, ἀλλὰ καὶ τοῦ χαλκοῦν εἶναι ddaipe-
£ M ^5 L4 > > ΕΣ ~ , ^ ,
74> θέντος Kai τοῦ ἰσοσκελές. ἀλλ᾽ οὐ τοῦ σχήματος ἢ πέρατος.
5
1o
15
20
25
30
ἀλλ᾽ οὐ πρώτων. τίνος οὖν πρώτου; εἰ δὴ τριγώνου, κατὰ τοῦτο
€ 4 ' ^ w x 4 , , M [4 , ,
ὑπάρχει καὶ τοῖς ἄλλοις, kai τούτου καθόλου ἐστὶν ἡ àmó-
δειξις.
> hu ’ [4 > ^ » , * 2 , >
Εἰ οὖν ἐστιν ἡ ἀποδεικτικὴ ἐπιστήμη ἐξ ἀναγκαίων dp-
- a A , , , 8 a » μ᾿ ΕἾ M ,
χῶν (ὃ yap ἐπίσταται, od δυνατὸν ἄλλως ἔχειν), rà δὲ καθ
2 > ^ ^
αὑτὰ ὑπάρχοντα ἀναγκαῖα τοῖς πράγμασιν (rà μὲν yap ἐν
^ L4 , [4 , ^ > ^ , ,
τῷ τί ἐστιν ὑπάρχει" τοῖς δ᾽ αὐτὰ ἐν τῷ τί ἐστιν ὑπάρχει
~ 4 ^
κατηγορουμένοις αὐτῶν, ὧν θάτερον τῶν ἀντικειμένων ἀνάγκη
ὑπάρχειν), φανερὸν ὅτι ἐκ τοιούτων τινῶν ἂν εἴη ὁ ἀποδει-
κτικὸς συλλογισμός: ἅπαν γὰρ ἢ οὕτως ὑπάρχει 7) κατὰ
, ‘ * , ᾽ > a
συμβεβηκός, τὰ δὲ συμβεβηκότα οὐκ ἀναγκαῖα.
Ἢ δὴ L4 , nn > M 0 rA a € > “ὃ
ἡ οὕτω λεκτέον, ἢ ἀρχὴν θεμένοις ὅτι ἡ ἀπόδειξις
> , , / * > » ^ % T! 3 Ld
ἀναγκαίων ἐστί, kai εἰ ἀποδέδεικται, οὐχ οἷόν τ᾽ ἄλλως
Μ , 3 , » ^ hi , , >
ἔχειν: ἐξ ἀναγκαίων dpa δεῖ εἶναι τὸν συλλογισμόν. ἐξ adn-
θῶν μὲν γὰρ ἔστι καὶ μὴ ἀποδεικνύντα συλλογίσασθαι, ἐξ
> , 3 , v > 3 -^ > , ^ ^ M
ἀναγκαίων δ᾽ οὐκ ἔστιν add’ ἢ dmo8euvóvra- τοῦτο yàp ἤδη
3 / , E. ^ 3 μὲ € > Ld > » ,
ἀποδείξεώς ἐστιν. σημεῖον δ᾽ ὅτι ἡ ἀπόδειξις ἐξ ἀναγκαίων,
ὅτι καὶ τὰς ἐνστάσεις οὕτω φέρομεν πρὸς τοὺς οἰομένους ἀπο-
z L4 > 3 , hal > 2 nn Ld , sh
δεικνύναι, ὅτι οὐκ ἀνάγκη, àv οἰώμεθα ἢ ὅλως ἐνδέχεσθαι
» - ? ~ , ^ > > , M Ld +s
ἄλλως ἢ ἕνεκά ye τοῦ λόγου. δῆλον δ᾽ ἐκ τούτων καὶ ὅτι εὐή-
e , »? - M 3 γι LÀ
Bets of λαμβάνειν οἰόμενοι καλῶς τὰς ἀρχάς, ἐὰν ἔνδοξος
^ € " 55 " 4 ε m 50» /
ἦ ἡ πρότασις καὶ ἀληθής, olov oi σοφισταὶ ὅτι τὸ ἐπίστα-
σθαι τὸ ἐπιστήμην ἔχειν. οὐ γὰρ τὸ ἔνδοξον ἡμῖν ἀρχή ἐστιν,
> * ‘ ^ ^ , M a 7 M > ^
ἀλλὰ τὸ πρῶτον τοῦ γένους περὶ ὃ δείκνυται: καὶ τἀληθὲς
Ἵ ^ > ~ Ld » , 3, , > ^ a
οὐ πᾶν οἰκεῖον. ὅτι δ᾽ ἐξ ἀναγκαίων εἶναι δεῖ τὸν συλλογι-
σμόν, φανερὸν καὶ ἐκ τῶνδε. εἰ γὰρ ὁ μὴ ἔχων λόγον τοῦ
^ , L4 > L , , , LA ? *- L4 M
διὰ τί οὔσης ἀποδείξεως οὐκ ἐπιστήμων, εἴη δ᾽ ἂν ὥστε τὸ A
A ~ , > 4 € , ‘ M M , 2
κατὰ τοῦ l' ἐξ ἀνάγκης ὑπάρχειν, τὸ δὲ B τὸ μέσον, δι
T > , ^ , 3 , , , *, » , ^
οὗ ἀπεδείχθη, μὴ ἐξ ἀνάγκης, οὐκ olde διότι. οὐ γάρ ἐστι τοῦτο
^ ,
διὰ τὸ μέσον: τὸ μὲν γὰρ ἐνδέχεται μὴ εἶναι, τὸ δὲ συμ-
^ ~ ^
πέρασμα ἀναγκαῖον. ἔτι ei τις μὴ olde viv ἔχων τὸν λόγον
x ^ 3
καὶ σῳζόμενος, σῳζομένου τοῦ πράγματος, μὴ ἐπιλελησμέ-
LAND , Lá , > n i] , ᾽ M
vos, οὐδὲ πρότερον Toe. φθαρείη δ᾽ ἂν τὸ μέσον, εἰ μὴ
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χει Al 13 οὕτω θετέον C? 14 ἀναγκαίων scripsi, habet ut vid. P:
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τῷ Bim ἡμῖν) ἣ μὴ ABCAn? 25 τὸ] τῷ BIC? 26 δεῖ] δὴ ἡ
33 καὶ om. 5 σωζόμενον σωζομένου n? 34 οὐδὲ] οὐδὲ dpa C
a a.
5. 74°39-6. 75°30
> ^ L4 L4 * M , , ,
ἀναγκαῖον, ὥστε ἕξει μὲν τὸν λόγον σῳζόμενος σῳζομένου
τοῦ πράγματος, οὐκ οἷδε δέ. οὐδ᾽ ἄρα πρότερον Ade. εἰ δὲ
^ w > 2, x - ^ ^ n Μ
μὴ ἔφθαρται, ἐνδέχεται δὲ φθαρῆναι, τὸ συμβαῖνον ἄν εἴη
b 3 , > , w 5 , L4
δυνατὸν καὶ ἐνδεχόμενον. ἀλλ᾽ ἔστιν ἀδύνατον οὕτως ἔχοντα
εἰδέναι
L4 ' 7T M , H > , T S
Orav μὲν οὖν τὸ συμπέρασμα ἐξ ἀνάγκης 7, οὐδὲν κω-
λύει τὸ μέσον μὴ ἀναγκαῖον εἶναι 8v οὗ ἐδείχθη (ἔστι ya,
: p
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τὸ ἀναγκαῖον kai μὴ ἐξ ἀναγκαίων συλλογίσασθαι, ὥσπερ
A 2 A M , > ~ L4 * M 4 3 > ,
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M M , 3 , LA , > ^
καὶ τὸ συμπέρασμα ἐξ ἀνάγκης, ὥσπερ kai ἐξ ἀληθῶν ἀλη-
θὲ LEM L4 A x A ^ ~ B > > , M ^
és ἀεί (ἔστω yàp τὸ A κατὰ τοῦ B ἐξ ἀνάγκης, καὶ τοῦτο
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ὅταν δὲ μὴ ἀναγκαῖον ἦ τὸ συμπέρασμα, οὐδὲ τὸ μέσον
ἀναγκαῖον οἷόν τ᾽ εἶναι (ἔστω yap τὸ A τῷ Γ᾿ μὴ ἐξ ἀνάγ-
κης ὑπάρχειν, τῷ δὲ B, καὶ τοῦτο τῷ Γ᾽ ἐξ ἀνάγκης" καὶ
10 A ἄρα τῷ I' ἐξ ἀνάγκης ὑπάρξει: ἀλλ᾽ οὐχ ὑπέκειτο).
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Ἐπεὶ τοίνυν €i ἐπίσταται ἀποδεικτικῶς, δεῖ ἐξ ἀνάγκης ὑπάρ
~ " X 4 Li > , ^ v M 3
ew, δῆλον ὅτι kai διὰ μέσου ἀναγκαίου δεῖ ἔχειν τὴν dmó-
» 97
δειξιν- ἢ οὐκ ἐπιστήσεται οὔτε διότι οὔτε ὅτι ἀνάγκη ἐκεῖνο el-
Σ 3 ^ b Fd > » , oA « 4 € > ~
vat, GAN ἢ οἰήσεται οὐκ εἰδώς, ἐὰν ὑπολάβῃ ὡς ἀναγκαῖον
τὸ μὴ ἀναγκαῖον, ἢ οὐδ᾽ οἰήσεται, ὁμοίως ἐάν τε τὸ ὅτι εἰδῇ
» ἢ i
N 4 , * > 5 ,
διὰ μέσων ἐάν τε τὸ διότι καὶ δι᾿ ἀμέσων.
Τῶν δὲ συμβεβηκότων μὴ καθ᾽ αὑτά, ὃν τρόπον διω-
ρίσθη τὰ καθ᾽ αὑτά, οὐκ ἔστιν ἐπιστήμη ἀποδεικτική. οὐ γὰρ
ἔστιν ἐξ ἀνάγκης δεῖξαι τὸ συμπέρασμα: τὸ συμβεβηκὸς
γὰρ ἐνδέχεται μὴ ὑπάρχειν: περὶ τοῦ τοιούτου γὰρ λέγω συμ-
3 L4 7 e L3
βεβηκότος. καίτοι ἀπορήσειεν ἄν τις ἴσως Tivos ἕνεκα ταῦτα
δεῖ ἐρωτᾶν περὶ τούτων, εἰ μὴ ἀνάγκη τὸ συμπέρασμα εἶναι"
οὐδὲν γὰρ διαφέρει εἴ τις ἐρόμενος τὰ τυχόντα εἶτα εἴπειεν τὸ
συμπέρασμα. δεῖ δ᾽ ἐρωτᾶν οὐχ ὡς ἀναγκαῖον εἶναι διὰ τὰ
ἠρωτημένα, ἀλλ᾽ ὅτι λέγειν ἀνάγκη τῷ ἐκεῖνα λέγοντι, καὶ
ἀληθῶς λέγειν, ἐὰν ἀληθῶς ἦ ὑπάρχοντα.
δ. M δ᾽ > 2 , € , M L4 UJ kd
Tei ἐξ ἀνάγκης ὑπάρχει περὶ ἕκαστον γένος ὅσα
* ^
καθ᾽ αὑτὰ ὑπάρχει καὶ ἧ ἕκαστον, φανερὸν ὅτι περὶ τῶν
καθ᾽ αὑτὰ ὑπαρχόντων al ἐπιστημονικαὶ ἀποδείξεις καὶ ἐκ
Th
b35 σωζόμενον σωζομένου Bln 37 δὲ om. B! ein+ καὶ C
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24 εἴπειεν] εἴποι ἕν fecit n
35
73°
IO
15
20
25
30
35
40
75°
lo
15
20
ANAAYTIKQN YETEPQN A
τῶν τοιούτων εἰσίν. τὰ μὲν yap συμβεβηκότα οὐκ ἀναγκαῖα,
ὥστ᾽ οὐκ ἀνάγκη τὸ συμπέρασμα εἰδέναι διότι ὑπάρχει, οὐδ᾽
, » LÀ M » [4 M , T € M /,
εἰ dei εἴη, μὴ Kal? αὑτὸ δέ, olov of διὰ σημείων συλλογι-
LH ^ ^ » t ^ ΕΣ > L4 * » , »$ ,
opot. τὸ yap καθ᾽ αὑτὸ οὐ καθ᾽ αὑτὸ ἐπιστήσεται, οὐδὲ διότι
a A , > , 4? M ^ ~ , 7 H , 3
(τὸ δὲ διότι ἐπίστασθαί ἐστι τὸ διὰ τοῦ αἰτίου ἐπίστασθαι). δι
αὑτὸ ἄρα δεῖ καὶ τὸ μέσον τῷ τρίτῳ καὶ τὸ πρῶτον τῷ μέσῳ
ὑπάρχειν.
^ t
Οὐκ dpa ἔστιν ἐξ ἄλλου γένους μεταβάντα δεῖξαι, οἷον 7
-^ > ^ ^
τὸ γεωμετρικὸν ἀριθμητικῇ. τρία ydp ἐστι τὰ ἐν ταῖς ἀπο-
δείξεσιν, ἕν μὲν τὸ ἀποδεικνύμενον, τὸ συμπέρασμα (τοῦτο
δ᾽ ἐστὶ τὸ ὑπάρχον γένει τινὶ καθ᾽ αὑτό), ἕν δὲ τὰ ἀξιώ-
> , > » M » T , ‘ , ^ t Fr
ματα (ἀξιώματα δ᾽ ἐστὶν ἐξ ὧν)" τρίτον TO γένος τὸ ὑποκεί-
T ^ 10 * ^ e € ^ , ^
μενον, ob τὰ πάθη xai rà καθ᾽ αὑτὰ συμβεβηκότα δηλοῖ
t > , , T ^ “ L4 5 , , , A ΕἸ ^
ἡ ἀπόδειξις. ἐξ ὧν μὲν οὖν ἡ ἀπόδειξις, ἐνδέχεται τὰ αὐτὰ
εἶναι: ὧν δὲ τὸ γένος ἕτερον, ὥσπερ ἀριθμητικῆς καὶ γεω-
μετρίας, οὐκ ἔστι τὴν ἀριθμητικὴν ἀπόδειξιν ἐφαρμόσαι ἐπὶ
τὰ τοῖς μεγέθεσι συμβεβηκότα, εἰ μὴ τὰ μεγέθη ἀριθμοί
εἰσι: τοῦτο δ᾽ ὡς ἐνδέχεται ἐπί τινων, ὕστερον λεχθήσεται.
L4 J 3 A 3 ? LER I L4 Ὅν , M ^ € 3 cd
ἡ δ᾽ ἀριθμητικὴ ἀπόδειξις ἀεὶ ἔχει TO γένος περὶ ὃ ἡ amó-
* t Ld t , e > - € ~ > , M
δειξις, καὶ at ἄλλαι ὁμοίως. ὥστ᾽ ἢ ἁπλῶς ἀνάγκη TO
᾽ M td had - , z € > , ,
αὐτὸ εἶναι γένος ἢ πῇ, εἰ μέλλει ἡ ἀπόδειξις μεταβαίνειν.
ἄλλως δ᾽ ὅτι ἀδύνατον, δῆλον: ἐκ γὰρ τοῦ αὐτοῦ γένους
> /, ^ L4 * x , > ^ x 3 [4 ,
ἀνάγκη τὰ ἄκρα kai rà μέσα εἶναι. εἰ yap μὴ καθ᾽ αὑτά,
συμβεβηκότα ἔσται. διὰ τοῦτο τῇ γεωμετρίᾳ οὐκ ἔστι δεῖξαι
v ~ > , , > , > » γα» - t , ,
ὅτι τῶν ἐναντίων μία ἐπιστήμη, ἀλλ᾽ odd’ ὅτι οἱ δύο κύβοι
κύβος: οὐδ᾽ ἄλλῃ ἐπιστήμῃ τὸ ἑτέρας, ἀλλ᾽ ἢ ὅσα οὕτως
LÀ ^ LÀ L4 > * , € M , M
ἔχει πρὸς ἄλληλα ὥστ᾽ εἶναι θάτερον ὑπὸ θάτερον, olov rà
ὀπτικὰ πρὸς γεωμετρίαν καὶ τὰ ἁρμονικὰ πρὸς ἀριθμητι-
3 ^ ^ A T A.
κήν. οὐδ᾽ εἴ τι ὑπάρχει ταῖς γραμμαῖς μὴ ἣ γραμμαὶ kai
ἡ ἐκ τῶν ἀρχῶν τῶν ἰδίων, οἷον εἰ καλλίστη τῶν γραμμῶν
€ *, ^ hal ᾽ , [4 ww ~ ^ > ^ A]
ἡ εὐθεῖα ἢ εἰ ἐναντίως ἔχει TH περιφερεῖ: οὐ yàp $4 τὸ
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ἴδιον γένος αὐτῶν, ὑπάρχει, ἀλλ᾽ ἧ κοινόν τι.
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avepóv δὲ xai ἐὰν wow ai προτάσεις καθόλου ἐξ ὧν ὃ
¢ > M EI
ὁ συλλογισμός, ὅτι ἀνάγκη καὶ τὸ συμπέρασμα ἀΐδιον
εἶναι τῆς τοιαύτης ἀποδείξεως καὶ τῆς ἁπλῶς εἰπεῖν ἀπο-
δείξεως. οὐκ ἔστιν ἄρα ἀπόδειξις τῶν φθαρτῶν οὐδ᾽ ἐπιστήμη
a35 διότι ἐπιστήσασθαι A 41 γένει) ἐν n 42 τὸϊ om. n br καθ᾽
αὐτὰ om. d 1ád]àd! 9 μέλλοι B et ut vid. P 13 ἄλλου
ὅτι nt “ghelleljnian® mepjepeinT : περιφερείᾳ 4 BCAP 22 ἔδιον
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a 4
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ἁπλῶς, GAN οὕτως ὥσπερ κατὰ συμβεβηκός, ὅτι o) Kal?
" , ^ > , A x b , L4 > > ,
ὅλου αὐτοῦ ἐστιν ἀλλὰ ποτὲ καὶ πώς. ὅταν δ᾽ f, ἀνάγκη
τὴν ἑτέραν μὴ καθόλου εἶναι πρότασιν καὶ φθαρτήν--φθαρ-
τὴν μὲν ὅτι ἔσται καὶ τὸ συμπέρασμα οὔσης, μὴ καθόλου δὲ
Ld ^ x v ~ 3 » L4 ,»I? T L4 > > v
ὅτι TQ μὲν ἔσται τῷ δ᾽ οὐκ ἔσται ἐφ᾽ Hv—wor’ οὐκ ἔστι συλ-
λογίσασθαι καθόλου, ἀλλ᾽ ὅτι νῦν. ὁμοίως δ᾽ ἔχει καὶ
^ € ^ 3 , > M € « A * , M > 2,
περὶ ὁρισμούς, ἐπείπερ ἐστὶν ὁ ὁρισμὸς ἢ ἀρχὴ ἀποδείξεως
^ > "ὃ θέ ὃ 7 ^ , rF > ,
ἢ ἀπόδειξις θέσει διαφέρουσα ἢ συμπέρασμά τι ἀποδείξεως.
« ~ ^
αἱ δὲ τῶν πολλάκις γινομένων ἀποδείξεις καὶ ἐπιστῆμαι, otov
L4 , L4 ^ oe b ^c? , . LET » δ
σελήνης ἐκλείψεως, δῆλον ὅτι fj μὲν τοιοῦδ᾽ εἰσίν, ἀεὶ εἰσίν,
δ᾽ *, 3 » A , > f - δ᾽ € » λι « ^
ἢ δ᾽ οὐκ ἀεί, κατὰ μέρος εἰσίν. ὥσπερ δ᾽ ἡ ἔκλειψις, ὡσαύ-
τως τοῖς ἄλλοις.
᾿Επεὶ δὲ φανερὸν ὅτι ἕκαστον ἀποδεῖξαι οὐκ ἔστιν ἀλλ᾽
ἢ ἐκ τῶν ἑκάστου ἀρχῶν, ἂν τὸ δεικνύμενον ὑπάρχῃ 7] ἐκεῖνο,
? L4 A , , ~ bad 3 > ~ M > ,
οὐκ ἔστι τὸ ἐπίστασθαι τοῦτο, ἂν ἐξ ἀληθῶν καὶ ἀναποδείκτων
δειχθῇ καὶ ἀμέσων. ἔστι γὰρ οὕτω δεῖξαι, ὥσπερ Βρύσων
τὸν τετραγωνισμόν. κατὰ κοινόν τε γὰρ δεικνύουσιν oi τοιοῦτοι
λό « * « , L4 , A M > 3 L4 ,
óyou ὃ Kal ἑτέρῳ ὑπάρξει: διὸ καὶ ἐπ’ ἄλλων ἐφαρ-
μόττουσιν οἱ λόγοι οὐ συγγενῶν. οὐκοῦν οὐχ 7j ἐκεῖνο ἐπίστα-
3 4A hi , 3. ^ bal * , τ 3 J
ται, ἀλλὰ κατὰ συμβεβηκός: od yàp àv ἐφήρμοττεν ἡ ἀπό-
δειξις καὶ ἐπ’ ἄλλο γένος.
@ > > , * A , "
Ἕκαστον δ᾽ ἐπιστάμεθα μὴ κατὰ συμβεβηκός, ὅταν
κατ᾽ ἐκεῖνο γινώσκωμεν καθ᾽ ὃ ὑπάρχει, ἐκ τῶν ἀρχῶν
^ ΓΝ: > ^ ^ 4 * > ^ » ν T7
τῶν ἐκείνου fj ἐκεῖνο, otov τὸ δυσὶν ὀρθαῖς ἴσας ἔχειν, ᾧ
ὑπάρχει καθ᾽ αὑτὸ τὸ εἰρημένον, ἐκ τῶν ἀρχῶν τῶν τούτου.
ὥστ᾽ εἰ καθ᾽ αὐτὸ κἀκεῖνο ὑπάρχει ᾧ ὑπάρχει, ἀνάγκη
* , > ~ LN , > M , > > e
τὸ μέσον ἐν TH αὐτῇ συγγενείᾳ εἶναι. εἰ δὲ μή, ἀλλ᾽ ὡς
τὰ ἁρμονικὰ 80 ἀριθμητικῆς. τὰ δὲ τοιαῦτα δείκνυται
X € , , 4, A x ^ Ld LONE 4 > ,
μὲν ὡσαύτως, διαφέρει δέ: τὸ μὲν yàp ὅτι ἑτέρας ἐπιστή-
us (τὸ γὰρ ὑποκείμενον γένος ἕτερον), τὸ δὲ διότι τῆς ἄνω,
ἧς καθ᾽ αὑτὰ τὰ πάθη ἐστίν. ὥστε καὶ ἐκ τούτων φανερὸν
L4 Uu v > a " € ^ > > "^ > ~ Li ,
ὅτι οὐκ ἔστιν ἀποδεῖξαι ἕκαστον ἁπλῶς ἀλλ᾽ ἢ ἐκ τῶν ἑκά-
> ^ > e
στου ἀρχῶν. ἀλλὰ τούτων ai ἀρχαὶ ἔχουσι τὸ κοινόν.
bas οὐ ΑΒΟΉΡ: τ' οὐ d: τοῦ Pv: om. T καθ᾽ ὅλον scripsi: καθόλον
edd. 26 δ᾽ ἢ] δὴ π 28 ἔσται om. ABCdPS οὔσης] τοιοῦτον coni.
Bonitz 2979 ... τῷ] τὸ... τὸ C'nP: $... 0 ABA 31 ὁρισμοῦ n
34 d] ain μὲν τοιοῦδ᾽ BP: μέντοι οὐδ᾽ A: μὲν rota(8' C : μὲν τοιοιδί d : μὲν
τούτου διότι 1: μὲν τοῦ διότι nm? ἀεὶ) ain 35 $] αἱ οὐ καὶ εἰ ἀπ
δ᾽ ἥδε π 39 ἄν] ὃ ἂν n 40 ὥστε oC 7638 κἀκεῖνο Bn*P :
κἀκείνῳ AY B*Cdn ᾧ ὑπάρχει om. n 14 ἔστι δεῖξαι n
25
30
35
40
768
Io
15
ANAAYTIKQN YETEPQN A
Εἰ δὲ φανερὸν τοῦτο, φανερὸν Kai ὅτι οὐκ ἔστι τὰς ἑκά-
στου ἰδίας ἀρχὰς ἀποδεῖξαι: ἔσονται γὰρ ἐκεῖναι ἁπάντων
ἀρχαί, καὶ ἐπιστήμη ἡ ἐκείνων κυρία πάντων. καὶ γὰρ ἐπί-
^ L4 , ~ > L4 » 4 9 , > ~
orarat μᾶλλον ὁ ἐκ τῶν ἀνώτερον αἰτίων εἰδώς: ἐκ τῶν
20 προτέρων γὰρ οἶδεν, ὅταν ἐκ μὴ αἰτιατῶν εἰδῇ αἰτίων. ὥστ᾽
» ^ * , bal , , , , LJ M
εἰ μᾶλλον οἷδε καὶ μάλιστα, κἂν ἐπιστήμη ἐκείνη εἴη kai
^ 1 , € > > , > > H , >
μᾶλλον καὶ μάλιστα. ἡ δ᾽ ἀπόδειξις οὐκ ἐφαρμόττει ἐπὶ
» , > » ^ « L4 € * $» M
ἄλλο γένος, ἀλλ᾽ ἣ ὡς εἴρηται ai γεωμετρικαὶ ἐπὶ τὰς
μηχανικὰς 7 ὀπτικὰς καὶ αἱ ἀριθμητικαὶ ἐπὶ τὰς ἀρ-
25 μονικάς.
^ » > M M ^ > ^ L4 M
Xarerov δ᾽ ἐστὶ τὸ γνῶναι εἰ oldev Tj μή. χαλεπὸν
γὰρ τὸ γνῶναι εἰ ἐκ τῶν ἑκάστου ἀρχῶν ἴσμεν ἢ μή" ὅπερ
3 ‘ ^ » , », 3 ha] L4 >? > 6 ^ ^
ἐστὶ τὸ εἰδέναι. οἰόμεθα δ᾽, av ἔχωμεν ἐξ ἀληθινῶν τινῶν
‘ * , > 7, A > , w 3 M
συλλογισμὸν kai πρώτων, ἐπίστασθαι. τὸ δ᾽ οὐκ ἔστιν, ἀλλὰ
30 συγγενῆ δεῖ εἶναι τοῖς πρώτοις.
, > » ^ > Li , ὧν 4 a Lid 4
Aéyw δ᾽ ἀρχὰς ἐν ἑκάστῳ γένει ταύτας ἃς ὅτι ἔστι
μὴ ἐνδέχεται δεῖξαι. τί μὲν οὖν σημαίνει καὶ τὰ πρῶτα καὶ
M 3 , 4 L4 > LÀ M M > A
τὰ ἐκ τούτων, λαμβάνεται, ὅτι δ᾽ ἔστι, Tas μὲν ἀρχὰς
ἀνάγκη λαμβάνειν, τὰ δ᾽ ἄλλα δεικνύναι: οἷον τί μονὰς
hal H * "θὺ * , H δὲ A 1o À ^ 4
35 ἢ τί TO εὐθὺ καὶ τρίγωνον, εἶναι δὲ τὴν μονάδα λαβεῖν καὶ
μέγεθος, τὰ δ᾽ ἕτερα δεικνύναι.
" » ^T = D ὡς: 3 ὡς D n
Ἔστι δ᾽ ὧν χρῶνται ev ταῖς ἀποδεικτικαῖς ἐπιστήμαις
* * to € F4 3 , ^ δὲ , M δὲ >
τὰ μὲν ἴδια ἑκάστης ἐπιστήμης τὰ δὲ κοινά, Kowa δὲ Kar
ἀναλογίαν, ἐπεὶ χρήσιμόν γε ὅσον ἐν τῷ ὑπὸ τὴν ἐπιστήμην
A
4o γένει- ἴδια μὲν otov γραμμὴν εἶναι τοιανδὶ καὶ τὸ εὐθύ,
M * T ‘ LÀ ᾽ * LÀ bal > P Ld L4 A ,
κοινὰ δὲ olov τὸ ἴσα ἀπὸ ἴσων ἄν ἀφέλῃ, ὅτι ἴσα τὰ λοιπά.
ἱκανὸν δ᾽ ἕκαστον τούτων ὅσον ἐν τῷ γένει" ταὐτὸ γὰρ ποιή-
76> oe, κἂν μὴ κατὰ πάντων λάβῃ ἀλλ᾽ ἐπὶ μεγεθῶν μόνον,
τῷ δ᾽ ἀριθμητικῷ ἐπ᾽ ἀριθμῶν.
Ἔστι δ᾽ ἴδια μὲν καὶ ἃ λαμβάνεται εἶναι, περὶ ἃ ἡ
> a
ἐπιστήμη θεωρεῖ rà ὑπάρχοντα καθ᾽ αὑτά, olov μονάδας ἡ
» , € * , ^ ‘ ^
5 ἀριθμητική, ἡ δὲ γεωμετρία σημεῖα καὶ γραμμάς. ταῦτα
^ 4 >
yap λαμβάνουσι τὸ εἶναι καὶ Todi εἶναι. τὰ δὲ τούτων πάθη
*
καθ᾽ αὑτά, τί μὲν σημαίνει ἕκαστον, λαμβάνουσιν, οἷον ἡ
μὲν ἀριθμητικὴ τί περιττὸν ἢ ἄρτιον 7j τετράγωνον 7 κύβος,
DUE N^ 19 ἀνωτέρων 434: ἀνωτέρω B? 20 πρότερον d ἐκ
om. n! 22 οὐκ fecit n 24 at om. 5 26-7 εἰ... γνῶναι om, n!
26 εἰ) ἢ A} χαλεπὸν... 27 γνῶναι om. C 32 τι codd. 7: ὅτι Ρ
5 kai!] καί τι Cd PS 37 οἷς ΟΣ 40 τοιάνδε C 41 79] ra C
4 μονάδα ἐν ἀριθμητικῇ d 7 μὲν fecit n
I0
9. 76*16-10. 77*1
€ δὲ , , A » a Ν , a * μὲ
ἡ δὲ γεωμετρία τί τὸ ἄλογον ἢ τὸ κεκλάσθαι ἢ νεύειν, ὅτι
δ᾽ ἔστι, δεικνύουσι διά τε τῶν κοινῶν καὶ ἐκ τῶν ἀποδεδει- 10
γμένων. καὶ ἡ ἀστρολογία ὡσαύτως. πᾶσα γὰρ ἀποδεικτικὴ
ἐπιστήμη περὶ τρία ἐστίν, ὅσα τε εἶναι τίθεται (ταῦτα δ᾽
ἐστὶ τὸ γένος, οὗ τῶν καθ᾽ αὑτὰ παθημάτων ἐστὶ θεωρητική),
καὶ τὰ κοινὰ λεγόμενα ἀξιώματα, ἐξ ὧν πρώτων ἀποδεί-
κνυσι, καὶ τρίτον τὰ πάθη, ὧν τί σημαίνει ἕκαστον λαμ- τς
βάνει. ἐνίας μέντοι ἐπιστήμας οὐδὲν κωλύει ἔνια τούτων παρο-
~ f M ,ὔ ‘ € 4 t ^ ' «
pav, olov τὸ γένος μὴ ὑποτίθεσθαι εἶναι, ἂν ἦ φανερὸν ὅτι
ν , ^ L4 , ^ - » ‘ L4 ‘ Ld M]
ἔστιν (οὐ yàp ὁμοίως δῆλον ὅτι ἀριθμὸς ἔστι καὶ ὅτι ψυχρὸν
* 4 M ^ , * li , * bal ^
kai θερμόν), kai rà πάθη μὴ λαμβάνειν τί σημαίνει, ἂν ἦ 9$-
ν " * ^ ‘ % 4 , , ^ LJ > ^
λα: ὥσπερ οὐδὲ rà κοινὰ οὐ λαμβάνει τί σημαίνει TO ἴσα ἀπὸ 20
LÀ 3 ^ L4 , , , RAND ^ 4 ,
ἴσων ἀφελεῖν, ὅτι γνώριμον. ἀλλ᾽ οὐδὲν ἧττον TH ye φύσει τρία
ταῦτά ἐστι, περὶ ὅ τε δείκνυσι καὶ ἃ δείκνυσι καὶ ἐξ ὧν.
, μ᾿ > e , γῸ» LÀ ^ » , »,
Οὐκ ἔστι δ᾽ ὑπόθεσις οὐδ᾽ αἴτημα, ὃ ἀνάγκη εἶναι δι
€ ^ a ^ , , + jJ M ^ » "Hi € » ,
αὑτὸ Kal δοκεῖν ἀνάγκη. οὐ yap πρὸς τὸν ἔξω λόγον ἡ ἀπό-
δειξις, ἀλλὰ πρὸς τὸν ἐν τῇ ψυχῇ, ἐπεὶ οὐδὲ συλλογισμός. 25
> A ^ L4 ? ~ ^ ^ 4 , > Ay ^ ^
del yàp ἔστιν ἐνστῆναι πρὸς τὸν ἔξω λόγον, ἀλλὰ πρὸς τὸν
μὲ , , > 7 L4 * 7 ^ L4 , »
ἔσω λόγον οὐκ dei. ὅσα μὲν οὖν δεικτὰ ὄντα λαμβάνει αὐὖ-
* a L4 ^)5 2A * ^ , ^
τὸς μὴ δείξας, ταῦτ᾽, ἐὰν μὲν δοκοῦντα λαμβάνῃ τῷ pav-
θάνοντι, ὑποτίθεται, καὶ ἔστιν οὐχ ἁπλῶς ὑπόθεσις ἀλλὰ
^ , ^ , a * “a ^ , , 4 , na M
πρὸς ἐκεῖνον μόνον, dv δὲ ἢ μηδεμιᾶς ἐνούσης δόξης ἢ καὶ 30
ἐναντίας ἐνούσης λαμβάνῃ τὸ αὐτό, αἰτεῖται. καὶ τούτῳ δια-
φέρει ὑπόθεσις καὶ αἴτημα: ἔστι γὰρ αἴτημα τὸ ὑπεναντίον
~ , ~ , μι « LJ > M μι
τοῦ μανθάνοντος τῇ δόξη, ἢ 6 dv τις ἀποδεικτὸν ὄν λαμ-
, * ^ ^ ,
βάνῃ καὶ χρῆται μὴ δείξας.
Li hi 4 L4 , JA € Zz PANG ‘ bl * A
Οἱ μὲν οὖν ὅροι οὐκ εἰσὶν ὑποθέσεις (οὐδὲν yàp εἶναι ἢ μὴ as
λέγεται), ἀλλ᾽ ἐν ταῖς προτάσεσιν αἱ ὑποθέσεις, τοὺς δ᾽
σ , , ^ ~ > 2 « rd , M ^
ὅρους μόνον ξυνίεσθαι Set: τοῦτο δ᾽ οὐχ ὑπόθεσις (εἰ μὴ kai
^ ? , € , , , » ? " » ^
τὸ ἀκούειν ὑπόθεσίν τις εἶναι φήσει), ἀλλ᾽ ὅσων ὄντων τῷ
ἐκεῖνα εἶναι γίνεται τὸ συμπέρασμα. (οὐδ᾽ ὁ γεωμέτρης ψευδῆ
L4 7 ΄ ' v , « > a ^ ^
ὑποτίθεται, ὥσπερ τινὲς ἔφασαν, λέγοντες ὡς οὐ δεῖ τῷ ψεύ- 4o
Lj ‘ ' , ^ ,
8e. χρῆσθαι, τὸν δὲ γεωμέτρην ψεύδεσθαι λέγοντα ποδι-
αίαν τὴν οὐ ποδιαίαν ἢ εὐθεῖαν τὴν γεγραμμένην οὐκ εὐθεῖαν
οὖσαν. ὁ δὲ γεωμέτρης οὐδὲν συμπεραίνεται τῷ τήνδε εἶναι 778
bio ἐκ ravom.d 14 κοινὰ ἅ λέγομεν n ἀποδεικνύουσι 19 λαμ-
βάνων d — r(om. n! 27 ἔσω) ἑστῶτα d 30 οὔσης d 31 καὶ τοῦτο d
32 ἔστε γὰρ αἴτημα om. πὶ 33 ἢ codd. P: secl. Hayduck 35 οὐδὲν
A BdnP : οὐδὲ ΒΚ 36 λέγεται scripsi : λέγονται codd. 38 ἀλλ᾽ ὅσων
fecit st 39 ὁ om. n 40 τῷ Om. 2 7751 γεωμέτρης περαίνεται nl
ANAAYTIKON YETEPQN A
γραμμὴν ἣν αὐτὸς ἔφθεγκται, ἀλλὰ τὰ διὰ τούτων δη-
λούμενα.) ἔτι τὸ αἴτημα καὶ ὑπόθεσις πᾶσα ἢ ὡς ὅλον ἢ ὡς
ἐν μέρει, οἱ δ᾽ ὅροι οὐδέτερον τούτων.
5 Εἴδη μὲν οὖν εἶναι ἢ ἕν τι παρὰ τὰ πολλὰ οὐκ ἀνάγκη,
εἰ ἀπόδειξις ἔσται, εἶναι μέντοι ἕν κατὰ πολλῶν ἀληθὲς εἰ-
πεῖν ἀνάγκη" οὐ γὰρ ἔσται τὸ καθόλου, dv μὴ τοῦτο Jj: ἐὰν
4 ‘ ὧν A b d 4 LI ,
δὲ τὸ καθόλου μὴ 7, TO μέσον οὐκ ἔσται, ὥστ᾽ οὐδ᾽ ἀπόδειξις.
δεῖ ἄρα τι ἕν καὶ τὸ αὐτὸ ἐπὶ πλειόνων εἶναι μὴ ὁμώνυμον.
x ^ ^ , , L4 y M » Uu 4
10 TÓ. δὲ μὴ ἐνδέχεσθαι ἅμα φάναι καὶ ἀποῴφαναι οὐδεμία
λαμβάνει ἀπόδειξις, ἀλλ᾽ ἢ ἐὰν δέῃ δεῖξαι καὶ τὸ συμπέ-
ρασμα οὕτως. δείκνυται δὲ λαβοῦσι τὸ πρῶτον κατὰ τοῦ μέ-
σου, ὅτι ἀληθές, ἀποφάναι δ᾽ οὐκ ἀληθές. τὸ δὲ μέσον οὐ-
δὲν διαφέρει εἶναι καὶ μὴ εἶναι λαβεῖν, ὡς δ᾽ αὔτως καὶ
4 7 , 4 Ij > LI > 5 , ^ ,
15 τὸ τρίτον. εἰ yàp ἐδόθη, καθ᾽ οὗ ἄνθρωπον ἀληθὲς εἰπεῖν, εἰ
καὶ μὴ ἄνθρωπον ἀληθές, ἀλλ᾽ εἰ μόνον ἄνθρωπον ζῷον εἶ-
yan ^ ,
vat, μὴ ζῷον δὲ μή, ἔσται [yap] ἀληθὲς εἰπεῖν Καλλίαν, εἰ
καὶ μὴ Καλλίαν, ὅμως ζῷον, μὴ ζῷον δ᾽ οὔ. αἴτιον δ᾽ ὅτι
τὸ πρῶτον οὐ μόνον κατὰ τοῦ μέσου λέγεται ἀλλὰ καὶ κατ᾽
L4 ὃ * * f » 4 À Lo σ > δ᾽ > * J *
20 ἄλλου διὰ τὸ εἶναι ἐπὶ πλειόνων, ὥστ᾽ οὐδ᾽ εἰ τὸ μέσον καὶ
αὐτό ἐστι καὶ μὴ αὐτό, πρὸς τὸ συμπέρασμα οὐδὲν διαφέρει.
Me 3 , hal > 4 e *, M , , , ,
TO δ᾽ ἅπαν φάναι ἢ ἀποφάναι ἡ εἰς τὸ ἀδύνατον ἀπόδειξις
a Lj
λαμβάνει, καὶ ταῦτα οὐδ᾽ ἀεὶ καθόλου, ἀλλ᾽ ὅσον ἱκανόν,
[i * LER ^ n , > » νυ ~ L tT '
ἱκανὸν δ᾽ ἐπὶ τοῦ γένους. λέγω δ᾽ ἐπὶ τοῦ γένους olov περὶ
a , * > L , LA LÀ ^ ,
25 ὃ γένος tas ἀποδείξεις φέρει, ὥσπερ εἴρηται καὶ πρότερον.
2 ~ 4 -^ t > ~ > Là ^
Ἐπικοινωνοῦσι δὲ πᾶσαι αἱ ἐπιστῆμαι ἀλλήλαις κατὰ
τὰ κοινά (κοινὰ δὲ λέγω οἷς χρῶνται ὡς ἐκ τούτων ἀπο-
L4 3 ? ΕΣ ‘ L 4 , »95 a N 4,
δεικνύντες, GAN’ οὐ περὶ ὧν δεικνύουσιν οὐδ᾽ 6 detxvdovow),
καὶ ἡ διαλεκτικὴ πάσαις, καὶ εἴ τις καθόλου πειρῷτο δει-
, ^ , " oe , a 3 , bl L4
3o «viva, τὰ κοινά, olov ὅτι ἅπαν φάναι ἢ ἀποφάναι, ἢ ὅτι
» > ^ oW - - 4 LÀ να ^ A *, LÀ
ἴσα ἀπὸ ἴσων, ἢ τῶν τοιούτων ἄττα. ἡ δὲ διαλεκτικὴ οὐκ ἔστιν
οὕτως ὡρισμένων τινῶν, οὐδὲ γένους τινὸς ἑνός. οὐ γὰρ ἂν ἠρώτα"
^ ~ ,
ἀποδεικνύντα yàp οὐκ ἔστιν ἐρωτᾶν διὰ τὸ τῶν ἀντικειμένων
*21)v]anofav? τελούμενα d 3 ἔτι fecit n 5-9 Ei$9. . . ὁμώνυμον
hic codd. P: in 75b24 interpretatur T: an ad 83735 transponenda?
7 ἔστιν n Qemn 12 λαμβάνουσι n τὸ om. nt 14 woav-
tas C 16 dAnOes+etnety d! ἀλλ᾽ ἢ Bi: ἀλλὰ fecit n elvot-+ πᾶν
ACdnP 17 μή fecit » ἔστι n yàp seclusi: δ᾽ s €... 18
Καλλίαν om. 71 17 ἢ B* 18 ὁμοίως Bd 19-20 kar’...
elvacom. ἢ 23 οὐδὲν δεῖ n 24 Aéyw ... yévousom.C 27 rà
κοινὰ om, mn! 28 οὐδ᾽ ὃ δεικνύουσιν om. 7% 31 drra ABC
32 évds om. 2
IO. 77*2-12. 77°25
L4 4 » * 2 , 7 M ^ > ^
ὄντων μὴ δείκνυσθαι τὸ αὐτό. δέδεικται δὲ τοῦτο ἐν τοῖς
περὶ συλλογισμοῦ. 35
12 Εἰ δὲ τὸ αὐτό ἐστιν ἐρώτημα συλλογιστικὸν καὶ mpó-
τασις ἀντιφάσεως, προτάσεις δὲ Kal? ἑκάστην ἐπιστήμην
, ^ € \ € > t€ / v » 2
ἐξ ὧν 6 συλλογισμὸς ὁ καθ᾽ ἑκάστην, ein dv τι ἐρώτημα
ἐπιστημονικόν, ἐξ ὧν ὁ καθ᾽ ἑκάστην οἰκεῖος γίνεται συλλο-
γισμός. δῆλον dpa ὅτι οὐ πᾶν ἐρώτημα γεωμετρικὸν ἂν 4o
εἴη οὐδ᾽ ἰατρικόν, ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων: ἀλλ᾽ ἐξ
a ὃ L4 , * T [4 , 3 , bl "^ 2 ^ b
ὧν δείκνυταί τι περὶ ὧν ἡ γεωμετρία ἐστίν, ἢ ἃ ἐκ τῶν 77
ΕΣ ~ "A ^ , σ M > , € ,
αὐτῶν δείκνυται τῇ γεωμετρίᾳ, ὥσπερ τὰ ὀπτικά. ὁμοίως
b M » & ~ Ld \ * M , M , e
δὲ kai ἐπὶ τῶν ἄλλων. καὶ περὶ. μὲν τούτων καὶ λόγον vde-
κτέον ἐκ τῶν γεωμετρικῶν ἀρχῶν καὶ συμπερασμάτων,
περὶ δὲ τῶν ἀρχῶν λόγον οὐχ ὑφεκτέον τῷ γεωμέτρῃ $5
γεωμέτρης: ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων ἐπιστημῶν. οὔτε
πᾶν ἄρα ἕκαστον ἐπιστήμονα ἐρώτημα ἐρωτητέον, οὐθ᾽ ἅπαν
τὸ ἐρωτώμενον ἀποκριτέον περὶ ἑκάστου, ἀλλὰ τὰ κατὰ τὴν
ἐπιστήμην διορισθέντα. εἰ δὲ διαλέξεται γεωμέτρῃ f$ γεω-
μέτρης οὕτως, φανερὸν ὅτι καὶ καλῶς, ἐὰν ἐκ τούτων τι τὸ
δεικνύῃ: εἰ δὲ μή, οὐ καλῶς. δῆλον δ᾽ ὅτι οὐδ᾽ ἐλέγχει
, > > n 4 , " > *, n v >
γεωμέτρην add’ ἢ Kata συμβεβηκός: ὥστ᾽ οὐκ av εἴη ἐν
ἀγεωμετρήτοις περὶ γεωμετρίας διαλεκτέον: λήσει γὰρ ὁ
TA ΄ ε , x M LT ~ Ww L4
φαύλως διαλεγόμενος. ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων ἔχει
ἐπιστημῶν. 15
"ER ἣν δ᾽ v a > , 7. L4 *
εἰ ἔστι γεωμετρικὰ ἐρωτήματα, ἄρ᾽ ἔστι καὶ
ἀγεωμέτρητα; καὶ παρ᾽ ἑκάστην ἐπιστήμην τὰ κατὰ τὴν
ἄγνοιαν τὴν ποίαν γεωμετρικά ἐστιν; καὶ πότερον
ὃ κατὰ τὴν ἄγνοιαν cvMoywuós 6 ἐκ τῶν ἀντικει-
μένων συλλογισμός, ἢ ὁ παραλογιομός, κατὰ γεωμετρίαν 20
δέ, ἢ «ó» ἐξ ἄλλης τέχνης, οἷον τὸ μουσικόν ἐστιν ἐρώτημα
ἀγεωμέτρητον περὶ γεωμετρίας, τὸ δὲ τὰς παραλλήλους
συμπίπτειν οἴεσθαι γεωμετρικόν πως καὶ ἀγεωμέτρητον ἄλ-
λον τρόπον; διττὸν γὰρ τοῦτο, ὥσπερ τὸ ἄρρυθμον, καὶ τὸ
μὲν ἕτερον ἀγεωμέτρητον τῷ μὴ ἔχειν [ὥσπερ τὸ ἄρρυθμον), 25
331 πρότασις nt 39 dom, n by dv+4 ABCd dom. ABC*d
2 domep] ἐστὶν ὥσπερ n 7 ἕκαστον τὸν ἐπιστήμονα n: ἐπιστήμονα d:
om. ΟἹ 8 τὰ om. d 9 διαλέξεται-- τῷ n 11 δὲ μή) δὴ d
δηλονότι d 13 ἀγεωμετρήτῳ C 14 φαῦλος d 16 ἄρ᾽ n
17 koic- à 18 ποίαν A?P : ποιὰν ABCdn €ariw-F xai ἀγεωμέτρητα
f: +4 ἀγεωμέτρητα Bekker 19 6? om. 5 20 ó om. Cn παρα-
συλλογισμός 4411 Β1᾽43 21 ὁ adieci 22 παραλλήλας n 25 τὸ d
ὥσπερ τὸ ἄρρυθμον secl. Mure
4985 Q
ANAAYTIKQN YETEPQN A
^ , L4 ~ , LÀ ‘ L4 LÀ σ ‘ ul ?
τὸ δ᾽ ἕτερον τῷ φαύλως ἔχειν: kai ἡ ἄγνοια αὕτη kai ἡ ἐκ
τῶν τοιούτων ἀρχῶν ἐναντία. ἐν δὲ τοῖς μαθήμασιν οὐκ ἔστιν
ε , e , σ * a > M LE] A ,
ὁμοίως 6 παραλογισμός, ὅτι τὸ μέσον ἐστὶν dei τὸ διττόν"
κατά τε γὰρ τούτου παντός, καὶ τοῦτο πάλιν κατ᾽ ἄλλου
30 λέγεται παντός (τὸ δὲ κατηγορούμενον οὐ λέγεται πᾶν), ταῦτα
δ᾽ ἔστιν οἷον ὁρᾶν τῇ νοήσει, ἐν δὲ τοῖς λόγοις λανθάνει. dpa
πᾶς κύκλος σχῆμα; ἄν δὲ γράψῃ, δῆλον. τί δέ; τὰ ἔπη
κύκλος; φανερὸν ὅτι οὐκ ἔστιν.
Οὐ δεῖ δ᾽ ἔνστασιν εἰς αὐτὸ φέρειν, av ἦ ἡ πρότασις
35 ἐπακτική. ὥσπερ γὰρ οὐδὲ πρότασίς ἐστιν ἣ μὴ ἔστιν ἐπὶ
, ᾽ ^ L4 » V 4 > ^ , » *
πλειόνων (od yàp ἔσται ἐπὶ πάντων, ἐκ τῶν καθόλου δ᾽ ὃ
, ~ L4 395» L4 « > 3 ^
συλλογισμός), δῆλον ὅτι οὐδ᾽ ἔνστασις. ai αὐταὶ yàp mpo-
τάσεις καὶ ἐνστάσεις. ἣν γὰρ φέρει ἔνστασιν, αὕτη γένοιτ᾽
ἂν πρότασις ἢ ἀποδεικτικὴ ἢ διαλεκτική.
4» Συμβαίνει δ' ἐνίους ἀσυλλογίστως λέγειν διὰ τὸ λαμ-
, > , ^ e , x € ^ ^
Bavew ἀμφοτέροις τὰ ἑπόμενα, olov xai ὁ Kaweds ποιεῖ,
- ^ ^ , ^ , > , * A A ~
78* ὅτι τὸ πῦρ ἐν TH πολλαπλασίᾳ ἀναλογίᾳ: kai yap TO πῦρ
^ Lj LÀ M L4 L4 , , 4 »
ταχὺ γεννᾶται, ws φησι, καὶ αὕτη ἡ ἀναλογία. οὕτω ὃ
> μὴ , 3 > > ~ L4 , , -
οὐκ ἔστι συλλογισμός: ἀλλ᾽ εἰ τῇ ταχίστῃ ἀναλογίᾳ ἔπε-
ται ἡ πολλαπλάσιος καὶ τῷ πυρὶ ἡ ταχίστη ἐν τῇ κινήσει
> , 3. 4 ‘ ρα 3 > , , » ^
5 ἀναλογία. ἐνίοτε μὲν οὖν οὐκ ἐνδέχεται συλλογίσασθαι ἐκ τῶν
, € »*:5 Li > ΕΣ > ca
6 εἰλημμένων, ὁτὲ δ᾽ ἐνδέχεται, ἀλλ᾽ οὐχ ὁρᾶται.
6 Εἰ δ᾽ ἦν
ἀδύνατον ἐκ ψεύδους ἀληθὲς δεῖξαι, ῥάδιον dv ἦν τὸ ἀνα-
λύειν: ἀντέστρεφε γὰρ dv ἐξ ἀνάγκης. ἔστω γὰρ τὸ A ov
τούτου δ᾽ ὄντος ταδὶ ἔστιν, ἃ olSa ὅτι ἔστιν, οἷον τὸ B. ἐκ
1o τούτων ἄρα δείξω ὅτι ἔστιν ἐκεῖνο. ἀντιστρέφει δὲ μᾶλλον
A > a x Ld RANDY M ΄
τὰ ἐν τοῖς μαθήμασιν, ὅτι οὐδὲν συμβεβηκὸς λαμβάνουσιν
> e. ^ , ὔ ^ > ^ , » >
(ἀλλὰ καὶ τούτῳ διαφέρουσι τῶν ἐν τοῖς διαλόγοις) dM
L4 ,
ὁρωμούς.
Αὔξεται 8 οὐ διὰ τῶν μέσων, ἀλλὰ τῷ προσλαμ-
15 βάνειν, οἷον τὸ A τοῦ B, τοῦτο δὲ τοῦ I', πάλιν τοῦτο τοῦ A,
καὶ τοῦτ᾽ εἰς ἄπειρον. καὶ εἰς τὸ πλάγιον, οἷον τὸ A καὶ
^ ~ M A ^ L4 » * ^ a
κατὰ τοῦ l' kai κατὰ τοῦ E, olov ἔστιν ἀριθμὸς ποσὸς ἢ
b26 τῷ) τὸ d xai? om, Aldina 28 παρασυλλογισμός A rot
om, C*d 29 te] ye B τοῦτο] τούτου B? 32 γράφῃ n τί
δαί; τὸ ἔπος 34 εἰς αὐτὸ an corrupta? ἂν $) ἐν fut vid. PT, an
recte? 36 δ᾽ om. n 3972n 3 διαλεκτική om. n 18*2 αὕτη
ἡ] ἡ αὐτὴ 4: αὕτηπὶ οὗτος ἀ δ᾽ om. C1 5 οὖν om. ὦ 12 τοῦτο fi
14 αὔξεται fecit & 15 roüró? -Ἐ δὲ n 16 «ai? om. n 17 ]Bn
12. 77°26-13. 78°10
A] L4 -^ ?, I? T € * > 4 ^ » [5
kai ἄπειρος τοῦτο ἐφ᾽ ᾧ A, 6 περιττὸς ἀριθμὸς toads ἐφ
οὗ B, ἀριθμὸς περιττὸς ἐφ᾽ οὗ I^ ἔστιν ἄρα τὸ A κατὰ
τοῦ l'. καὶ ἔστιν 6 ἄρτιος ποσὸς ἀριθμὸς ἐφ᾽ οὗ A, ὃ ἄρ- :ο
τιος ἀριθμὸς ἐφ᾽ οὗ E- ἔστιν ἄρα τὸ A κατὰ τοῦ E.
13 Τὸ δ᾽ ὅτι διαφέρει καὶ τὸ διότι ἐπίστασθαι, πρῶτον
μὲν ἐν τῇ αὐτῇ ἐπιστήμῃ, καὶ ἐν ταύτῃ διχῶς, ἕνα μὲν
τρόπον ἐὰν μὴ δι’ ἀμέσων γίνηται ὃ συλλογισμός (οὐ γὰρ
λαμβάνεται τὸ πρῶτον αἴτιον, ἡ δὲ τοῦ διότι ἐπιστήμη κατὰ 25
τὸ πρῶτον αἴτιον), ἄλλον δὲ εἰ δι’ ἀμέσων μέν, ἀλλὰ
M A ~ 7 3, ^ ^ » , ^ ~
μὴ διὰ τοῦ αἰτίου ἀλλὰ τῶν ἀντιστρεφόντων διὰ τοῦ γνωρι-
μωτέρου. κωλύει γὰρ οὐδὲν τῶν ἀντικατηγορουμένων γνωρι-
μώτερον εἶναι ἐνίοτε τὸ μὴ αἴτιον, ὥστ᾽ ἔσται διὰ τούτου ἡ
ἀπόδειξις, οἷον ὅτι ἐγγὺς οἱ πλάνητες διὰ τοῦ μὴ στίλβειν. 3o
ἔστω ἐφ᾽ à Γ᾽ πλάνητες, ἐφ᾽ à B τὸ μὴ στίλβειν, ἐφ᾽ &
A τὸ ἐγγὺς εἶναι. ἀληθὲς δὴ τὸ B κατὰ τοῦ Γ εἰπεῖν: οἱ
γὰρ πλάνητες οὐ στίλβουσιν. ἀλλὰ καὶ τὸ A κατὰ τοῦ Β' τὸ
M M > , , a > » , > >
yàp μὴ στίλβον ἐγγύς ἐστι" τοῦτο δ᾽ εἰλήφθω δι᾽ ἐπαγω-
Lj hal LI », L4 > , T 4 ^ L4 , "- >
γῆς ἢ δι’ αἰσθήσεως. ἀνάγκη οὖν τὸ A τῷ Γ᾽ ὑπάρχειν, ὥστ᾽ 35
ἀποδέδεικται ὅτι οἱ πλάνητες ἐγγύς εἰσιν. οὗτος οὖν ὃ συλ-
λογισμὸς οὐ τοῦ διότι ἀλλὰ τοῦ ὅτι ἐστίν: οὐ γὰρ διὰ τὸ μὴ
3
στίλβειν ἐγγύς εἰσιν, ἀλλὰ διὰ τὸ ἐγγὺς εἶναι οὐ στίλβουσιν.
3 ^ A A A , , 05 M LÀ
ἐγχωρεῖ δὲ καὶ διὰ θατέρου θάτερον δειχθῆναι, καὶ ἔσται
τοῦ διότι ἡ ἀπόδειξις, οἷον ἔστω τὸ D πλάνητες, ἐφ᾽ à Bao
τὸ ἐγγὺς εἶναι, τὸ A τὸ μὴ στώβειν: ὑπάρχει δὴ καὶ τὸ 78>
B τῷ Γ καὶ τὸ A τῷ B, ὥστε καὶ τῷ Γ τὸ A [τὸ μὴ ord-
M w ~ , € , Μ᾿ M ^
Bew]. καὶ ἔστι τοῦ διότι 6 συλλογισμός: εἴληπται yap τὸ
πρῶτον αἴτιον. πάλιν ὡς τὴν σελήνην δεικνύουσιν ὅτι σφαι-
ροειδής, διὰ τῶν αὐξήσεων--εἰἶ γὰρ τὸ αὐξανόμενον οὕτω s
, , , ᾽ « ta A a”
σφαιροειδές, αὐξάνει δ᾽ ἡ σελήνη, φανερὸν ὅτι σφαιροει-
l4 L4 A ^ ^ " rf Li , > ,
δής---οὕτω μὲν οὖν τοῦ ὅτι γέγονεν ὁ συλλογισμός, ἀνάπαλιν
δὲ τεθέντος τοῦ μέσου τοῦ διότι: οὐ γὰρ διὰ τὰς αὐξήσεις
σφαιροειδής ἐστιν, ἀλλὰ διὰ τὸ σφαιροειδὴς εἶναι λαμβά-
νει τὰς αὐξήσεις τοιαύτας. σελήνη ἐφ᾽ à I, σφαιροειδὴς το
418 A om. d?: τὸ aC 21 E! om. s! 25700m.d 7... 26
αἴτιον om. C 26 ἄλλων 4101 ei] εἰ μὴ πὶ 30 πλανῆται n διὰ...
31 πλάνητες om. A 30 76 C 3100 C πλανῆται 5 of BC
35 y fecit B: B Ad 39 ἔστι ἃ b2 kal! .. . στίλβειν] dore καὶ τῷ
y τὸ a καὶ τὸ a τῷ β τὸ μὴ στίλβειν ABCd: καὶ τὸ A τῷ Β τὸ μὴ στίλβειν, Gore
καὶ τῷ Γ τὸ A Bekker: Gore καὶ τῷ Γ τὸ A, τὸ μὴ στίλβειν Waitz: τὸ μὴ
στίλβειν seclusi 6 αὐξάνεται n 7 οὗτος d οὖν om. B γίνεται
συλλογισμός n 10 σφαιροειδὲς n
13
13
15
20
25
35
40
79*
ANAAYTIKQN YZTEPON A
ἐφ’ à B, αὔξησις ἐφ’ ᾧ A. ἐφ᾽ ὧν δὲ τὰ μέσα μὴ
ἀντιστρέφει καὶ ἔστι γνωριμώτερον τὸ ἀναίτιον, τὸ ὅτι μὲν
δείκνυται, τὸ διότι δ᾽ οὔ.
Ἔτι ἐφ᾽ ὧν τὸ μέσον ἔξω τίθεται.
^ AJ ᾿ , ~ " ^ ᾽ ~ ^ e > ^ >
καὶ yap ev τούτοις τοῦ ὅτι Kal ov τοῦ διότι ἡ ἀπόδειξις" οὐ
γὰρ λέγεται τὸ αἴτιον. οἷον διὰ τί οὐκ ἀναπνεῖ ὁ τοῖχος;
ὅτι οὐ ζῷον. εἰ γὰρ τοῦτο τοῦ μὴ ἀναπνεῖν αἴτιον, ἔδει τὸ
^ L4 LE ^ > ¢ » , >t ^
ζῷον εἶναι αἴτιον τοῦ ἀναπνεῖν, olov εἰ ἡ ἀπόφασις αἰτία τοῦ
‘ ~ > ^ >
μὴ ὑπάρχειν, ἡ κατάφασις τοῦ ὑπάρχειν, ὥσπερ εἰ τὸ ἀσύμ-
μετρα εἶναι τὰ θερμὰ καὶ τὰ ψυχρὰ τοῦ μὴ ὑγιαίνειν, τὸ
σύμμετρα εἶναι τοῦ ὑγιαίνειν, -ὁμοίως δὲ καὶ εἰ ἡ κατάφα-
σις τοῦ ὑπάρχειν, ἡ ἀπόφασις τοῦ μὴ ὑπάρχειν. ἐπὶ δὲ
~ o0 > , % , ^ , > ‘
τῶν οὕτως ἀποδεδομένων οὐ συμβαίνει τὸ λεχθέν: od yap
ἅπαν ἀναπνεῖ ζῷον. ὁ δὲ συλλογισμὸς γίνεται τῆς τοιαύ-
» » > ~ , , w M ~ 77?
τῆς αἰτίας ἐν τῷ μέσῳ σχήματι. olov ἔστω τὸ A ζῷον, ἐφ
ᾧ B τὸ ἀναπνεῖν, ἐφ’ ᾧ Γ τοῖχος. τῷ μὲν οὖν B παντὶ
- 4 x ~ ^ A > , ^ “ A »
ὑπάρχει τὸ A (πᾶν yap τὸ dvamvéov ζῷον), τῷ δὲ Γ᾽ οὐ-
, σ > * * ~ , Ld , L4 > ~ t ^
θενί, ὥστε οὐδὲ τὸ B τῷ Γ οὐθενί: οὐκ dpa ἀναπνεῖ à τοῖ-
χος. ἐοίκασι δ᾽ αἱ τοιαῦται τῶν αἰτιῶν τοῖς καθ᾽ ὑπερ-
βολὴν εἰρημένοις: τοῦτο δ᾽ ἔστι τὸ πλέον ἀποστήσαντα τὸ μέ-
> ^ T * ^5 , - > rf > "ἢ
σον εἰπεῖν, οἷον τὸ τοῦ “Avaydpotos, ὅτι ἐν Σκύθαις οὐκ εἴ-
i, $, γον 3 LÀ
civ αὐλητρίδες, οὐδὲ yàp ἄμπελοι.
Κατὰ μὲν δὴ τὴν αὐτὴν ἐπιστήμην καὶ κατὰ τὴν τῶν
, y T # > ~ a A ^ i
μέσων θέσιν αὗται διαφοραί εἰσι τοῦ ὅτι πρὸς τὸν τοῦ διότι
συλλογισμόν: ἄλλον δὲ τρόπον διαφέρει τὸ διότι τοῦ ὅτι
~ , Μ > , Li , L3 ^ » 3 ,ὔ
τῷ δι’ ἄλλης ἐπιστήμης ἑκάτερον θεωρεῖν. τοιαῦτα δ᾽ ἐστίν
-Ὁ L4 » A L4 σ > 4 t ^ ,
ὅσα οὕτως ἔχει πρὸς ἄλληλα ὥστ᾽ εἶναι θάτερον ὑπὸ θάτε-
ρον, οἷον τὰ ὀπτικὰ πρὸς γεωμετρίαν καὶ τὰ μηχανικὰ
πρὸς στερεομετρίαν καὶ τὰ ἁρμονικὰ πρὸς ἀριθμητικὴν καὶ
τὰ φαινόμενα πρὸς ἀστρολογικήν. σχεδὸν δὲ συνώνυμοί εἰ-
σιν ἔνιαι τούτων τῶν ἐπιστημῶν, οἷον ἀστρολογία 7| τε μα-
€ *
Ünuaruc) καὶ ἡ vavrucj, kal áppovuc) 7j τε μαθηματικὴ
bir αὐξήσεις n δὲ om. C! 12 ἀντιστρέφῃ An 14 τὸ ὅτι B
15 λέγει" οἷον- ὅτι Ο ἀναπνέει ABC 16 ἀναπνεῖν CnP*T τ ἀναπνέειν
ABd 19 ψυχρὰ καὶ θερμὰ C rà om. Ad τὸ Aldina: ra codd.
21 ἐπὶ] εἰ fecit B 22 ἀποδιδομένων n 25 οὗ ro B ABCd TÓ
om.C τὸ Ald Groad τῷ δὲ ΓῚ τὸ δὲβ 4Ὶ οὐδενί π
27 οὔτε AB οὐδενί n 30 ᾿ἀναχάρσιδος Cn P^ 31 αὐλητρίδες
n PT: αὐληταί ABCd 32 δὴ] οὖν n τῶν om. C1 33 ἀμέσων B* :
αὐτῶν ÁBd αὗται-Ἐ αἱ d 35 τὸ ABCdP* 37 καὶ om. d 40 ἔνια B
olov om. d
13. 7811-15. 79736
a L4 * ^ > P4 4 ^ ^ A x e ~ +
kai ἡ κατὰ τὴν ἀκοήν. ἐνταῦθα yap τὸ μὲν ὅτι τῶν αἰσθη-
τικῶν εἰδέναι, τὸ δὲ διότι τῶν μαθηματικῶν: οὗτοι γὰρ ἔχουσι
τῶν αἰτίων τὰς ἀποδείξεις, καὶ πολλάκις οὐκ ἴσασι τὸ ὅτι, κα-
θάπερ οἱ τὸ καθόλου θεωροῦντες πολλάκις ἔνια τῶν καθ᾽ ἕκαστον s
, " > > / LÀ M ^ Ld L4 , »
οὐκ ἴσασι OU ἀνεπισκεψίαν. ἔστι δὲ ταῦτα ὅσα ἕτερόν τι ὄντα
τὴν οὐσίαν κέχρηται τοῖς εἴδεσιν. τὰ γὰρ μαθήματα περὶ εἴδη
, MJ M
ἐστίν' οὐ yàp Kal” ὑποκειμένου τινός" εἰ yàp kai καθ᾽ ὑποκει-
, ^ ^ LE] 2 3 3 id , € Cd
pévov Twos τὰ γεωμετρικά ἐστιν, ἀλλ᾽ οὐχ ἣ ye καθ᾽ ὑποκειμέ-
* * A > * 4
νου. ἔχει δὲ καὶ πρὸς τὴν ὀπτικήν, ὡς αὕτη πρὸς THY γεωμε- 1o
4 , « * ^
τρίαν, ἄλλη πρὸς ταύτην, olov τὸ περὶ τῆς ἴριδος: τὸ μὲν
^ Ld ~ ἰδέ ^ 8é ὃ , > ^ -^ € ~ -^ ^
yàp ὅτι φυσικοῦ εἰδέναι, τὸ δὲ διότι ὀπτικοῦ, ἢ ἁπλῶς ἢ τοῦ
κατὰ τὸ μάθημα. πολλαὶ δὲ καὶ τῶν μὴ ὑπ’ ἀλλήλας
ἐπιστημῶν ἔχουσιν οὕτως, οἷον ἰατρικὴ πρὸς γεωμετρίαν: ὅτι
μὲν γὰρ τὰ ἕλκη τὰ περιφερῆ βραδύτερον ὑγιάζεται, τοῦ 15
ἰατροῦ εἰδέναι, διότι δὲ τοῦ γεωμέτρου.
Té δὲ V4 > ^ aX A ~ ,
14 Ov δὲ σχημάτων ἐπιστημονικὸν μάλιστα τὸ πρῶτόν
ἐστιν. αἷ τε γὰρ μαθηματικαὶ τῶν ἐπιστημῶν διὰ τούτου
φέρουσι τὰς ἀποδείξεις, οἷον ἀριθμητικὴ καὶ γεωμετρία καὶ
* -^ ~ ~
ὀπτική, Kal σχεδὸν ws εἰπεῖν ὅσαι τοῦ διότι ποιοῦνται τὴν 20
ta -* ^ μὲ ^ e 3 4 a A ; a ,
σκέψιν: ἢ yàp ὅλως ἢ ws ἐπὶ τὸ πολὺ Kai ἐν τοῖς πλεί-
στοις διὰ τούτου τοῦ σχήματος ὁ τοῦ διότι συλλογισμός. ὥστε
κἂν διὰ τοῦτ᾽ εἴη μάλιστα ἐπιστημονικόν: κυριώτατον γὰρ
τοῦ εἰδέναι τὸ διότι θεωρεῖν. εἶτα τὴν τοῦ τί ἐστιν ἐπιστήμην
διὰ μόνου τούτου θηρεῦσαι δυνατόν. ἐν μὲν γὰρ τῷ μέσῳ 25
σχήματι οὐ γίνεται κατηγορικὸς συλλογισμός, ἡ δὲ τοῦ
τί ἐστιν ἐπιστήμη καταφάσεως: ἐν δὲ τῷ ἐσχάτῳ yiveTar
μὲν ἀλλ᾽ οὐ καθόλου, τὸ δὲ τί ἐστι τῶν καθόλου ἐστίν" οὐ
γὰρ πῇ ἐστι ζῷον δίπουν ὁ ἄνθρωπος. ἔτι τοῦτο μὲν ἐκείνων
οὐδὲν προσδεῖται, ἐκεῖνα δὲ διὰ τούτου καταπυκνοῦται καὶ 30
L4 e * > 4 » LÀ M] ^ Ld
αὔξεται, ἕως av eis rà ἄμεσα ἔλθῃ. φανερὸν οὖν ὅτι κυ-
^5 ^ ^
ριώτατον τοῦ ἐπίστασθαι τὸ πρῶτον σχῆμα.
~ , ἢ e
IS Ὥσπερ δὲ ὑπάρχειν τὸ A τῷ B ἐνεδέχετο ἀτόμως, οὕτω
M ^ , > ^ , t Ld bl
καὶ μὴ ὑπάρχειν ἐγχωρεῖ. λέγω δὲ τὸ ἀτόμως ὑπάρχειν ἢ
bi , ^
μὴ ὑπάρχειν τὸ μὴ εἶναι αὐτῶν μέσον": οὕτω yàp οὐκέτι ἔσται 35
> » soe oF ^ So + L4 H Rd M M A
κατ᾽ ἄλλο τὸ ὑπάρχειν 7 μὴ ὑπάρχειν. ὅταν μὲν οὖν ἢ TO
7974 αἰτιῶν C 8-9 εἰ -- τινὸς om, nt 9 γεωμετρικά C, fecit
n: γεωμετρητά ABd οὐχί ye B 10 atrnt+yed I2 τοῦ om.
Aldina 17 τὸ om. m! 20 ὡς om. dn 23 kai f τοῦτ᾽ τοῦ
ἂν πὶ 27 ἐσχάτῳ τι ἔσται d 29 ἔτι] etd 3I μέσα n! 33-4 οὕτω
«+ ἀτόμως om. πὶ 35 τῷ C!
40
79°
5
το
15
20
25
ANAAYTIKQN YZTEPON A
ἢ τὸ B ἐν ὅλῳ τινὶ ἦ, ἢ kai ἄμφω, οὐκ ἐνδέχεται τὸ A τῷ
B πρώτως μὴ ὑπάρχειν. ἔστω γὰρ τὸ A ἐν ὅλῳ τῷ I.
, "^. > M A v > L4 ^ > ^ A 4 A
οὐκοῦν εἰ τὸ B μὴ ἔστιν ἐν ὅλῳ τῷ I (ἐγχωρεῖ yap τὸ μὲν
A εἶναι ἔν τινι ὅλω, τὸ δὲ B μὴ εἶναι ἐν τούτῳ), συλλο-
; μὴ 2),
γισμὸς ἔσται τοῦ μὴ ὑπάρχειν τὸ A τῷ DB- εἰ yàp TQ μὲν
A παντὶ τὸ I’, τῷ δὲ B μηδενί, οὐδενὶ τῷ B τὸ A. ὁμοίως
δὲ M » A B ᾽ Ld , * Lu > ~ ^ *
€ καὶ εἰ τὸ B ἐν ὅλῳ τινί ἐστιν, οἷον ἐν τῷ A+ τὸ μὲν
γὰρ 4 παντὶ τῷ Β ὑπάρχει, τὸ δὲ Α οὐδενὶ τῷ 4, ὥστε
τὸ Α οὐδενὶ τῷ Β ὑπάρξει διὰ συλλογισμοῦ. τὸν αὐτὸν
δὲ τρόπον δειχθήσεται καὶ εἰ ἄμφω ἐν ὅλῳ τινί ἐστιν. ὅτι
δ᾽ ἐνδέχεται τὸ Β μὴ εἶναι ἐν ᾧ ὅλῳ ἐστὶ τὸ Α͂, ἢ πάλιν
‘ 3 T ΑἹ M] 3 ^ ~ Ld ^ 2
τὸ Α ἐν ᾧ τὸ Β, φανερὸν ἐκ τῶν συστοιχιῶν, ὅσαι μὴ ἐπαλ-
λάττουσιν ἀλλήλαις. εἰ γὰρ μηδὲν τῶν ἐν τῇ A Γ 4 συ-
στοιχίᾳ κατὰ μηδενὸς κατηγορεῖται τῶν ἐν τῇ Β Ε Z, τὸ
δ᾽ A ἐν ὅλῳ ἐστὶ τῷ O συστοίχῳ ὄντι, φανερὸν ὅτι τὸ Β
, » 2 ^ > , ^ e , e ,
οὐκ ἔσται ἐν TH O- ἐπαλλάξουσι yàp ai συστοιχίαι. ὁμοίως
^ M , A B , Ld , > oN δὲ δέ >
δὲ καὶ εἰ τὸ B ἐν ὅλῳ τινί ἐστιν. ἐὰν δὲ μηδέτερον jj ἐν
e [4 A [i / A * ^ > , 3 ,
ὅλῳ μηδενί, μὴ ὑπάρχῃ δὲ τὸ A τῷ B, ἀνάγκη ἀτόμως
μὴ ὑπάρχειν. εἰ γὰρ ἔσται τι μέσον, ἀνάγκη θάτερον av-
τῶν ἐν ὅλῳ τινὶ εἶναι. ἢ γὰρ ἐν τῷ πρώτῳ σχήματι 7) ἐν
τῷ μέσῳ ἔσται 6 συλλογισμός. εἰ μὲν οὖν ἐν τῷ πρώτῳ,
* L4 > Ld , x x a a ^ ^
τὸ B ἔσται ἐν ὅλῳ τινί (καταφατικὴν yap δεῖ τὴν πρὸς τοῦτο
γενέσθαι πρότασιν), εἰ δ᾽ ἐν τῷ μέσῳ, ὁπότερον ἔτυχεν
(πρὸς ἀμφοτέροις γὰρ ληφθέντος τοῦ στερητικοῦ γίνεται συλ-
λογισμός: ἀμφοτέρων δ᾽ ἀποφατικῶν οὐσῶν οὐκ ἔσται).
Φ A T L4 > r4 P » L4 a L4 Ls 2 id
avepóv οὖν ὅτι ἐνδέχεταί Te ἄλλο ἄλλῳ μὴ ὑπάρχειν ἀτό-
μως, καὶ πότ᾽ ἐνδέχεται καὶ πῶς, εἰρήκαμεν.
Ἄγνοια δ᾽ ἡ μὴ kar ἀπόφασιν ἀλλὰ κατὰ διάθε-
σιν λεγομένη ἔστι μὲν ἡ διὰ συλλογισμοῦ γινομένη ἀπάτη,
αὕτη δ᾽ ἐν μὲν τοῖς πρώτως ὑπάρχουσιν ἢ μὴ ὑπάρχουσι
P ^ Ll M Ld Lj ^ € , L4 ,ὔ
συμβαίνει διχῶς: ἢ γὰρ ὅταν ἁπλῶς ὑπολάβῃ ὑπάρχειν
^ ^ x , ^ Ld δ A AA ~ Xr , M D ,
ἢ μὴ ὑπάρχειν, 7 ὅταν διὰ συλλογισμοῦ λάβῃ τὴν ᾿ὑπό-
ληψιν. τῆς μὲν οὖν ἁπλῆς ὑπολήψεως ἁπλῆ ἡ ἀπάτη, τῆς
437 τὸϊ om. 5 40 ἔν om. f br τῷδ nP : τῶν ABCd 3A
om. n! τῷ....4 οὐδενὶ 0m. ABd 3rdvn ἀτῶνβ ABICd ὑὕὑπάρ-
xen 6-160... B] Aw τῷ β πὶ 6 ὅλῳ om. dn? 3] καὶ n?
14] ὅλῳ 3, συστοίχων B 9 κατὰ] καὶ κατὰ Al Bld) 11 @] εϑ
Ad) 13 ὑπάρχει ἢ 16é¢om.C 17 τούτῳ dn 18 γίνεσθαι"
21 re] τι dn ἄλλο om. Bekker 23 ἀλλ ἢ π 24 γενομένη Β
25 μὲν om. ἡ ἢ μὴ ὑπάρχουσι om. C1
τό
I5. 79°37-16. 80721
δὲ διὰ συλλογισμοῦ πλείους. μὴ ὑπαρχέτω yap τὸ A μη-
δενὶ τῷ Β ἀτόμως: οὐκοῦν ἐὰν συλλογίζηται ὑπάρχειν τὸ
A τῷ B, μέσον λαβὼν τὸ I', ἠπατημένος ἔσται διὰ συλ-
λογισμοῦ. ἐνδέχεται μὲν οὖν ἀμφοτέρας τὰς προτάσεις εἶ-
ναι ψευδεῖς, ἐνδέχεται δὲ τὴν ἑτέραν μόνον. εἰ γὰρ μήτε
M 4 ^ « , , 4 M ^ Ww
τὸ A μηδενὶ τῶν Γ ὑπάρχει μήτε τὸ Γ᾽ μηδενὶ τῶν B, εἴ-
ληπται δ᾽ ἑκατέρα ἀνάπαλιν, ἄμφω ψευδεῖς ἔσονται. ἐγ-
^ δ᾽ σ LÀ A Γ i] ^ A M B σ , [4 M
χωρεῖ δ᾽ οὕτως ἔχειν τὸ Γ πρὸς τὸ A καὶ B ὥστε μήτε ὑπὸ
τὸ A εἶναι μήτε καθόλου τῷ Β. τὸ μὲν γὰρ Β ἀδύνατον
> Ld , , A » 7 , ^ M A t ,
εἶναι ἐν ὅλῳ τινί (πρώτως yap ἐλέγετο αὐτῷ τὸ A μὴ ὑπάρ-
AY \ A , ,» 7 -^ ^ LJ t 06.
xew), τὸ δὲ A οὐκ ἀνάγκη πᾶσι τοῖς οὖσιν εἶναι καθόλου,
35
ὥστ᾽ ἀμφότεραι ψευδεῖς. ἀλλὰ καὶ τὴν ἑτέραν ἐνδέχεται 4o
ἀληθῇ λαμβάνειν, οὐ μέντοι ὁποτέραν ἔτυχεν, ἀλλὰ τὴν
m
J ‘A , 3: x L4 M M ,
ATI: yàp I B πρότασις dei ψευδὴς ἔσται διὰ τὸ ἐν μη-
devi εἶναι τὸ B, τὴν δὲ A I ἐγχωρεῖ, οἷον εἰ τὸ A καὶ τῷ
Γ καὶ τῷ Β ὑπάρχει ἀτόμως (ὅταν γὰρ πρώτως κατ-
^ » ^ À , nd $, y] , w ὃ ,
ηγορῆται ταὐτὸ πλειόνων, οὐδέτερον ἐν οὐδετέρῳ ἔσται). διαφέ-
39 » , $095» » b 3, , € ,
pet δ᾽ οὐδέν, οὐδ᾽ εἰ μὴ ἀτόμως ὑπάρχει.
* * 4 Lo € P4 3 , a , ‘
H μὲν οὖν τοῦ ὑπάρχειν ἀπάτη διὰ τούτων τε καὶ
" , Lé % A , L4 Ld ^ e ,
οὕτω γίνεται μόνως (οὐ yàp ἦν ev ἄλλῳ σχήματι τοῦ ὑπάρ-
χειν συλλογισμός), ἡ δὲ τοῦ μὴ ὑπάρχειν ἔν τε τῷ πρώ-
* > ~ Li L4 ^ d LJ
τῳ Kal ἐν τῷ μέσῳ σχήματι. πρῶτον οὖν εἴπωμεν mooa-
~ > ^ fd x ~ > ^ ^
χῶς ἐν τῷ πρώτῳ γίνεται, kal πῶς ἐχουσῶν τῶν προτά-
᾽ , b 7 > , ~ , ^ , A
σεων. ἐνδέχεται μὲν οὖν ἀμφοτέρων ψευδῶν οὐσῶν, olov εἰ τὸ
* ^ τ ~ e€ 4 > , »* A ~
A xai TQ Γ kai τῷ B ὑπάρχει ἀτόμως: ἐὰν yap ληφθῇ
τὸ μὲν A τῷ Γ᾽ μηδενί, τὸ δὲ I παντὶ τῷ B, ψευδεῖς
at προτάσεις. ἐνδέχεται δὲ καὶ τῆς ἑτέρας ψευδοῦς οὔσης,
805
5
καὶ ταύτης ὁποτέρας ἔτυχεν. ἐγχωρεῖ yàp τὴν μὲν A Dis
ἀληθῆ εἶναι, τὴν δὲ I' B ψευδῆ, τὴν μὲν A I ἀληθῆ ὅτι
οὐ πᾶσι τοῖς οὖσιν ὑπάρχει τὸ A, τὴν δὲ I' B ψευδῆ ὅτι
ἀδύνατον ὑπάρχειν τῷ B τὸ IT, à μηδενὶ ὑπάρχει τὸ Α'
οὐ γὰρ ἔτι ἀληθὴς ἔσται ἡ A I' πρότασις: ἅμα δέ, εἰ καὶ
εἰσὶν ἀμφότεραι ἀληθεῖς, καὶ τὸ συμπέρασμα ἔσται ἀληθές.
ἀλλὰ καὶ τὴν I' B ἐνδέχεται ἀληθῆ εἶναι τῆς ἑτέρας οὔσης
b30 τῶν B ABCd 34 ὑπάρχειν A: ὑπάρχῃ Β 36-7 καὶ... A
om. nt 37 τῷ] τοῦ C? 38 atron 41 μέντοι- γε 80"! ἐν
om. A 2 τῷ] τὸ Β 3 yàp fecit C πρῶτον ABd 4 e€vnP:
om. ABCd διαφέρει... 5 ὑπάρχει A*C?d?nP : om. ABCd 8 recom.
ΕΟ: δὲ n 9 εἴπομεν n 16 δὲ By Βά 18 ὑπάρχειν ἀδύνατον n:
ἀδύνατον ὑπάρχει Bekker 19 εἰ καὶ ABCP : καὶ cid: καὶ n 21 Byn
ANAAYTIKON YITEPQN A
ψευδοῦς, οἷον εἰ τὸ B kai ev τῷ Γ kai ev τῷ A ἐστίν'
, , * , [4 A‘ , σ 3 n , a
ἀνάγκη yap θάτερον ὑπὸ θάτερον εἶναι, ὥστ᾽ dv λάβῃ τὸ
A μηδενὶ τῷ Γ᾽ ὑπάρχειν, ψευδὴς ἔσται ἡ πρότασις. φα-
25 νερὸν οὖν ὅτι καὶ τῆς ἑτέρας ψευδοῦς οὔσης καὶ ἀμφοῖν ἔσται
ψευδὴς ὁ συλλογισμός.
Ἔν δὲ τῷ μέσῳ σχήματι ὅλας μὲν εἶναι τὰς προτάσεις
: :
5 , ^ ΕΣ *, , Ld M 1 A ~
ἀμφοτέρας ψευδεῖς οὐκ ἐνδέχεται: ὅταν yap τὸ A παντὶ τῷ
Β ὑπάρχῃ, οὐδὲν ἔσται λαβεῖν ὃ τῷ μὲν ἑτέρῳ παντὶ θατέρῳ
, $, M t , ^ ? " # ^ ,
30 δ᾽ οὐδενὶ ὑπάρξει: δεῖ δ᾽ οὕτω λαμβάνειν τὰς προτάσεις
ὥστε τῷ μὲν ὑπάρχειν τῷ δὲ μὴ ὑπάρχειν, εἴπερ ἔσται συλ-
λογισμός. εἰ οὖν οὕτω λαμβανόμεναι ψευδεῖς, δῆλον ὡς ἐναν-
^ >? , σ΄͵ ^ > > , * »ὔ * €
Tuus ἀνάπαλιν ἕξουσι: τοῦτο δ᾽ ἀδύνατον. ἐπί τι δ᾽ ἑκα-
τέραν οὐδὲν κωλύει ψευδῆ εἶναι, οἷον εἰ τὸ I καὶ τῷ A καὶ
~ M L4 , n A ~ ‘ * ^ L4 ,
3s TQ B τινὶ ὑπάρχοι: dv yàp τῷ μὲν A παντὶ ληφθῇ ὑπάρ-
~ A , ^ * > , t ,
xov, TQ δὲ B μηδενί, ψευδεῖς μὲν ἀμφότεραι αἱ mporá-
, , Ed > > »* iy a > , * /
σεις, οὐ μέντοι ὅλαι ἀλλ᾽ ἐπί τι. καὶ ἀνάπαλιν δὲ τεθέν-
τος τοῦ στερητικοῦ ὡσαύτως. τὴν δ᾽ ἑτέραν εἶναι ψευδῆ καὶ
ὁποτερανοῦν ἐνδέχεται. ὃ γὰρ ὑπάρχει τῷ A παντί, καὶ
~ e , »* T ~ ^ ^ Ld Ul 4
4o7@ DB ὑπάρχει: ἐὰν οὖν ληφθῇ τῷ μὲν A ὅλῳ ὑπάρχειν
8o* τὸ I, τῷ δὲ B ὅλῳ μὴ ὑπάρχειν, ἡ μὲν I Α ἀληθὴς ἔσται,
ἡ δὲ D B ψευδής. πάλιν ὃ τῷ B μηδενὶ ὑπάρχει, οὐδὲ τῷ
A παντὶ ὑπάρξει" εἰ γὰρ τῷ A, καὶ τῷ B- ἀλλ᾽ οὐχ ὑπῆρ-
χεν. ἐὰν οὖν ληφθῇ τὸ Γ τῷ μὲν A ὅλῳ ὑπάρχειν, τῷ δὲ
sB μηδενί, ἡ μὲν I' B. πρότασις ἀληθής, ἡ δ᾽ ἑτέρα ψευ-
δής. ὁμοίως δὲ καὶ μετατεθέντος τοῦ στερητικοῦ. ὃ γὰρ μη-
δενὶ ὑπάρχει τῷ A, οὐδὲ τῷ B οὐδενὶ ὑπάρξει: ἐὰν οὖν λη-
^ Ἧς ~ 4 μὲ * € , ^ M Ld
$0g τὸ Γ τῷ μὲν A ὅλῳ μὴ ὑπάρχειν, τῷ δὲ B ὅλῳ
[4 , [4 A D A , aA 03 L4 L4 e ὦ δὲ
ὑπάρχειν, ἡ μὲν πρότασις" ἀληθὴς ἔσται, ἡ ἑτέρα δὲ
Ld x , ^ M ^ t , ^
το ψευδής. καὶ πάλιν, ὃ παντὶ τῷ B ὑπάρχει, μηδενὶ λα-
^ ^ L4 , ^ > 4 , ? ^ £f
Bev τῷ A ὑπάρχον ψεῦδος. ἀνάγκη ydp, εἰ τῷ B παντί,
M ^ A * , $4. ^ ^ ^ M ‘
καὶ TQ A τινὶ ὑπάρχειν: ἐὰν οὖν ληφθῇ τῷ μὲν B παντὶ
ὑπάρχειν τὸ D, τῷ δὲ A μηδενί, ἡ μὲν I B ἀληθὴς ἔσται,
ἡ δὲ Γ Α ψευδής. φανερὸν οὖν ὅτι καὶ ἀμφοτέρων οὐσῶν
τὸ ψευδῶν καὶ τῆς ἑτέρας μόνον ἔσται συλλογισμὸς ἀπατη-
τικὸς ἐν τοῖς ἀτόμοις.
423 yàp om. n 24 τῶν ABdn 29 ἔστι C 30 ὑπάρχει ἡ
33 ἑκατέραν CnP: ἑκάτερον ABd 35 ὑπάρχει οἷον dvd 37 ἐπί τι
ἐπε" — 560m. C 40 B ὑπάρχῃ A: B ὑπάρξει Bekker br ὑπάρχῃ d
5 atv By B ἀληθὴς 4- ἔσται ἢ ἡ ὑπάρχῃ τῷ a 9 IA scripsi:
ay codd. 11 ὑπάρχειν n I37@yn 15 μόνως d
16. 8022-17. 81 Ὁ
1; Ἔν δὲ τοῖς μὴ ἀτόμως ὑπάρχουσιν [ἢ μὴ ὑπάρχου-
σιν], ὅταν μὲν διὰ τοῦ οἰκείου μέσου γίνηται τοῦ ψεύδους à
συλλογισμός, οὐχ οἷόν τε ἀμφοτέρας ψευδεῖς εἶναι τὰς
P4 > ^ , ^ ^ ^ , L4 ,
προτάσεις, ἀλλὰ μόνον τὴν πρὸς τῷ μείζονι ἄκρῳ. (λέγω 20
δ᾽ οἰκεῖον μέσον δι’ οὗ γίνεται τῆς ἀντιφάσεως ὁ συλ-
λογισμός.) ὑπαρχέτω γὰρ τὸ Α τῷ Β διὰ μέσου τοῦ Γ.
ἐπεὶ οὖν ἀνάγκη τὴν Γ᾽ B καταφατικὴν λαμβάνεσθαι συλ-
λογισμοῦ γινομένου, δῆλον ὅτι ἀεὶ αὕτη ἔσται ἀληθής. οὐ
γὰρ ἀντιστρέφεται. ἡ δὲ A I ψευδής: ταύτης γὰρ ἀντι- 25
στρεφομένης ἐναντίος γίνεται ὁ συλλογισμός. ὁμοίως δὲ καὶ
> 9 E] y D ‘ , * x >
εἰ ἐξ ἄλλης συστοιχίας ληφθείη τὸ μέσον, olov τὸ A εἰ
καὶ ἐν τῷ A ὅλῳ ἐστι καὶ κατὰ τοῦ B κατηγορεῖται παν-
Tos’ ἀνάγκη γὰρ τὴν μὲν 4 B πρότασιν μένειν, τὴν δ᾽
ee > , LA > € ^ 7 Ny , / L4 3 LEAL I
ἑτέραν ἀντιστρέφεσθαι, ὥσθ᾽ ἡ μὲν det ἀληθής, ἡ δ᾽ dei 30
ψευδής. καὶ σχεδὸν 7j γε τοιαύτη ἀπάτη ἡ αὐτή ἐστι τῇ
διὰ τοῦ οἰκείου μέσου. ἐὰν δὲ μὴ διὰ τοῦ οἰκείου μέσου γίνη-
ται ὁ συλλογισμός, ὅταν μὲν ὑπὸ τὸ A jj τὸ μέσον, τῷ
δὲ Β μηδενὶ ὑπάρχῃ, ἀνάγκη ψευδεῖς εἶναι ἀμφοτέρας.
ληπτέαι γὰρ ἐναντίως ἢ ὡς ἔχουσιν αἱ προτάσεις, εἰ μέλ- 35
λει συλλογισμὸς ἔσεσθαι: οὕτω δὲ λαμβανομένων ἀμφό-
H ^ > x M Ld ^ ig ,
Tepat γίνονται ψευδεῖς. olov ei τὸ μὲν A ὅλῳ τῷ A ὑπάρ-
^ * Bs ~ > , M ,
xe, τὸ δὲ A μηδενὶ τῶν B: ἀντιστραφέντων yap τούτων.
/, , Ld * e , 3 ,
συλλογισμός τ᾽ ἔσται Kal ai προτάσεις ἀμφότεραι ψευ-
δεῖς. ὅταν δὲ μὴ ἧἦ ὑπὸ τὸ A τὸ μέσον, οἷον τὸ A, ἡ 40
μὲν A A ἀληθὴς ἔσται, ἡ δὲ A B ψευδής. ἡ μὲν yap A A 81"
ἀληθής, ὅτι οὐκ ἦν ἐν τῷ A τὸ A, ἡ δὲ A B ψευδής, ὅτι
ἦν ἀληθής, κἂν τὸ συμπέρασμα ἦν ἀληθές: ἀλλ᾽ ἦν
ψεῦδος.
Διὰ δὲ τοῦ μέσου σχήματος γινομένης τῆς ἀπάτης,
2 ‘ A *, 3 , ^ ^ ,
ἀμφοτέρας μὲν οὐκ ἐνδέχεται ψευδεῖς εἶναι τὰς προτάσεις
σ μὲ ^ A € ' M > M , , ^ ^
ὅλας (ὅταν yàp ἢ τὸ B ὑπὸ τὸ A, οὐδὲν ἐνδέχεται TH μὲν
παντὶ τῷ δὲ μηδενὶ ὑπάρχειν, καθάπερ ἐλέχθη καὶ πρότε-
pov), τὴν ἑτέραν δ᾽ ἐγχωρεῖ, καὶ ὁποτέραν ἔτυχεν. εἰ γὰρ
οι
Β17 ἀτόμως A B?Cn: ἀτόμοις Bd ἢ μὴ ὑπάρχουσιν om. ABn 18 μὲν
-Ἔ οὖν d γίνεται n 23 By BC 24 ἀεὶ om. d ἐστὶν C : μὲν
ἔσται n 26 ὁ ἐναντίος γίνεται n 28 ὅλως n 29 8B fecit π
32 ἐὰν... μέσου om. C! : μέσον om. n! 36 dudorépov B 20 τ᾽
om. C 8121 ἔσται οἴη. B8 Cr! ἡ... 2 ψευδής om. C 2 δὲ
B8 ABdn 3 καὶ AB 7 μέντα C 9 δ᾽ ἑτέραν
B:8d
ANAAYTIKQN YETEPQN A
1070 IX καὶ τῷ A καὶ τῷ B ὑπάρχει, ἐὰν ληφθῇ τῷ μὲν A
ὑπάρχειν τῷ δὲ B μὴ ὑπάρχειν, ἡ μὲν I A ἀληθὴς ἔσται,
ἡ δ᾽ ἑτέρα ψευδής. πάλιν δ᾽ εἰ τῷ μὲν Β ληφθείη τὸ Γ
ὑπάρχον, τῷ δὲ A μηδενί, ἡ μὲν I' B ἀληθὴς ἔσται, ἡ δ᾽
ἑτέρα ψευδής.
> A * T. X ^ 3 , Ld ,
15 Ἐὰν μὲν οὖν στερητικὸς jj τῆς ἀπάτης ὁ συλλογιομός,
εἴρηται πότε καὶ διὰ τίνων ἔσται ἡ ἀπάτη" ἐὰν δὲ κατα-
, L4 ‘ * ^ », , , > , > ,
φατικός, ὅταν μὲν διὰ τοῦ οἰκείου μέσου, ἀδύνατον dudoré-
4 ^ > , ‘A ‘A , LJ LÀ
pas εἶναι ψευδεῖς: ἀνάγκη yàp τὴν I' B μένειν, εἴπερ ἔσται
, , Y f * , σ ε
συλλογισμός, καθάπερ ἐλέχθη καὶ πρότερον. ὥστε ἡ Α Γ
20 ἀεὶ ἔσται ψευδής: αὕτη γάρ ἐστιν ἡ ἀντιστρεφομένη. ὁμοίως
δὲ καὶ εἰ ἐξ ἄλλης συστοιχίας λαμβάνοιτο τὸ μέσον, ὥσ-
περ ἐλέχθη καὶ ἐπὶ τῆς στερητικῆς ἀπάτης" ἀνάγκη γὰρ
τὴν μὲν 4 B μένειν, τὴν δ᾽ A A ἀντιστρέφεσθαι, καὶ ἡ
ἀπάτη ἡ αὐτὴ τῇ πρότερον. ὅταν δὲ μὴ διὰ τοῦ οἰκείου, ἐὰν
A ki € * * - 4 L4 >? , L4 e , A
Ὡς μὲν ἦ τὸ A ὑπὸ τὸ A, αὕτη μὲν ἔσται ἀληθής, ἡ ἑτέρα δὲ
, » - A ^ s L4 , a ? L4
ψευδής" ἐγχωρεῖ yàp τὸ A πλεώσιν ὑπάρχειν ἃ οὐκ ἔστιν
ὑπ᾽ ἄλληλα. ἐὰν δὲ μὴ ἦ τὸ A ὑπὸ τὸ A, αὕτη μὲν ἀεὶ
δῆλον ὅτι ἔσται ψευδής (καταφατικὴ γὰρ λαμβανεται),
τὴν δὲ A B ἐνδέχεται καὶ ἀληθῆ εἶναι καὶ ψευδῆ: οὐδὲν
‘ , ' x ~ M € , M b
3o yàp κωλύει τὸ μὲν A τῷ 4 μηδενὶ ὑπάρχειν, τὸ δὲ A
τῷ B παντί, οἷον ζῷον ἐπιστήμῃ, ἐπιστήμη δὲ μουσικῇ. οὐδ᾽
T , Αἴ * ~ , Ἂν ᾿ -
αὖ μήτε τὸ A μηδενὶ τῶν A μήτε τὸ A μηδενὶ τῶν B.
A Ld b L4 ~ 4 t * a * 3
[φανερὸν οὖν ὅτι μὴ ὄντος τοῦ μέσου ὑπὸ τὸ Α καὶ ἀμφο-
τέρας ἐγχωρεῖ ψευδεῖς εἶναι καὶ ὁποτέραν ἔτυχεν.
45 lloscaxós μὲν οὖν καὶ διὰ τίνων ἐγχωρεῖ γίνεσθαι τὰς
κατὰ συλλογισμὸν ἀπάτας ἔν τε τοῖς ἀμέσοις καὶ ἐν τοῖς
δι’ ἀποδείξεως, φανερόν.
Φανερὸν δὲ καὶ ὅτι, εἴ τις αἴσθησις ἐκλέλοιπεν, ἀνάγκη
‘ , , A , , ^ > , ^ LJ
Kal ἐπιστήμην twa ἐκλελοιπέναι, ἣν ἀδύνατον λαβεῖν, εἴπερ
, ^ , ^ ^ > , Ld » t ^ > ,
4o μανθάνομεν ἢ ἐπαγωγῇ ἢ ἀποδείξει, ἔστι δ᾽ ἡ μὲν ἀπόδει-
815 ξις ἐκ τῶν καθόλου, ἡ δ᾽ ἐπαγωγὴ ἐκ τῶν κατὰ μέρος,
, , * ^ , ^ ^ 3 , ~ > Lj
ἀδύνατον δὲ rà καθόλου θεωρῆσαι μὴ δι’ ἐπαγωγῆς (ἐπεὶ
aro καὶ τὸ a B! ὑπάρχει ἐὰν cf: ὑπάρχοι ἐὰν ABCd: ὑπάρχοιεν avn
11 A scripsi: ay codd. 138y 8 ἀληθὲς n τό δὲ-ἦπ 18 By B
I9 dere--yàp n AT' scripsi: ya codd. 21 καὶ ἣ ἡ λαμβάνοι d
23 τὸ uy n. ἡτγεη 24 τῇ om. t! μὴ οπι. ἀ: μὴ ἦ π 25 δὲ
ἑτέρα C 29 BA Bekker 30 yàp om. n! δὲ om. B! 31 pov-
σικήν n 32 7a B AB 33-4 φανερὸν... ἔτυχεν seclusi: om. P
36reom.C — roi? μὴ " 38 δῆλον δὲ( 40 ἔσται n b2 δὲ] ren
18
17. 81*10-19. 81535
τ M 2 > , , L4 3 > ~ ,
καὶ τὰ ἐξ ἀφαιρέσεως λεγόμενα ἔσται δι’ ἐπαγωγῆς γνώ-
ριμα ποιεῖν, ὅτι ὑπάρχει ἑκάστῳ γένει ἔνια, καὶ εἰ μὴ χω-
ριστά ἐστιν, fj τοιονδὶ ἕκαστον), ἐπαχθῆναι δὲ μὴ ἔχοντας αἴ- 5
σθησιν ἀδύνατον. τῶν γὰρ Kal? ἕκαστον ἡ αἴσθησις": οὐ γὰρ
ἐνδέχεται λαβεῖν αὐτῶν τὴν ἐπιστήμην" οὔτε γὰρ ἐκ τῶν κα-
θόλου ἄνευ ἐπαγωγῆς, οὔτε δι’ ἐπαγωγῆς ἄνευ τῆς αἷ-
σθήσεως.
"Ἔστι δὲ πᾶ λλ M 8 * ~ L4 M * M 10
19 ἂς συλλογισμὸς διὰ τριῶν ὅρων, kai ὁ μὲν
ὃ 4 8 t) L4 « , A A ^ F ὃ ‘ * € ,
exvivat δυνάμενος ὅτι ὑπάρχει τὸ τῷ ιὰ τὸ ὑπάρ-
xew τῷ B καὶ τοῦτο τῷ I, ὁ δὲ στερητικός, τὴν μὲν ἑτέραν
, » L4 € a L4 Ld A , LANE 4
πρότασιν ἔχων ὅτι ὑπάρχει τι ἄλλο ἄλλῳ, τὴν δ᾽ ἑτέραν
Ld , e Ld M 7T L4 ε M 3 M M t
ὅτι οὐχ ὑπάρχει. φανερὸν οὖν ὅτι αἱ μὲν ἀρχαὶ kai αἱ Ae-
γόμεναι ὑποθέσεις αὗταί εἰσι: λαβόντα γὰρ ταῦτα οὕτως 15
3 , , L4 A ~ e 4 A ~
ἀνάγκη δεικνύναι, olov ὅτι τὸ A τῷ I ὑπάρχει διὰ τοῦ B,
πάλιν δ᾽ ὅτι τὸ A τῷ B δι’ ἄλλου μέσου, καὶ ὅτι τὸ B
~ € , ^ s. T , LA *
τῷ l' ὡσαύτως. κατὰ μὲν οὖν δόξαν συλλογιζομένοις καὶ
, ~ ~ a ~ , L4 > 1 Ll
μόνον διαλεκτικῶς δῆλον ὅτι τοῦτο μόνον σκεπτέον, εἰ ἐξ ὧν
2 , , , a Ld , A » 3 "
ἐνδέχεται ἐνδοξοτάτων γίνεται 6 συλλογισμός, ὥστ᾽ εἰ καὶ 20
μὴ ἔστι τι τῇ ἀληθεί τῶν A B μέσον, δοκεῖ δὲ εἶναι, 6
διὰ τούτου συλλογιζόμενος συλλελόγισται διαλεκτικῶς" πρὸς
> 3 L4 , ~ [4 ἐς ^ ^ v 32 Ld
δ᾽ ἀλήθειαν ἐκ τῶν ὑπαρχόντων δεῖ σκοπεῖν. ἔχει δ᾽ οὕτως"
᾽ * L4 ^ , A * 3 Lá ^ A A:
ἐπειδὴ ἔστιν ὃ αὐτὸ μὲν κατ᾽ ἄλλου κατηγορεῖται μὴ κατὰ
συμβεβηκός--λέγω δὲ τὸ κατὰ συμβεβηκός, οἷον τὸ λευ- 25
Kóv ποτ᾽ ἐκεῖνό φαμεν εἶναι ἄνθρωπον, οὐχ ὁμοίως λέγοντες
καὶ τὸν ἄνθρωπον λευκόν: ὃ μὲν γὰρ οὐχ ἕτερόν τι ὧν Aev-
H » 4 A L4 L4 H ^ > , 4
κὄς ἐστι, τὸ δὲ λευκόν, ὅτι συμβέβηκε τῷ ἀνθρώπῳ εἶναι
λευκῷ--ἔστιν οὖν ἔνια τοιαῦτα ὥστε καθ᾽ αὑτὰ κατηγορεῖσθαι.
"Ei A A ^ ^ , ^ x , € id L4
στω δὴ τὸ I" τοιοῦτον ὃ αὐτὸ μὲν μηκέτι ὑπάρχει ἄλλῳ, 3o
4, * ‘ l4 M 2 » L4 [4 *
τούτῳ δὲ τὸ B πρώτῳ, kai οὐκ ἔστιν ἄλλο μεταξύ. καὶ
πάλιν τὸ E τῷ Z ὡσαύτως, καὶ τοῦτο τῷ B. ἄρ᾽ οὖν τοῦτο
» f ^ "^ > , > ΝΜ ΕΣ x , >
ἀνάγκη στῆναι, ἢ ἐνδέχεται els ἄπειρον ἰέναι; καὶ πάλιν εἰ
τοῦ μὲν A μηδὲν κατηγορεῖται καθ᾽ αὑτό, τὸ δὲ A τῷ Θ
, M M ~
ὑπάρχει πρώτῳ, μεταξὺ δὲ μηδενὶ προτέρῳ, kai τὸ O τῷ 35
b3 γνώριμα-Ἐ ἄν τις βούλεται γνώριμα n sala” 6 ἀδύνατον
om, 51 yàp τῶν Al: yap B! II δείκνυται λεγόμενος n 17 δι᾽
om. 51 20 el om, ml 21 μὴ om. A4?B*Cdm?P εἶναι] μὴ n, fecit
B: μὴ εἶναι A?C? ὁ om. d 25 rot om. C?, fecit d 26 ἐκεῖνό]
pév n 27 λευκός scripsi, habet ut vid. P : λευκόν codd. 28 δὲ om. nl
308 τὸ αὐτὸ C Διτῷβ B 32T0 eró CnT τούτῳ τὸ πὶ 33
στῆναι fecit ἡ 34 δὲ om.d 6] θβ πὶ 35 τῷ] τὸ n
ANAAYTIKQN YZTEPON A
A ~ ~ T b “- ν > , ^ *
H, kai τοῦτο τῷ B, dpa καὶ τοῦτο ἵστασθαι ἀνάγκη, ἢ Kai
- »} , , , ΝΜ » f, la M LJ ~ ,
τοῦτ᾽ ἐνδέχεται εἰς ἄπειρον ἰέναι; διαφέρει δὲ τοῦτο τοῦ mpó-
“- Ld ‘ ,ὔ > T » , > ,
τερον τοσοῦτον, ὅτι TO μέν ἐστιν, ἄρα ἐνδέχεται ἀρξαμένῳ
» ^ , a 4 € , CER a > » LÀ H a » a
ἀπὸ τοιούτου ὃ μηδενὶ ὑπάρχει ἑτέρῳ ἀλλ᾽ ἄλλο ἐκείνῳ, ἐπὶ
4o τὸ ἄνω εἰς ἄπειρον ἰέναι, θάτερον δὲ ἀρξάμενον ἀπὸ τοιούτου
4 ^
82" ὃ αὐτὸ μὲν ἄλλου, ἐκείνου δὲ μηδὲν κατηγορεῖται, ἐπὶ τὸ
2 κάτω σκοπεῖν εἰ ἐνδέχεται εἰς ἄπειρον ἰέναι.
» Ἔτι τὰ μεταξὺ
ᾶ , > ὃ , v t [4 ,ὔ ^ » , »
p' ἐνδέχεται ἄπειρα εἶναι ὡρισμένων τῶν ἄκρων; λέγω ὃ
> A ~ [4 , , , δι κα M ~
olov εἰ τὸ A τῷ I’ ὑπάρχει, μέσον δ᾽ αὐτῶν τὸ B, τοῦ
ςδὲ B καὶ τοῦ A ἕτερα, τούτων δ᾽ ἄλλα, dpa καὶ ταῦτα
, L4 > , ,7 n > , L4 ^ ^
εἰς ἄπειρον ἐνδέχεται ἰέναι, ἢ ἀδύνατον; ἔστι δὲ τοῦτο ako-
a ,
πεῖν ταὐτὸ kal εἰ ai ἀποδείξεις els ἄπειρον ἔρχονται, Kal
, w > , c ^ A Ld ,
εἰ ἔστιν ἀπόδειξις ἅπαντος, ἢ πρὸς ἄλληλα περαίνεται.
ὋὉμοίως δὲ λέγω καὶ ἐπὶ τῶν στερητικῶν συλλογισμῶν
1o καὶ προτάσεων, οἷον εἰ τὸ A μὴ ὑπάρχει τῷ B. μηδενί, ἤτοι
πρώτῳ, 3] ἔσται τι μεταξὺ ᾧ προτέρῳ οὐχ ὑπάρχει (οἷον εἰ
τῷ Η, ὃ τῷ B ὑπάρχει παντί), καὶ πάλιν τούτου ἔτι ἄλλῳ
Pi * ~ a ~ X [4 , * A
προτέρῳ, olov εἰ τῷ Θ, ὃ τῷ Η παντὶ ὑπάρχει. καὶ yàp
>
ἐπὶ τούτων ἢ ἄπειρα ols ὑπάρχει προτέροις, 7) ἵσταται.
, * b ~ , , > Ld , LÀ ? M
15 "Emi δὲ τῶν ἀντιστρεφόντων οὐχ ὁμοίως ἔχει. οὐ yap
> a > ES
ἔστιν ἐν τοῖς ἀντικατηγορουμένοις οὗ πρώτου κατηγορεῖται ἢ
τελευταίου" πάντα γὰρ πρὸς πάντα ταύτῃ γε ὁμοίως ἔχει, εἴτ᾽
, * L4 A , % ^ , Ww» > , ,
ἐστὶν ἄπειρα τὰ κατ᾽ αὐτοῦ κατηγορούμενα, εἴτ᾽ ἀμφότερά ἐστι
τὰ ἀπορηθέντα ἄπειρα πλὴν εἰ μὴ ὁμοίως ἐνδέχεται ἀντι-
20 στρέφειν, ἀλλὰ τὸ μὲν ὡς συμβεβηκός, τὸ δ᾽ ὡς κατηγορίαν.
"0. 4 T A a , *, H » 7 ,
T. μὲν οὖν τὰ μεταξὺ οὐκ ἐνδέχεται ἄπειρα εἶναι, εἰ 20
ἐπὶ τὸ κάτω καὶ τὸ ἄνω ἵστανται αἱ κατηγορίαι, δῆλον.
λέ δ᾽ Μ A A » v A 06A ^ , δὲ
ἔγω ἄνω μὲν τὴν ἐπὶ τὸ καθόλου μᾶλλον, κάτω δὲ
4 ^
τὴν ἐπὶ TO κατὰ μέρος. εἰ yàp τοῦ A κατηγορουμένου κατὰ
as TOU Z ἄπειρα τὰ μεταξύ, ἐφ᾽ ὧν B, δῆλον ὅτι ἐνδέχοιτ᾽
b. @ 4 > M ^ > L4
dv ὥστε καὶ ἀπὸ τοῦ A ἐπὶ τὸ κάτω ἕτερον ἑτέρου κατηγο-
^ , Lid A M » * 4 ἐλθ ^ v ^
ρεῖσθαι εἰς ἄπειρον (πρὶν yap ἐπὶ τὸ Z ἐλθεῖν, ἄπειρα τὰ
b37 τοῦ] τὸ d προτέρου C 38 dpa... ἀρξαμένῳ] ἀρξάμενον C
39 τούτου d ἄλλο ὃ d 8222 ἄπειρα n ἔπειτα μεταξὺ n ἢ αἱ
AnP : om. Bd 8 εἰ om.r! mepatye. P 10 ὑπάρχῃ ἢ" II εἰ]
ἢ 41 12 τῷ" A?n et ut vid. P: τὸ 4.84 1376 An: τὸ ABd ὃ)
3584 I4 ἢ ἄπειρα) ai dmepia n οἷς. . . προτέροις] ἢ συνυπάρχει
ἐν τοῖς ἑτέροις d οἷς + οὐχ π 16 ἔστιν om. Ad κατηγορου-
μένοις 418ὰ 17 ταῦτα B yap fecit n 18 εἴτ᾽] ἐπ’ A? nP8
25 τὰ] τὸ δὲ πὶ
21
I9. 8136-21. 82^19
5 * > A “- 33:5 M LÀ Ld * δον *
μεταξύ) καὶ ἀπὸ τοῦ Z ἐπὶ τὸ ἄνω ἄπειρα, πρὶν ἐπὶ τὸ A
? ^ σ A , ^ > - Ν ^ X > ,
ἐλθεῖν. wor εἰ ταῦτα ἀδύνατα, καὶ ToU A καὶ Z ἀδύνατον
» , *, * ^ » , L4 M L4 ,
ἄπειρα εἶναι μεταξύ. οὐδὲ yap εἴ τις λέγοι ὅτι τὰ μέν ἐστι 30
τῶν Α Β Ζ ἐχόμενα ἀλλήλων ὥστε μὴ εἶναι μεταξύ, τὰ δ᾽ οὐκ
ἔστι λαβεῖν, οὐδὲν διαφέρει. 6 γὰρ av λάβω τῶν B, ἔσται
4 ^ δ 4" 4 nn L4 A * n » » »
πρὸς τὸ A 1j πρὸς τὸ Z ἢ ἄπειρα τὰ μεταξὺ ἢ οὔ. ad
οὗ δὴ πρῶτον ἄπειρα, εἴτ᾽ εὐθὺς εἴτε μὴ εὐθύς, οὐδὲν διαφέ-
peu τὰ γὰρ μετὰ ταῦτα ἄπειρά ἐστιν. 35
Φανερὸν δὲ καὶ ἐπὶ τῆς στερητικῆς ἀποδείξεως ὅτι στή-
^ »
σεται, εἴπερ ἐπὶ τῆς κατηγορικῆς ἵσταται ἐπ᾽ ἀμφότερα.
ἔστω γὰρ μὴ ἐνδεχόμενον μήτε ἐπὶ τὸ ἄνω ἀπὸ τοῦ jorá-
» LÀ LE , 3 LÀ ^ » AS ^ LÀ
Tov εἰς ἄπειρον ἰέναι (λέγω δ᾽ ὕστατον ὃ αὐτὸ μὲν ἄλλῳ
μηδενὶ ὑπάρχει, ἐκείνῳ δὲ ἄλλο, οἷον τὸ Ζ) μήτε ἀπὸ τοῦ 82>
πρώτου ἐπὶ τὸ ὕστατον (λέγω δὲ πρῶτον ὃ αὐτὸ μὲν κατ᾽
ἄλλου, κατ᾽ ἐκείνου δὲ μηδὲν ἀλλο). εἰ δὴ ταῦτ᾽ ἔστι, καὶ
ἐπὶ τῆς ἀποφάσεως στήσεται. τριχῶς γὰρ δείκνυται μὴ
. , na ^ T7 hi M I. ^ * 4 $ ^ δὲ
ὑπάρχον. ἢ yàp ᾧ μὲν τὸ I, τὸ B ὑπάρχει παντί, ᾧ δὲ 5
^ , b ^ ^ x ΓΑ " » * ~ LE ὦ
τὸ B, οὐδενὶ τὸ A. τοῦ μὲν τοίνυν BI, kai ἀεὶ τοῦ ἑτέρου
διαστήματος, ἀνάγκη βαδίζειν εἰς ἄμεσα: κατηγορικὸν γὰρ
^ x La 1 , δ ~ L4 > ¥ 2 [4 ca
τοῦτο τὸ διάστημα. τὸ δ᾽ ἕτερον δῆλον ὅτι εἰ ἄλλῳ οὐχ ὑπάρ-
χει προτέρῳ, οἷον τῷ 4, τοῦτο δεήσει τῷ Β παντὶ ὑπάρ-
t , ͵ * -^ , > * , H ^
xew. καὶ εἰ πάλιν ἄλλῳ τοῦ 4 προτέρῳ ody ὑπάρχει, ἐκεῖνο 1o
, ~ * € , LA » , + € > V Li » σ
δεήσει τῷ 4 παντὶ ὑπάρχειν. ὥστ᾽ ἐπεὶ ἡ ἐπὶ τὸ ἄνω ἵστα-
ται ὅδός, καὶ ἡ ἐπὶ τὸ Α στήσεται, καὶ ἔσται τι πρῶτον
ᾧ οὐχ ὑπάρχει. 13
Πάλιν εἰ τὸ μὲν B παντὶ τῷ A, τῷ δὲ Dia
μηδενί, τὸ A τῶν I οὐδενὶ ὑπάρχει. πάλιν τοῦτο εἰ δεῖ δεῖ-
~ v * ^ ^ ΕΑ , , ^ A
far, δῆλον ὅτι 7) διὰ τοῦ ἄνω τρόπου δειχθήσεται ἢ διὰ 15
τούτου ἢ τοῦ τρίτου. ὁ μὲν οὖν πρῶτος εἴρηται, 6 δὲ δεύτε-
, a » n 4 ^ ^ bI
pos δειχθήσεται. οὕτω δ᾽ dv δεικνύοι, olov τὸ A τῷ μὲν
B παντὶ ὑπάρχει, τῷ δὲ I οὐδενί, εἰ ἀνάγκη ὑπάρχειν τι
TQ B. καὶ πάλιν εἰ τοῦτο τῷ I μὴ ὑπάρξει, ἄλλο τῷ A
420 Ζ] τοῦ £m. 31 ABZ coni. Waitz: αβγ ABdn: αβ M 32 yap
λαβὼν τὸ B πὶ 33 3? om. mi: 3 εἰ d? οὔ... 34 πρῶτον om. ni
39 ἄλλο d by éxefvo d. μήτ᾽ +atrén ὑπὸ ANB 57a BB!
6B καὶ y n 8 ἄλλῳ fecit n 9 πρότερον B! τὸ β πὶ 10 ἐκείνῳ
ΑΒ14 II 7G ad ἄνω] κάτω P, fecit n I2 ἡ fecit n Als
ABd: ἄνω n?P πρώτῳ ABd I3 ¢0m. n! 14 τῶν ABdnP:
τῷ D δεῖ] δὲ πὶ 16 δὲ τρίτος nt 17 δεικνύοι MIP: δεικνύῃ
ABdn δ AB'dnP*: a A*B 18 εἰ om. d 19 ὑπάρξῃ n
ἀλλ᾽ à A
ANAAYTIKQN YETEPQN A
€ , a ~ > L4 Ld » ~ > ^ Α t ,
20 ὑπάρχει, ὃ τῷ I οὐχ ὑπάρχει. οὐκοῦν ἐπεὶ τὸ ὑπάρχειν
21 ἀεὶ τῷ ἀνωτέρω ἵσταται, στήσεται καὶ τὸ μὴ ὑπάρχειν.
Li
21 (9)
δὲ τρίτος τρόπος ἦν' ef τὸ μὲν A τῷ B παντὶ ὑπάρχει, τὸ
δὲ I μὴ ὑπάρχει, οὐ παντὶ ὑπάρχει τὸ I ᾧ τὸ A. πά-
λιν δὲ τοῦτο 7 διὰ τῶν ἄνω εἰρημένων ἢ ὁμοίως δειχθήσεται.
, , ‘A A . > > LÀ , »" 4 B
25 ἐκείνως μὲν δὴ ἵσταται, εἰ δ᾽ οὕτω, πάλιν λήψεται τὸ
TQ E ὑπάρχειν, ᾧ τὸ Γ' μὴ παντὶ ὑπάρχει. καὶ τοῦτο πά-
λιν ὁμοίως. ἐπεὶ δ᾽ ὑπόκειται ἵστασθαι καὶ ἐπὶ τὸ κάτω,
δῆλον ὅτι στήσεται καὶ τὸ Γ᾿ οὐχ ὑπάρχον.
Φ ^ > L4 ^ kAJ M ^ € ^ , > ^ ,
avepov δ᾽ ὅτι kai ἐὰν μὴ μιᾷ ὁδῷ δεικνύηται ἀλλὰ má-
3o Gals, ὁτὲ μὲν ἐκ τοῦ πρώτου σχήματος, ὁτὲ δὲ ἐκ τοῦ δευτέρου
ἢ τρίτου, ὅτι καὶ οὕτω στήσεται: πεπερασμέναι γάρ εἰσιν αἱ
ὁδοί, τὰ δὲ πεπερασμένα πεπερασμενάκις ἀνάγκη πεπε-
ράνθαι πάντα.
MO, * ^ * X ~ , Ww M > 4 ~ € ,
T. μὲν οὖν ἐπὶ τῆς στερήσεως, εἴπερ Kal ἐπὶ τοῦ ὑπάρ-
35 Xew, ἵσταται, δῆλον. ὅτι δ᾽ ἐπ᾽ ἐκείνων, λογικῶς μὲν
θεωροῦσιν ὧδε φανερόν.
E * A 4 ~ H ~ , > [4 SHA Ἢ
"IL μὲν οὖν τῶν ἐν τῷ TL εστι κατηγορουμένων ONAOV’ 22
», * L4 «€ 7 hal 3 M 8 , + A >
εἰ yap ἔστιν ὁρίσασθαι ἢ εἰ γνωστὸν τὸ τί ἦν εἶναι, τὰ ὃ
ἄπειρα μὴ ἔστι διελθεῖν, ἀνάγκη πεπεράνθαι τὰ ἐν τῷ τί
, , 4 4 T , LÀ * >
83% ἐστι κατηγορούμενα. καθόλου δὲ ὧδε λέγομεν. ἔστι yap εἰ-
πεῖν ἀληθῶς τὸ λευκὸν βαδίζειν καὶ τὸ μέγα ἐκεῖνο ξύλον
^ , A] , , M A L4 n
εἶναι, καὶ πάλιν τὸ ξύλον μέγα εἶναι kai τὸν ἄνθρωπον Ba-
δίζειν. ἕτερον δή ἐστι τὸ οὕτως εἰπεῖν καὶ τὸ ἐκείνως. ὅταν
QA A M * ~ tA /, , L4 T
ςμὲν yap τὸ λευκὸν εἶναι φῶ ξύλον, τότε λέγω ὅτι ᾧ συμ-
βέβηκε λευκῷ εἶναι ξύλον ἐστίν, ἀλλ᾽ οὐχ ὡς τὸ ὑποκείμε-
^ , A , , M A LÀ a bal wn» «uw
vov TQ ξύλῳ τὸ λευκόν ἐστι" Kal yap οὔτε λευκὸν ὃν οὔθ᾽ ὅπερ
λευκόν τι ἐγένετο ξύλον, ὥστ᾽ οὐκ ἔστιν ἀλλ᾽ ἢ κατὰ συμβε-
, L4 ^ A , A] ^ , LÀ - ,
βηκός. ὅταν δὲ τὸ ξύλον λευκὸν εἶναι φῶ, ody ὅτι ἕτερόν
, , , , , M L Φ' ΄
το τί ἐστι λευκόν, ἐκείνῳ δὲ συμβέβηκε ξύλῳ εἶναι, οἷον ὅταν
‘ A ^ ^ , ^ σ « L4
τὸ μουσικὸν λευκὸν εἶναι φῶ (τότε yàp ὅτι ὁ ἄνθρωπος
λευκός ἐστιν, ᾧ συμβέβηκεν εἶναι μουσικῷ, λέγω), ἀλλὰ
τὸ ξύλον ἐστὶ τὸ ὑποκείμενον, ὅπερ καὶ ἐγένετο, οὐχ ἕτερόν
an ^ σ 4 bal 2, , *, ^ ^ ^ LÀ
τι ὃν ἢ ὅπερ ξύλον ἢ ξύλον τί. εἰ δὴ δεῖ νομοθετῆσαι, ἔστω
b20 ἐπὶ n! 23 μὴ ὑπάρχῃ n τὸ δὲ y ni! 26 παντὶ ὑπάρχῃ Aln
32 πεπερασμενάκις om. n3: πεπερασμένως n?PC: πολλάκις PY? 33 ἅ-
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κατηγορεῖν, ἢ κατηγορεῖν μὲν μὴ ἁπλῶς, κατὰ συμβεβη-
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τὸ κατηγορούμενον κατηγορεῖσθαι ἀεί, οὗ κατηγορεῖται,
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ξεις ἀποδεικνύουσιν. ὥστε ἢ ἐν τῷ τί ἐστιν ἢ ὅτι ποιὸν ἣ πο-
σὸν ἣ πρός τι T) ποιοῦν τι ἣ πάσχον 1] ποὺ 1) ποτέ, ὅταν ἕν καθ᾽
ἑνὸς κατηγορηθῇ.
» ^ NON ΕΣ , , a , ^ - σ
Ἔτι τὰ μὲν οὐσίαν σημαίνοντα ὅπερ ἐκεῖνο ἢ ὅπερ
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, , 3 A bi $, » € 2, λέ
σίαν σημαίνει, ἀλλὰ Kar’ ἄλλου ὑποκειμένου λέγεται
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ὁ ἄνθρωπος οὔτε ὅπερ λευκὸν οὔτε ὅπερ λευκόν τι, ἀλλὰ ζῷον
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σημαίνει, δεῖ κατά τινος ὑποκειμένου κατηγορεῖσθαι, καὶ
μὴ εἶναί τι λευκὸν ὃ οὐχ ἕτερόν τι Óv λευκόν ἐστιν. τὰ
γὰρ εἴδη χαιρέτω: τερετίσματά τε γάρ ἐστι, καὶ εἰ ἔστιν,
H ~
οὐδὲν πρὸς τὸν λόγον ἐστίν: al yap ἀποδείξεις περὶ τῶν τοι-
οὕτων εἰσίν.
"E 3 ^ LÀ “ὃ δὸ L4 > ^ 4, δὲ
τι εἰ μὴ ἔστι τόδε τοῦδε ποιότης κἀκεῖνο τούτου, μηδὲ
ποιότητος ποιότης, ἀδύνατον ἀντικατηγορεῖσθαι ἀλλήλων
σ > , > b A *, , , -^ , ^
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ηθῶς οὐκ ἐνδέχεται. ἢ γάρ τοι ὡς οὐσία κατηγορηθή-
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€ δέδεικται ὅτι οὐκ ἔσται ἄπειρα, οὔτ᾽ ἐπὶ τὸ κάτω οὔτ᾽ ἐπὶ
τὸ ἄνω (οἷον ἄνθρωπος δίπουν, τοῦτο ζῷον, τοῦτο δ᾽ ἕτερον"
οὐδὲ τὸ ζῷον κατ᾽ ἀνθρώπου, τοῦτο δὲ κατὰ KoAMov, τοῦτο
δὲ > LÀ > ^ L *, ^ A A > , L4
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ν p 3 , ^ > LÀ *, LÀ
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^ ^ .- > >
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> ra A ? v € A LJ ^
ἐκείνην yàp οὐκ ἔστιν ὁρίσασθαι ἧς τὰ ἄπειρα κατηγορεῖται.
315 ro! + μὲν n 17 ἔστω n? 19 οὗ om. x! 21 ἢ fecit B
25 σημαίνει BdP*: σημαίνειν An 26 σημαίνῃ Ad 27 μήτε ὅπερ
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33 re om. A? 35 post efolv an transponenda εἴδη... ὁμώνυμον ex
TI*5-9? 36 τόδε τοῦδε nD* : τοῦτο τουδὶ ABd 38 εἰπεῖν ἐνδέχεται,
ἀντικατηγορεῖσθαι 5 b2 86 om. dn 4 οὗτε f 5 πᾶσαν A
7 ὥστ᾽ om. nt 8 ἔσται n
15
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ANAAYTIKQN ΥΣΤΕΡΩΝ A
ds μὲν δὴ γένη ἀλλήλων οὐκ ἀντικατηγορηθήσεται-: ἔσται
γὰρ αὐτὸ ὅπερ αὐτό τι. οὐδὲ μὴν τοῦ ποιοῦ 3 τῶν ἄλλων
ΕΣ , bal Li ^ ‘ ^ ra M
οὐδέν, dv μὴ xarà συμβεβηκὸς κατηγορηθῇ: πάντα yap
ταῦτα συμβέβηκε καὶ κατὰ τῶν οὐσιῶν κατηγορεῖται. ἀλλὰ
δὴ ὅτι οὐδ᾽ εἰς τὸ ἄνω ἄπειρα ἔσται: ἑκάστου γὰρ κατηγορεῖ-
ται ὃ ἂν σημαίνῃ ἣ ποιόν τι ἢ ποσόν τι ἤ τι τῶν τοιούτων
ἢ τὰ ἐν τῇ οὐσίᾳ: ταῦτα δὲ πεπέρανται, καὶ τὰ γένη τῶν
^ ^ δὰ
κατηγοριῶν πεπέρανται" ἢ γὰρ ποιὸν ἢ ποσὸν ἢ πρός τι ἢ
ποιοῦν ἢ πάσχον ἢ ποὺ ἢ ποτέ.
Li , να jy .:᾽΄ὦν
Υπόκειται δὴ ἕν καθ᾽ ἑνὸς
a , δ A [4 ~ e M , *, ^
κατηγορεῖσθαι, αὐτὰ δὲ αὐτῶν, ὅσα μὴ τί ἐστι, μὴ κατ-
^ , 4 > , > 4 ^ ^
ηγορεῖσθαι. συμβεβηκότα γάρ ἐστι πάντα, ἀλλὰ τὰ μὲν
καθ’ αὑτά, τὰ δὲ καθ᾽ ἕτερον τρόπον: ταῦτα δὲ πάντα
καθ᾽ ὑποκειμένου τινὸς κατηγορεῖσθαί φαμεν, τὸ δὲ συμβε-
βηκὸς οὐκ εἶναι ὑποκείμενόν τι: οὐδὲν γὰρ τῶν τοιούτων τί-
4 a 3 L4 , ^ , a , > »,
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* x L4 * - 3 ε , * o» > A] Y
αὐτὸ ἄλλου καὶ τοῦτο καθ᾽ ἑτέρου. οὔτ᾽ eis τὸ ἄνω
L4 a > e 8 »ν 3 > * , ε , ,
dpa ἕν καθ᾽ ἑνὸς οὔτ᾽ εἰς τὸ κάτω ὑπάρχειν λεχθήσεται.
᾽ Φ 4 A , ^ La Ld Uu ~ ,
Kal? ὧν μὲν yàp λέγεται τὰ συμβεβηκότα, ὅσα ἐν TH oU-
σίᾳ ἑκάστου, ταῦτα δὲ οὐκ ἄπειρα: ἄνω δὲ ταῦτά τε καὶ
^ , > , , LJ , , LÀ ,
τὰ συμβεβηκότα, ἀμφότερα οὐκ ἄπειρα. ἀνάγκη dpa εἶναί
^ ^ 4 ^
τι οὗ πρῶτόν τι κατηγορεῖται καὶ τούτου ἄλλο, Kat τοῦτο
σ M , « ᾿ , L4 , L4 , L4
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κατ᾽ ἐκείνου ἄλλο πρότερον κατηγορεῖται.
φ M T , , > t d T v ?
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ἄλλος, εἰ ὧν πρότερα ἅττα κατηγορεῖται, ἔστι τούτων ἀπό-
EN > » 3 , L4 f L4 > ^
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^ * MJ ^ τω, wo» »c / » > [4 , ^
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A Bdn 17 δὴ scripsi: δὲ codd. 18 αὐτῶν 4 τί om. d! μὴ om. A!
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εἰσόμεθα δι’ ἀποδείξεως. εἰ οὖν μηδὲ βέλτιον ἔχομεν πρὸς
᾽ ^ ~ ? é + L4 LIS 2 , ᾽ > Li
αὐτὰ τοῦ εἰδέναι, οὐκ ἔσται οὐδὲν ἐπίστασθαι δι’ ἀποδείξεως
ἁπλῶς, ἀλλ᾽ ἐξ ὑποθέσεως.
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4, > ~ b 4 ^ M ^
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, >
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* > ^ ^
nyopovpeva ἐνδέχεται εἶναι ἐν ταῖς ἀποδεικτικαῖς ἐπιστήμαις,
M τ € ,΄ > ΄ t * * > , ,ὔ > ^ L4
περὶ ὧν ἡ σκέψις ἐστίν. ἡ μὲν yàp ἀπόδειξίς ἐστι τῶν ὅσα
, > € M ^ ^
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ὅσα re yàp [ἐν] ἐκείνοις ἐνυπάρχει ἐν τῷ τί ἐστι, Kal οἷς αὐτὰ
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pos ἐν τῷ λόγῳ αὐτοῦ, kai πάλιν πλῆθος ἢ τὸ διαιρετὸν
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4 E ^ ^ 4^ ^
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χοντι: τοῦτο δ᾽ εἰ ἔστι, πρῶτον 6 ἀριθμὸς ἐνυπάρξει ὑπάρ-
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? ~ * +O? 3) * L4 L4 L4 , x *
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m^ w > 4 x nn L4 eer e ΕΣ , A A
ταῦτα ἄπειρα: οὐδὲ yàp ἂν εἴη ὁρίσασθαι. ὥστ᾽ εἰ rà μὲν
κατηγορούμενα καθ᾽ αὑτὰ πάντα λέγεται, ταῦτα δὲ μὴ
ἄπειρα, ἵσταιτο ἂν τὰ ἐπὶ τὸ ἄνω, ὥστε καὶ ἐπὶ τὸ κάτω.
? 3 σ 3 M > ~ x L4 Ld to
Εἰ δ᾽ οὕτω, καὶ rà ἐν τῷ μεταξὺ δύο ὅρων dei me-
, » ^ LJ ^ M: ‘ ^ > L4 Ld
περασμένα. et δὲ τοῦτο, δῆλον ἤδη kai τῶν ἀποδείξεων ὅτι
ἀνάγκη ἀρχάς τε εἶναι, καὶ μὴ πάντων εἶναι ἀπόδειξιν,
σ LÀ n , > 3 , , ^ & X » ,
ὅπερ ἔφαμέν twas λέγειν Kat’ ἀρχάς. ef yap εἰσὶν ἀρχαί,
v , > 3 * Mo» > L4 , L4 M
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M ^ . ^ IND) Y» , M ^ M
yàp εἶναι τούτων ὁποτερονοῦν οὐδὲν ἄλλο ἐστὶν 7) τὸ εἶναι μη-
8423 μὴ om. n! 4 μηδὲν B! 5 αὐτὰ τοῦ] αὐτοῦ d 6 ἀλλ᾽
om. At 7 μὲν] τὸ μὲν d 8 συντομώτερον φανερόν n n
om. # ἐστι τῶν P : ἐστι αὕτη AB: ἐστι αὕτη τῶν A3: ἐστι d : αὕτη fecit n
13 v codd. P*: secl. Jaeger UmdpyeedPT ἐν... αὐτὰ om. n! 17 τῷ"
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ἐνυπάρχοντι n 20 πρῶτος n! ἐνυπάρξει ἐνυπάρχουσιν n 22 ἐν
om. pP 28 teravro ἂν rà Ad, fecit n: ἴσταιντο ἂν rà B 31 reom.d
32 φαμέν n κατ᾽ nT, fecit B: καὶ τὰς A: κατὰ τὰς d 34 εἶναιβ
T τούτου n
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35 δὲν διάστημα ἄμεσον kai ἀδιαίρετον, ἀλλὰ πάντα διαιρετά.
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τῷ yap ἐντὸς ἐμβάλλεσθαι ὅρον, ἀλλ᾽ οὐ τῷ προσλαμ-
σ ΕΣ > ^
βάνεσθαι ἀποδείκνυται τὸ ἀποδεικνύμενον, ὥστ᾽ εἰ τοῦτ᾽ εἰς
L4 ᾽ , LEA , ‘A > -^ 4 Ld LÀ
ἄπειρον ἐνδέχεται ἰέναι, ἐνδέχοιτ᾽ ἂν δύο ὅρων ἄπειρα με-
AY , 3 a a > 3 A > σ ε
ταξὺ εἶναι μέσα. ἀλλὰ τοῦτ᾽ ἀδύνατον, εἰ ἵστανται αἱ κατ-
b , LER 4 ν b M , v A LÀ δέ
84> ηγορίαι ἐπὶ τὸ ἄνω καὶ τὸ κάτω. ὅτι δὲ ἵστανται, δέδει-
κται λογικῶς μὲν πρότερον, ἀναλυτικῶς δὲ νῦν.
La A 4
Δεδειγμένων δὲ τούτων φανερὸν ὅτι, ἐάν τι TO αὐτὸ
ὃ E. € , * ^ M ^ 4 ^
voiv ὑπάρχῃ, olov τὸ A τῷ τε Γ᾽ καὶ τῷ A, μὴ κατ-
,ὔ UJ , hl ~ ^ M ^
s Nyopoupevov θατέρου κατὰ θατέρου, ἢ μηδαμῶς ἢ μὴ κατὰ
, ^ ,
παντός, ὅτι οὐκ ἀεὶ κατὰ κοινόν τι ὑπάρξει. οἷον τῷ ἰσο-
σκελεῖ καὶ τῷ σκαληνεῖ τὸ δυσὶν ὀρθαῖς ἴσας ἔχειν κατὰ
κοινόν τι ὑπάρχει (5 γὰρ σχῆμά τι, ὑπάρχει, καὶ οὐχ
To" ^ » 3 3 * o μ v ^ ^ »
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Γ καὶ 4 κατ᾽ ἄλλο κοινόν, κἀκεῖνο καθ᾽ ἕτερον, ὥστε
, or Ay » ^ > 4 Ld > 2 > Pd
δύο ὅρων μεταξὺ ἄπειροι av ἐμπίπτοιεν Spor. ἀλλ᾽ ἀδύνα-
τον. κατὰ μὲν τοίνυν κοινόν τι ὑπάρχειν οὐκ ἀνάγκη ἀεὶ
,
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ig τοι τῷ αὐτῷ γένει καὶ ex τῶν αὐτῶν ἀτόμων ἀνάγκη τοὺς
~ LÀ
ὅρους εἶναι, εἴπερ τῶν καθ᾽ αὑτὸ ὑπαρχόντων ἔσται τὸ κοι-
vóv: οὐ yap ἦν ἐξ ἄλλου γένους εἰς ἄλλο διαβῆναι τὰ δει-
ta
κνύμενα.
a M A LÀ [2 4 ^ B € rA ,
Φανερὸν δὲ xai ὅτι, ὅταν τὸ A τῷ ὑπάρχῃ, εἰ
A] LÀ , L4 a“ L4 ^ ^ B Li , ^
20 μὲν ἔστι τι μέσον, ἔστι δεῖξαι ὅτι τὸ A τῷ ὑπάρχει, καὶ
- ~ /, > , t
στοιχεῖα τούτου ἔστι ταὐτὰ kal τοσαῦθ᾽ ὅσα μέσα ἐστίν: ai
^ δὰ “- y Li
yàp ἄμεσοι προτάσεις στοιχεῖα, ἢ πᾶσαι ἢ ai καθόλου. εἰ
«
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μη ,
€ A Ld , ? € , M a7 *, * ^ A ,
ὁδὸς αὕτη ἐστίν. ὁμοίως δὲ kai εἰ τὸ A τῷ B μὴ ὑπάρχει,
as εἰ μὲν ἔστιν 1) μέσον 1j πρότερον ᾧ οὐχ ὑπάρχει, ἔστιν ἀπό-
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δειξις, εἰ δὲ μή, οὐκ ἔστιν, ἀλλ᾽ ἀρχή, καὶ στοιχεῖα τοσαῦτ
€ , > M ~ Uu
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εἶναι 11 ἐνδεχοιντ᾽ d ἄπειρα-- τὰ n bs θατέρου κατὰ om. n!
6 ἀεὶ om. πὶ 7 σκαληνῷ A Bdn? δυσὶν codd. PY? : τέτρασιν PY?
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B 9 ἑκάτερον nt II καὶ τῷ D 12-13 ὅροι... μὲν om. m!
14 εἴπερ coni. Jaeger: ἔπειπερ codd. μέσα B: ἄμεσα rà π 16 αὑτὰ
B 17 τὰ) κατὰ τὰ Β 19 ὑπάρχει n 21 ταὐτὰ scripsi: ταῦτα
codd. 22 atom. 5 25 9] τι ἢ π 26 ἀρχαὶ P 27 ἐστὶν
om. A γὰρ- ἐκ π
23
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δείξεώς εἰσιν. καὶ ὥσπερ ἔνιαι ἀρχαί εἰσιν ἀναπόδεικτοι, ὅτι
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ἐστὶ τόδε τοδὶ καὶ ὑπάρχει τόδε τῳδί, οὕτω καὶ ὅτι οὐκ ἔστι
, M 39) € y , , - , * ^ t *
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δὲ μὴ εἶναί τι ἔσονται ἀρχαί.
Ὅταν δὲ δέῃ δεῖξαι, ληπτέον
a ~ ^ ^ L4 A * ΄ e ,
ὃ τοῦ B πρῶτον κατηγορεῖται. ἔστω τὸ D, καὶ τούτου ὁμοίως
M 4 L4 >. L4 *, , > > , ,
τὸ 4. xai οὕτως dei βαδίζοντι οὐδέποτ᾽ ἐξωτέρω πρότασις
οὐδ᾽ ὑπάρχον λαμβάνεται τοῦ A ἐν τῷ δεικνύναι, ἀλλ᾽ ἀεὶ
^ >
τὸ μέσον πυκνοῦται, ἕως ἀδιαίρετα γένηται καὶ ἕν. ἔστι ὃ
€ ^ Li
ἕν ὅταν ἄμεσον γένηται, καὶ μία πρότασις ἁπλῶς ἡ ἄμε-
* σ ? ^ L4 L4 > ^ € ^ ^ >
gos. Kal ὥσπερ ev τοῖς ἄλλοις ἡ ἀρχὴ ἁπλοῦν, τοῦτο ὃ
? % ^ ^ 3 > > , * ~ > * L4
ov ταὐτὸ πανταχοῦ, ἀλλ᾽ ἐν βάρει μὲν μνᾶ, ἐν δὲ μέλει
δίεσις, ἄλλο δ᾽ ἐν ἄλλῳ, οὕτως ἐν συλλογισμῷ τὸ ἕν
, » » ᾽ 2 ν᾽, > 4 L4 ^ ?
πρότασις ἄμεσος, ev δ᾽ ἀποδείξει καὶ ἐπιστήμῃ ὁ νοῦς. ἐν
μὲν οὖν τοῖς δεικτικοῖς συλλογισμοῖς τοῦ ὑπάρχοντος οὐδὲν ἔξω
πίπτει, ἐν δὲ τοῖς στερητικοῖς, ἔνθα μὲν ὃ δεῖ ὑπάρχειν,
οὐδὲν τούτου ἔξω πίπτει, οἷον εἰ τὸ A τῷ Β διὰ τοῦ Γ μή
(εἰ γὰρ τῷ μὲν B παντὶ τὸ I, τῷ δὲ Γ μηδενὶ τὸ A): πά-
Aw av δέῃ ὅτι τῷ Γ τὸ A οὐδενὶ ὑπάρχει, μέσον ληπτέον
^ A a 4 >t P4 oA * 2 ^
τοῦ A καὶ Γ, kai οὕτως del πορεύσεται. ἐὰν δὲ δέῃ δεῖξαι
L4 4 ~ ? Li a ~ 4 ~ M ^
ὅτι TO A τῷ E οὐχ ὑπάρχει τῷ τὸ Γ᾽ τῷ μὲν A παντὶ
ὑπάρχειν, τῷ δὲ Ε μηδενί [ἢ μὴ παντί], τοῦ Ε οὐδέποτ᾽ ἔξω
πεσεῖται" τοῦτο δ᾽ ἐστὶν ᾧ δεῖ ὑπάρχειν. ἐπὶ δὲ τοῦ τρίτου
4 » > > ka ^ L4 ^ ^ ^ » , > »
τρόπου, οὔτε ἀφ᾽ οὗ δεῖ οὔτε ὃ Set στερῆσαι οὐδέποτ᾽ ἔξω
βαδιεῖται.
24 Οὔσης δ᾽ ἀποδείξεως τῆς μὲν καθόλου τῆς δὲ κατὰ
, x - ^ ^ ^ M ^ 3
μέρος, kai τῆς μὲν κατηγορικῆς τῆς δὲ στερητικῆς, ἀμφι-
σβητεῖται ποτέρα βελτίων. ὡς δ᾽ αὔτως καὶ περὶ τῆς ἀπο-
δεικνύναι λεγομένης καὶ τῆς εἰς τὸ ἀδύνατον ἀγούσης ἀπο-
δείξεως. πρῶτον μὲν οὖν ἐπισκεψώμεθα περὶ τῆς καθόλου
$ ^ ^ ^
καὶ τῆς κατὰ μέρος: δηλώσαντες δὲ τοῦτο, kai περὶ τῆς
δεικνύναι λεγομένης καὶ τῆς εἰς τὸ ἀδύνατον εἴπωμεν.
Δόξειε μὲν οὖν τάχ᾽ dv τισιν (8i σκοποῦσιν ἡ κατὰ
b28 καὶ... εἰσιν om. B! 30 τῳδὶ Bild οὐχ B 31 δὲ om. n!
33 4] a A Bd βαδίζοντι D: βαδίζων A Bn? : βαδίζον dn 34 Umdpxov-+
ἔτι ὦ 35 ἐν εἴ δ᾽ ἐν m? 36 ἄμεσος n? καὶ om. πὶ 8531 ó om. n
38et4- μὴ P? 4 μή om. nl 5 τὸ μὲν AT Bid τῷ Ald τῷ..-
τὸ] 10... τῷ Bld 6róy τῷ ἃ 1 πορεύεται "2 δὲ οἵη. m: δὲ
μὴ d! 8 τῷ τὸ] τὸ τοῦ d: τῷ πὶ τὸ nl 9 ὑπάρχει d τὸ B!
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περὶ om. d 17 ἐπισκεψόμεθα n 20nd
39
ar
853
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I5
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ANAAYTIKQN YETEPQN A
μέρος εἶναι βελτίων. εἰ yap καθ᾽ ἣν μᾶλλον ἐπιστάμεθα
ἀπόδειξιν βελτίων ἀπόδειξις (αὕτη γὰρ ἀρετὴ ἀποδείξεως),
~ > > ὕ - Ld , A] » ~ »
μᾶλλον δ᾽ ἐπιστάμεθα ἕκαστον ὅταν αὐτὸ εἰδῶμεν Kal
€ 4 ^ Ld , w a * , Ld
αὑτὸ ἢ ὅταν κατ᾽ ἄλλο (olov τὸν μουσικὸν Κορίσκον ὅταν
25 ὅτι ὃ Κορίσκος μουσικὸς ἢ ὅταν ὅτι ἅνθρωπος μουσικός"
ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων), ἡ δὲ καθόλου ὅτι ἄλλο, οὐχ
ὅτι αὐτὸ τετύχηκεν ἐπιδείκνυσιν (οἷον ὅτι τὸ ἰσοσκελὲς οὐχ ὅτι
, A > > σ΄ , t b ^ , σ , , >?
ἰσοσκελὲς ἀλλ᾽ ὅτι τρίγωνον), ἡ δὲ κατὰ μέρος ὅτι αὐτό----αἰ
δὴ λ , M € e Ww , , € ^ , ^
ἡ βελτίων μὲν ἡ Kal? αὑτό, τοιαύτη δ᾽ ἡ κατὰ μέρος τῆς
30 καθόλου μᾶλλον, καὶ βελτίων ἂν ἡ κατὰ μέρος ἀπόδειξις
LÀ v 5 * * , M L4 iT Ἂν > 7
εἴη. ἔτι εἰ TO μὲν καθόλου μὴ ἔστι τι παρὰ τὰ καθ᾽ ἕκαστα,
« » 2 , , , ^ , ~ > a > ,
ἡ δ᾽ ἀπόδειξις δόξαν ἐμποιεῖ εἶναί τι τοῦτο καθ᾽ 6 amodet-
κνυσι, καί τινα φύσιν ὑπάρχειν ἐν τοῖς οὖσι ταύτην, οἷον
τριγώνου παρὰ τὰ τινὰ καὶ σχήματος παρὰ τὰ τινὰ καὶ
> ~ M * A > [7] s , δ᾽ ε M Ld
35 ἀριθμοῦ παρὰ τοὺς τινὰς ἀριθμούς, βελτίων ἡ περὶ ὄν-
-^ ^ w * ᾽ ^ * > , bl , bd L4
Tos ἢ μὴ ὄντος kai δι’ ἣν μὴ ἀπατηθήσεται ἢ δι᾿ Tv, ἔστι
δ᾽ ἡ μὲν καθόλου τοιαύτη (προϊόντες γὰρ δεικνύουσιν ὥσπερ
* ^ > A , Ld ^ nn ~ w A
περὶ τοῦ ava λόγον, οἷον ὅτι ὃ dv 4 τι τοιοῦτον ἔσται ἀνὰ
λόγον ὃ οὔτε γραμμὴ οὔτ᾽ ἀριθμὸς οὔτε στερεὸν οὔτ᾽ ἐπί-
85> πεδον, ἀλλὰ παρὰ ταῦτά τι)---εἰ οὖν καθόλου μὲν μᾶλλον
αὕτη, περὶ ὄντος δ᾽ ἧττον τῆς κατὰ μέρος καὶ ἐμποιεῖ δόξαν
ψευδῆ, χείρων ἂν εἴη ἡ καθόλου τῆς κατὰ μέρος.
a ^ x. , ^ ^ ? * ~ , ^ ^ x
H πρῶτον μὲν οὐδὲν μᾶλλον ἐπὶ τοῦ καθόλου ἣ τοῦ κατὰ
s μέρος ἅτερος λόγος ἐστίν; εἰ γὰρ τὸ δυσὶν ὀρθαῖς ὑπάρχει
μὴ jj ἰσοσκελὲς ἀλλ᾽ 4 τρίγωνον, ὁ εἰδὼς ὅτι ἰσοσκελὲς ἧτ-
t *, As « H A - , σ , b ^
Tov οἷδεν ἦ αὐτὸ ἢ ὁ εἰδὼς ὅτι τρίγωνον. ὅλως Te, εἰ μὲν μὴ
L4 rd , ?, bal w > , , 4
ὄντος ἧἦ τρίγωνον εἶτα δείκνυσιν, οὐκ ἂν εἴη ἀπόδειξις, εἰ δὲ
ὄντος, ὁ εἰδὼς ἔκαστον ἦ ἕκαστον ὑπάρχεϊ μᾶλλον οἶδεν. εἰ δὴ
‘ , ἜΝ λέ [4 M Lj , λό M A θ᾽
10 τὸ τρίγωνον ἐπὶ πλέον ἐστί, καὶ ὁ αὐτὸς λόγος, καὶ μὴ κα
ὁμωνυμίαν τὸ τρίγωνον, καὶ ὑπάρχει παντὶ τριγώνῳ τὸ δύο,
, ^ A , T , , * LE « b ,
οὐκ ἂν τὸ τρίγωνον 1j ἰσοσκελές, ἀλλὰ τὸ ἰσοσκελὲς 7j τρίγωνον,
Μ , ‘ , σ΄ « θ 5A id ^ ^
ἔχοι τοιαύτας τὰς γωνίας. ὥστε 6 kaÜóAov εἰδὼς μᾶλλον
ἴὸ « , a t A. , X , L4 € θό
οἶδεν ἡ ὑπάρχει ἣ ὁ κατὰ μέρος. βελτίων ἄρα ἡ καθό-
223 εἰδῶμεν BnT : ἴδωμεν Ad 25 ὅτι om. m ἄνθρωπος scripsi : dv-
θρωπος codd. : ὁ ἄνθρωπος PS 26 ἡ}: εἰ ABd 27 οὐχ ὅτι ἰσοσκελὲς
om. πὶ 428 ἡ] εἰ ABd ὅτι καθ᾽ αὑτό n? 29 βέλτιον n KIERIES
31 ἔτι δ᾽ εἰ fecit n 32 τοιοῦτο d 34 τὰ bis om. n 38 τὸ n!
ὃ om. n 39 ὃ 0m. n bz καὶ ef ποιεῖ n 340m. A 4 οὐδὲν
BnP : οὐδὲ A: οὐδ᾽ av d 5 ἅτερος om. n! ὑπάρχειν n? 6$
om, πὶ 740m. 2 8 cin nP: +9 ABd Io 76 om. d 12 $1]
εἴη B 13 ἔχει d 14 0] τὸ ABd: ὁ τὸ f
24. 85*21-86°7
^ ^ , Li 3 * » , * M 4
λου τῆς κατὰ μέρος. ἔτι εἰ μὲν εἴη τις λόγος εἷς καὶ μὴ 15
t ’ὔ x , w . «A Rane! LJ ^ t
ὁμωνυμία τὸ καθόλου, εἴη τ᾽ ἂν οὐδὲν ἧττον ἐνίων τῶν Kara
μέρος, ἀλλὰ καὶ μᾶλλον, ὅσῳ τὰ ἀφθαρτα ἐν ἐκείνοις
ἐστί, τὰ δὲ κατὰ μέρος φθαρτὰ μᾶλλον, ἔτι τε οὐδεμία
ἀνάγκη ὑπολαμβάνειν τι εἶναι τοῦτο παρὰ ταῦτα, ὅτι ἕν δη-
Aot, οὐδὲν μᾶλλον ἢ ἐπὶ τῶν ἄλλων ὅσα μὴ τὶ σημαίνει 20
> ᾽ ^ A ^ , ^ ^ » δὲ * *, Li > z^
ἀλλ᾽ ἢ ποιὸν ἢ πρός τι ἢ ποιεῖν. ef δὲ dpa, ody ἡ ἀπόδει-
,/ > * c» » ,
fw αἰτία ἀλλ᾽ ὁ ἀκούων.
€ , >
Ἔτι εἰ ἡ ἀπόδειξις μέν ἐστι συλλογισμὸς δεικτικὸς al-
, x ^ ^ , ^ , > J , T 4 »
Tías kai τοῦ διὰ τί, τὸ καθόλου δ᾽ αἰτιώτερον (ᾧ yap καθ
αὑτὸ ὑπάρχει τι, τοῦτο αὐτὸ αὑτῷ αἴτιον: τὸ δὲ καθόλου 25
~ LÀ L4 ^ , oe * e > ,
πρῶτον᾽ αἴτιον dpa τὸ καθόλου): ὥστε kai ἡ ἀπόδειξις BeA-
τίων' μᾶλλον yap τοῦ αἰτίου καὶ τοῦ διὰ τί ἐστιν. 27
L4 /
+ + "Ere, μέχρι 27
, ^ ‘ * , M , ,»5 Ds L4
τούτου ζητοῦμεν τὸ διὰ Tí, kai τότε οἰόμεθα εἰδέναι, ὅταν
b L4 L4 LJ ^ » ^ L4 , ^ M
μὴ ἦ ὅτι τι ἄλλο τοῦτο ἢ γινόμενον ἢ ὄν: τέλος yàp Kal
, à 0v » σ > n * , LÀ >
πέρας TO ἔσχατον ἤδη οὕτως ἐστίν. olov τίνος ἕνεκα ἦλθεν; 30
4, ~ ~ Lj
ὅπως λάβῃ τἀργύριον, τοῦτο δ᾽ ὅπως ἀποδῷ ὃ ὥφειλε, τοῦτο
δ᾽ ὅπως μὴ ἀδικήσῃ" καὶ οὕτως ἰόντες, ὅταν μηκέτι δι᾽
ἄλλο μηδ᾽ ἄλλου ἕνεκα, διὰ τοῦτο ὡς τέλος φαμὲν ἐλ-
~ τ 4 , M , » x La A ,
θεῖν καὶ εἶναι καὶ γίνεσθαι, καὶ τότε εἰδέναι μάλιστα διὰ τί
ἦλθεν. εἰ δὴ ὁμοίως ἔχει ἐπὶ πασῶν τῶν αἰτιῶν καὶ τῶν διὰ 35
τί, ἐπὶ δὲ τῶν ὅσα αἴτια οὕτως ὡς οὗ ἕνεκα οὕτως ἴσμεν
, 3 3^ 7 ~ » La , , LÀ L4
μάλιστα, kai ἐπὶ τῶν ἄλλων dpa τότε μάλιστα ἴσμεν, ὅταν
μηκέτι ὑπάρχῃ τοῦτο ὅτι ἄλλο. ὅταν μὲν οὖν γινώσκωμεν
σ ,ὕ € L4 LÀ L4 , , w £ ^
ὅτι τέτταρσιν al ἔξω ἴσαι ὅτι ἰσοσκελές, ἔτι λείπεται διὰ
τί τὸ ἰσοσκελές---ὅτι τρίγωνον, καὶ τοῦτο, ὅτι σχῆμα εὐ- 86?
, , ^ ^ , , » , ,
θύγραμμον. εἰ δὲ τοῦτο μηκέτι διότι ἄλλο, τότε μάλιστα
w M la * , L4 , L4 ,
ἴσμεν. kai καθόλου δὲ τότε" ἡ καθόλου apa βελτίων. 3
Ἔτι 3
σ * ~ FAI , , x L4 > , e
ὅσῳ av μᾶλλον κατὰ μέρος 7, eis rà ἄπειρα ἐμπίπτει, ἡ
' , » 4 € ~ M 4 , Ν , *
δὲ καθόλου εἰς τὸ ἁπλοῦν καὶ τὸ πέρας. ἔστι δ᾽, fj pers
3 a
ἄπειρα, οὐκ ἐπιστητά, 7j δὲ πεπέρανται, ἐπιστητά. ἧ dpa Ka-
? ^ , ^ -* Ἂς , > ^ M
θόλου, μᾶλλον ἐπιστητὰ ἢ 7 κατὰ μέρος. ἀποδεικτὰ dpa
δὰς εἷς om. ABd 16 τ᾽ om. 5 17-18 ἀλλὰ... μέρος om. zi!
17 ὅσα d I9 ὑπολαμβάνει d 20 οὐδὲν- yàp A? σημαίνῃ Al
21 3 om. A εἰ om. A ἡ om.d 25 αὐτὸ αὑτῷ ΒΑΡ: αὐτὸ αὐτῷ
A: αὐτῷ n 27 καὶ rod 29 ἄλλο- - ἢ nP* 31 ᾧ ὥφειλε fecit a
à fecit A 32 δ᾽ om. n! 34 καὶ ὃ καὶ ἢ τότε] τὸ m! 35 δὲ nt
36 airca+ αἴτια n! ὥσπερ Ad 38 μὲν om. A 8622 80 ἄλλο τι τὶ
3 τό τε fecit n 4 ὅσα μᾶλλον f 6-73... ἐπιστητὰ om. n!
ANAAYTIKQN YETEPQN A
μᾶλλον τὰ καθόλου. τῶν δ᾽ ἀποδεικτῶν μᾶλλον μᾶλλον
ἀπόδειξις. ἅμα γὰρ μᾶλλον τὰ πρός τι. βελτίων ἄρα ἡ
1o καθόλου, ἐπείπερ καὶ μᾶλλον ἀπόδειξις.
"E- » Lj f >
10 τι εἰ αἱρετωτέρα καθ
ἣν τοῦτο καὶ ἄλλο ἢ καθ᾽ ἣν τοῦτο μόνον οἶδεν: ὁ δὲ τὴν
, L4 7T M M x. , * M ,
καθόλου ἔχων οἶδε καὶ τὸ κατὰ μέρος, οὗτος δὲ τὴν καθό-
13 λου οὐκ older: ὥστε κἂν οὕτως" αἱρετωτέρα εἴη.
13 Ἔτι δὲ ὧδε.
τὸ γὰρ καθόλου μᾶλλον δεικνύναι ἐστὶ τὸ διὰ μέσου δει-
15 κνύναι ἐγγυτέρω ὄντος τῆς ἀρχῆς. ἐγγυτάτω δὲ τὸ dye-
^ 5 ^ ^ ~
cov: τοῦτο δ᾽ ἀρχή. εἰ οὖν ἡ ἐξ ἀρχῆς τῆς μὴ ἐξ ἀρχῆς,
€ ^ * , ^ ^ , L4 , , »
ἡ μᾶλλον ἐξ ἀρχῆς τῆς ἧττον ἀκριβεστέρα ἀπόδειξις. ἔστι
δὲ τοιαύτη ἡ καθόλου μᾶλλον: κρείττων «dp'» ἂν εἴη ἡ κα-
θόλον. οἷον εἰ ἔδει ἀποδεῖξαι τὸ A κατὰ τοῦ 4’ μέσα τὰ
20 ἐφ᾽ ὧν BI: ἀνωτέρω δὴ τὸ B, ὥστε ἡ διὰ τούτου καθόλου
μᾶλλον.
᾿Αλλὰ τῶν μὲν εἰρημένων ἔνια λογικά ἐστι: μάλιστα
δὲ δῆλον ὅτι ἡ καθόλου κυριωτέρα, ὅτι τῶν προτάσεων τὴν
μὲν προτέραν ἔχοντες ἴσμεν πως καὶ τὴν ὑστέραν καὶ ἔχομεν
25 δυνάμει, οἷον εἴ τις oldev ὅτι πᾶν τρίγωνον δυσὶν ὀρθαῖς,
οἷδέ πως καὶ τὸ ἰσοσκελὲς ὅτι δύο ὀρθαῖς, δυνάμει, καὶ
3 ^ 7 ^ » * " é LÀ x ? »
εἰ μὴ olde τὸ ἰσοσκελὲς ὅτι τρίγωνον: 6 δὲ ταύτην ἔχων
* , 3 / ΕΣ ^ L4 , »ν 5»
τὴν πρότασιν τὸ καθόλου οὐδαμῶς οἶδεν, οὔτε δυνάμει οὔτ
ἐνεργείᾳ. καὶ ἡ μὲν καθόλου νοητή, ἡ δὲ κατὰ μέρος εἰς
3o αἴσθησιν τελευτᾷ.
Ὅ A + L4 a6 a ^ a ,
τι μὲν οὖν ἡ καθόλου βελτίων τῆς κατὰ μέρος, To-
σαῦθ᾽ ἡμῖν εἰρήσθω" ὅτι δ᾽ ἡ δεικτικὴ τῆς στερητικῆς, ἐντεῦ-
θεν δῆλον. ἔστω γὰρ αὕτη ἡ ἀπόδειξις βελτίων τῶν ἄλλων
τῶν αὐτῶν ὑπαρχόντων, ἡ ἐξ ἐλαττόνων αἰτημάτων ἢ ὑπο-
35 θέσεων ἢ προτάσεων. εἰ γὰρ γνώριμοι ὁμοίως, τὸ θᾶττον
γνῶναι διὰ τούτων ὑπάρξει" τοῦτο δ᾽ αἱρετώτερον. λόγος δὲ
~ , a , € , > , / L4
τῆς προτάσεως, ὅτι βελτίων ἡ ἐξ ἐλαττόνων, καθόλου ὅδε:
εἰ γὰρ ὁμοίως εἴη τὸ γνώριμα εἶναι τὰ μέσα, τὰ δὲ πρό-
τερα γνωριμώτερα, ἔστω ἡ μὲν διὰ μέσων ἀπόδειξις τῶν
a8 μᾶλλον" ut vid. P: om. ABd: ἡ π Io xai μᾶλλον) μᾶλλον ἡ A Bd
εἰ om. DM 11 καθ᾽ ἣν τοῦτο] xal n! τὴν nP : τὸ ABd 12 τὴν]
τὸ ABd 17 3... ἀρχῆς om. n! ἡ 41:5 Bld 18 dp' adi.
Bekker 19 δεῖ B 20 ἡ] εἰ AB!d 24 μὲν- yàp n ἔχοντος d
34 αὐτῶν om. st! 36 ὑπάρχει n 37 ὅδε] δὲ A Bd: ὧδε Basileensis
38 76+ γνωριμὰ εἶναι τὰ μέσα rà δὲ πρότερα ἢ 30 τῶν] τῆς ABE
25
24. 8678-25. 86°34
BI ὅτι τὸ Α τῷ E ὑπάρχει, ἡ δὲ διὰ τῶν Z H ὅτι 86^
τὸ Α τῷ Ε. ὁμοίως δὴ ἔχει τὸ ὅτι τὸ Α τῷ 4 ὑπάρχει
* A - a , " * ^ , *
καὶ TO A τῷ E. τὸ δ᾽ ὅτι τὸ A τῷ A πρότερον kai γνω-
"n ^os ‘ ^ 1 s " » ^ >
ριμώτερον ἣ ὅτι τὸ A τῷ E> διὰ yap τούτου ἐκεῖνο ἀπο-
δείκνυται, πιστότερον δὲ τὸ δι’ οὗ. καὶ ἡ διὰ τῶν ἐλατ- 5
, » > , , ~ LÀ ^ > ^ €
τόνων dpa ἀπόδειξις βελτίων τῶν ἄλλων τῶν αὐτῶν ὑπαρ-
χόντων. ἀμφότεραι μὲν οὖν διά τε ὅρων τριῶν καὶ προτά-
σεων δύο δείκνυνται, ἀλλ᾽ ἡ μὲν εἶναί τι λαμβάνει, ἡ δὲ
καὶ εἶναι καὶ μὴ εἶναί τι: διὰ πλειόνων dpa, ὥστε χείρων.
" > M δέδ Ld 195 , δ' 3 ^
Ere ἐπειδὴ δέδεικται ὅτι ἀδύνατον ἀμφοτέρων οὐσῶν xo
στερητικῶν τῶν προτάσεων γενέσθαι συλλογισμόν, ἀλλὰ τὴν
μὲν δεῖ τοιαύτην εἶναι, τὴν δ᾽ ὅτι ὑπάρχει, ἔτι πρὸς τούτῳ
δεῖ τόδε λαβεῖν. τὰς μὲν γὰρ κατηγορικὰς αὐξανομένης τῆς
ἀποδείξεως ἀναγκαῖον γίνεσθαι πλείους, τὰς δὲ στερητικὰς
ἀδύνατον πλείους εἶναι μιᾶς ἐν ἅπαντι συλλογισμῷ. ἔστω 15
^ ὃ * L4 "d * A » 1»? μι M B ^ δὲ Γ [4 ,
yàp μηδενὶ ὑπάρχον τὸ ἐφ᾽ ὅσων τὸ B, τῷ δὲ I’ ὑπάρ-
χον παντὶ τὸ Β. ἂν δὴ δέῃ πάλιν αὔξειν ἀμφοτέρας τὰς
, , , , - * L4 ^ ^ *
προτάσεις, μέσον ἐμβλητέον. τοῦ μὲν A B ἔστω τὸ A, τοῦ δὲ
BI τὸ E. τὸ μὲν δὴ E φανερὸν ὅτι κατηγορικόν, τὸ δὲ 4
τοῦ μὲν Β κατηγορικόν, πρὸς δὲ τὸ A στερητικὸν κεῖται. 20
τὸ μὲν γὰρ A παντὸς τοῦ B, τὸ δὲ A οὐδενὶ δεῖ τῶν A
ὑπάρχειν. γίνεται οὖν μία στερητικὴ πρότασις ἡ τὸ A A. ὁ
δ᾽ αὐτὸς τρόπος καὶ ἐπὶ τῶν ἑτέρων συλλογισμῶν. ἀεὶ γὰρ
τὸ μέσον τῶν κατηγορικῶν ὅρων κατηγορικὸν ἐπ᾽ ἀμφότερα-
τοῦ δὲ στερητικοῦ ἐπὶ θάτερα στερητικὸν ἀναγκαῖον εἶναι, ὥστε 25
αὕτη μία τοιαύτη γίνεται πρότασις, αἱ δ᾽ ἄλλαι κατηγο-
ρικαί. εἰ δὴ γνωριμώτερον δι’ οὗ δείκνυται καὶ πιστότερον,
δείκνυται δ᾽ ἡ μὲν στερητικὴ διὰ τῆς κατηγορικῆς, αὕτη δὲ
δι’ ἐκενης οὐ δείκνυται, προτέρα καὶ γνωριμωτέρα οὖσα
* , , ^ " LÀ > > M ^ €
καὶ πιστοτέρα βελτίων dv εἴη. ἔτι εἰ ἀρχὴ συλλογισμοῦ ἡ 3o
καθόλου πρότασις ἄμεσος, ἔστι δ᾽ ἐν μὲν τῇ δεικτικῇ κατα-
> ^ ^
φατικὴ ἐν δὲ TH στερητικἢ ἀποφατικὴ ἡ καθόλου πρό-
b ^ ^ *
τασις, ἡ δὲ καταφατικὴ τῆς ἀποφατικῆς προτέρα καὶ
γνωριμωτέρα (διὰ γὰρ τὴν κατάφασιν ἡ ἀπόφασις γνώ-
b» δὲ ABd EZ ὑπάρχει... 3 d om. A 4 δείκνυται d
8 δείκνυται f 1I γίνεσθαι n 12 μὲν δὴ n I4 γενέσθαι d
15 τῷ B! δὴ] Set A Bd 20 a4- às ABd 22 ἡ τὸ A Δ om.
Aldina ἡ fecit B 23 yàp Sei n 24 τῶν- μὲν n 27 yvà-
puiov d δι’ ob προ: δ᾽ 6 ἀπ: διὸ AB 20 οὖσα καὶ γνωρι-
μωτέρα d
35
σι
Io
15
20
25
go
ANAAYTIKQN YZTEPQN A
ριμος, Kal προτέρα ἡ κατάφασις, ὥσπερ καὶ τὸ εἶναι
τοῦ μὴ εἶναι)" ὥστε βελτίων ἡ ἀρχὴ τῆς δεικτικῆς ἢ τῆς
στερητικῆς" ἡ δὲ βελτίοσιν ἀρχαῖς χρωμένη βελτίων. ἔτι
ἀρχοειδεστέρα: ἄνευ γὰρ τῆς δεικνυούσης οὐκ ἔστιν ἡ στε-
ρητική.
Ἐπεὶ δ᾽ ἡ κατηγορικὴ τῆς στερητικῆς βελτίων, δῆλον
e ^ ^ , M > rA > , ^ > 7 , t
ὅτι kai τῆς εἰς τὸ ἀδύνατον ἀγούσης. δεῖ δ᾽ εἰδέναι τίς ἡ
διαφορὰ αὐτῶν. ἔστω δὴ τὸ A μηδενὶ ὑπάρχον τῷ B, τῷ
δὲ Γ τὸ B παντί: ἀνάγκη δὴ τῷ D' μηδενὶ ὑπάρχειν τὸ A.
” A *. , X τ LA LJ > ,
οὕτω μὲν οὖν ληφθέντων δεικτικὴ ἡ στερητικὴ ἂν εἴη ἀπόδειξις
σ * ^ $, € , ε 3 , ^ td 4 {ς᾽
ὅτι τὸ A τῷ Γ᾽ ody ὑπάρχει. ἡ δ᾽ εἰς τὸ ἀδύνατον ὧδ
ἔχει. εἰ δέοι δεῖξαι ὅτι τὸ A τῷ B οὐχ ὑπάρχει, ληπτέον
€ , ‘ A ~ L4 LA M ~
ὑπάρχειν, καὶ τὸ B τῷ I, ὥστε συμβαίνει τὸ A τῷ I
ὑπάρχειν. τοῦτο δ᾽ ἔστω γνώριμον καὶ ὁμολογούμενον ὅτι
> ΄ 3 w Tr 4 ~ L4 ig » 4 ^
ἀδύνατον. οὐκ dpa οἷόν re τὸ A τῷ B ὑπάρχειν. εἰ οὖν τὸ
B τῷ I ὁμολογεῖται ὑπάρχειν, τὸ A τῷ B ἀδύνατον ὑπάρ-
xew. οἱ μὲν οὖν ὅροι ὁμοίως τάττονται, διαφέρει δὲ τὸ
ómorépa ἂν fj γνωριμωτέρα ἡ πρότασις ἡ στερητική, πότερον
Ld A ~ , t , -^ L4 M ~ Ld x
ὅτι τὸ A τῷ B οὐχ ὑπάρχει ἢ ὅτι τὸ A τῷ Γ. ὅταν μὲν
οὖν jj τὸ συμπέρασμα γνωριμώτερον ὅτι οὐκ ἔστιν, ἡ εἰς τὸ
> ΄ a = f Ld > € 3 ^ ^
ἀδύνατον γίνεται ἀπόδειξις, ὅταν δ᾽ ἡ ἐν τῷ συλλογισμῷ,
€ > 4 Cd b r4 € a A ^ B ^ Ld
ἡ ἀποδεικτική. φύσει δὲ προτέρα ἡ ὅτι τὸ A τῷ Β ἣ ὅτι
τὸ Α τῷ Γ. πρότερα γάρ ἐστι τοῦ συμπεράσματος ἐξ ὧν
τὸ συμπέρασμα" ἔστι δὲ τὸ μὲν A τῷ D μὴ ὑπάρχειν συμ-
¥ 4 * ^ > T ^ , , εἶ
πέρασμα, τὸ δὲ Α τῷ Β ἐξ οὗ τὸ συμπέρασμα. οὐ γὰρ
εἰ cupPaiver ἀναιρεῖσθαί τι, τοῦτο συμπέρασμά ἐστιν, ἐκεῖνα
δὲ ἐξ ὧν, ἀλλὰ τὸ μὲν ἐξ οὗ συλλογισμός ἐστιν ὃ ἂν
L4 w L4 ^ Ld a , -^ É ^ L4 L4
οὕτως ἔχῃ ὥστε ἢ ὅλον πρὸς μέρος ἢ μέρος πρὸς ὅλον ἔχειν,
Lj Ἂς 4 M , > L4 L4 4
ai δὲ τὸ A Γ kai Β Γ προτάσεις οὐκ ἔχουσιν οὕτω πρὸς
ἀλλήλας. εἰ οὖν ἡ ἐκ γνωριμωτέρων καὶ προτέρων κρείττων,
4 4 > 3 , , ^ b , , > > € A
εἰσὶ δ᾽ ἀμφότεραι ἐκ τοῦ μὴ εἶναί τι πισταί, ἀλλ᾽ ἡ μὲν
> , € 2 , t , , Li ^ bal » ^
ex προτέρου ἡ δ᾽ ἐξ ὑστέρου, βελτίων ἁπλῶς ἂν εἴη τῆς
εἰς τὸ ἀδύνατον ἡ στερητικὴ ἀπόδειξις, ὥστε καὶ ἡ ταύτης
βελτίων ἡ κατηγορικὴ δῆλον ὅτι καὶ τῆς εἰς τὸ ἀδύνατόν
ἐστι βελτίων.
8743 ὑπάρχειν d 4 670m. d τῶν γ Adn ὑπάρχει d 5 εἴη
ἡ π 8 B--6é n 1o B] Γ coni. Maier 1 ὅτι... ἢ 0m.d
Body ὑπάρχει n 18 πρότερον A Bd 22 6 dy] ἐὰν n 23 ὅλον
ἔχει n 24 10€ ABd xaid-rÓó n By C*: aB ABCdnP
25 ἡ ἐκ om. B! 26 ἐκ] μὲν ἐκ n 29 τὸ fecit B
26
25. 86^35-30. 87°25
> , 3 , , 3 * , *
27 ‘AxpiBeorépa δ᾽ ἐπιστήμη ἐπιστήμης καὶ προτέρα 7 re
τοῦ ὅτι καὶ διότι ἡ αὐτή, ἀλλὰ μὴ χωρὶς τοῦ ὅτι τῆς τοῦ
Li -
διότι, xai ἡ μὴ Kal? ὑποκειμένον τῆς καθ᾽ ὑποκειμένον,
οἷον ἀριθμητικὴ ἁρμονικῆς, καὶ ἡ ἐξ ἐλαττόνων τῆς ἐκ mpoo-
θέσεως, οἷον γεωμετρίας ἀριθμητική. λέγω δ᾽ ἐκ προσθέ- 35
^ , ‘ M ,
σεως, olov μονὰς οὐσία áÜeros, στιγμὴ δὲ οὐσία Üerós: ra-
τὴν ἐκ προσθέσεως.
28 , > 9 , ? M € € 8 ΄ L4 > ^ ,
Mia δ᾽ ἐπιστήμη ἐστὶν ἡ ἑνὸς γένους, ὅσα ἐκ τῶν πρώ-
των σύγκειται καὶ μέρη ἐστὶν ἢ πάθη τούτων καθ᾽ αὐτά. ἑτέρα
δ᾽ ἐπιστήμη ἐστὶν ἑτέρας, ὅσων ai ἀρχαὶ μήτ᾽ ἐκ τῶν αὐ- 4o
τῶν μήθ᾽ ἅτεραι ἐκ τῶν ἑτέρων. τούτου δὲ σημεῖον, ὅταν εἰς 87>
τὰ ἀναπόδεικτα ἔλθῃ: δεῖ γὰρ αὐτὰ ἐν τῷ αὐτῷ γένει el-
ναι τοῖς ἀποδεδειγμένοις. σημεῖον δὲ καὶ τούτου, ὅταν τὰ
δεικνύμενα δι᾽ αὐτῶν ἐν ταὐτῷ γένει ὦσι καὶ συγγενῆ.
29 ἥἤλείους δ᾽ ἀποδείξεις εἶναι τοῦ αὐτοῦ ἐγχωρεῖ οὐ μόνον 5
ἐκ τῆς αὐτῆς συστοιχίας λαμβάνοντι μὴ τὸ συνεχὲς μέσον,
οἷον τῶν Α Β τὸ Γ καὶ 4 καὶ Ζ, ἀλλὰ καὶ ἐξ ἑτέρας. οἷον
ἔστω τὸ Α μεταβάλλειν, τὸ δ᾽ ἐφ᾽ ᾧ 4 κινεῖσθαι, τὸ δὲ Β
ἥδεσθαι, καὶ πάλιν τὸ Η ἠρεμίζεσθαι. ἀληθὲς οὖν καὶ τὸ A
~ +: 4 - ^ et ^ € , ^
τοῦ B xai τὸ A τοῦ 4 κατηγορεῖν: ὁ yàp ἡδόμενος κινεῖται το
καὶ τὸ κινούμενον μεταβάλλει. πάλιν τὸ A τοῦ H καὶ τὸ ἢ
^ > * -^ ^ A € t , , ,
τοῦ B ἀληθὲς κατηγορεῖν: πᾶς yap ὁ ἡδόμενος ἠρεμίζεται
* e ΕΣ , , oe 3 e¢ H ‘
Kai ὁ ἠρεμιζόμενος μεταβάλλει. ὥστε δι᾽ ἑτέρων μέσων Kai
οὐκ ἐκ τῆς αὐτῆς συστοιχίας ὁ συλλογισμός. οὐ μὴν ὥστε μη-
δέτερον κατὰ μηδετέρου λέγεσθαι τῶν μέσων: ἀνάγκη γὰρ τς
τῷ αὐτῷ τινι ἄμφω ὑπάρχειν. ἐπισκέψασθαι δὲ καὶ διὰ
τῶν ἄλλων σχημάτων ὁσαχῶς ἐνδέχεται τοῦ αὐτοῦ γενέσθαι
συλλογισμόν.
30 Τοῦ δ᾽ ἀπὸ τύχης οὐκ ἔστιν ἐπιστήμη δι’ ἀποδείξεως.
οὔτε γὰρ ὡς ἀναγκαῖον οὔθ᾽ ὡς ἐπὶ τὸ πολὺ τὸ ἀπὸ τύχης 20
> , > A] ^ ^ , L4 δ᾽ > 45
ἐστίν, ἀλλα τὸ παρὰ ταῦτα γινόμενον: ἡ ἀπόδειξις θα-
^ » > , ^
Tépov τούτων. más yàp συλλογισμὸς ἢ 9v ἀναγκαίων ἢ
~ M , * *
διὰ τῶν ὡς ἐπὶ τὸ πολὺ mporácewv: Kal εἰ μὲν ai mporá-
^ * > a » ,
σεις ἀναγκαῖαι, καὶ τὸ συμπέρασμα ἀναγκαῖον, εἰ δ᾽ ὡς
^ a
ἐπὶ τὸ πολύ, kai τὸ συμπέρασμα τοιοῦτον. ὥστ᾽ εἰ τὸ ἀπὸ 25
32 χωρὶς-[-ἡ n 34, 35 προθέσεως πὶ 36 δὲ- μονὰς n ἄθετος
n: θετή n* 37 προθέσεως n! 40 δ᾽ om. n ὅσον A bi drepa
coni. Mure, habet ut vid. P: ἕτεραι Bn: érepa Ad ἀἐκ)Ὶ μήτε ἐκ n!
D
4 συγγενῆ εἴη n 17 γίνεσθαι d. 20 οὔτε yap] οὐδὲ Ad οὔτ᾽ ἐπὶ
25 τὸδ om, A
30
35
40
88s
το
15
ANAAYTIKQN YETEPQN A
τύχης μήθ᾽ ws ἐπὶ τὸ πολὺ μήτ᾽ ἀναγκαῖον, οὐκ ἂν εἴη
αὐτοῦ ἀπόδειξις.
Οὐδὲ δι’ αἰσθήσεως ἔστιν ἐπίστασθαι. εἰ γὰρ καὶ ἔστιν 31
ἡ αἴσθησις τοῦ τοιοῦδε καὶ μὴ τοῦδέ τινος, ἀλλ᾽ αἰσθάνεσθαί
γε ἀναγκαῖον τόδε τι καὶ ποὺ καὶ νῦν. τὸ δὲ καθόλου καὶ
» * ^ 2 L4 ᾽ [4 > A , , A ^ >
ἐπὶ πᾶσιν ἀδύνατον αἰσθάνεσθαι: od yap τόδε οὐδὲ viv: οὐ
‘A ^ bal , A ‘A >. ^ Lj ,
γὰρ ἄν ἦν καθόλου: τὸ γὰρ ἀεὶ καὶ πανταχοῦ καθόλου
A > A T € * > 7, , ^ ,
φαμὲν εἶναι. ἐπεὶ οὖν ai μὲν ἀποδείξεις καθόλου, ταῦτα ὃ
L4 »
οὐκ ἔστιν αἰσθάνεσθαι, φανερὸν ὅτι οὐδ᾽ ἐπίστασθαι δι᾽ αἰσθή-
LÀ , ^ M
σεως ἔστιν, ἀλλὰ δῆλον ὅτι kai εἰ ἦν αἰσθάνεσθαι τὸ τρί-
L4 ^ ^ bà
γωνον ὅτι δυσὶν ὀρθαῖς ἴσας ἔχει τὰς γωνίας, ἐζητοῦμεν àv
» , M 3 σ ἐν > L4 > Le
ἀπόδειξιν καὶ οὐχ ὥσπερ φασί τινες ἠπιστάμεθα- αἰσθάνε-
σθαι μὲν γὰρ ἀνάγκη καθ᾽ ἕκαστον, ἡ δ᾽ ἐπιστήμη τὸ τὸ
, P > , * 4 , , M ^ , Ld
καθόλου γνωρίζειν ἐστίν. διὸ Kai εἰ ἐπὶ τῆς σελήνης ὄντες
ἑωρῶμεν ἀντιφράττουσαν τὴν γῆν, οὐκ àv ἤδειμεν τὴν αἰτίαν
Lj x , ᾽ — ἢ 6 A bal e" ^ , , M
τῆς ἐκλείψεως. Tjo0üvóueÜa yap ἂν ὅτι viv ἐκλείπει, καὶ
οὐ διότι ὅλως" οὐ γὰρ ἦν τοῦ καθόλου αἴσθησις. οὐ μὴν ἀλλ᾽
, ~ ^ ~ L4 -^ ^ , ^
ἐκ τοῦ θεωρεῖν τοῦτο πολλάκις συμβαῖνον τὸ καθόλου dv θη-
ρεύσαντες ἀπόδειξιν εἴχομεν: ἐκ γὰρ τῶν καθ᾽ ἕκαστα πλει-
ὄνων τὸ καθόλου δῆλον. τὸ δὲ καθόλου τίμιον, ὅτι δηλοῖ τὸ
αἴτιον: ὥστε περὶ τῶν τοιούτων ἡ καθόλου τιμιωτέρα τῶν αἰ-
σθήσεων καὶ τῆς νοήσεως, ὅσων ἕτερον τὸ αἴτιον- περὶ δὲ
P i " "
τῶν πρώτων ἄλλος λόγος.
Φανερὸν οὖν ὅτι ἀδύνατον τῷ αἰσθάνεσθαι ἐπίστασθαί τι
τῶν ἀποδεικτῶν, εἰ μή τις τὸ αἰσθάνεσθαι τοῦτο λέγει, τὸ
> , LÀ , 3 L » , " 5, ,
ἐπιστήμην ἔχειν δι’ ἀποδείξεως. ἔστι μέντοι ἔνια ἀναγόμενα
? , , w > -^ , L4 ^ >
εἰς αἰσθήσεως ἔκλευψιν ἐν τοῖς προβλήμασιν. ἔνια yàp εἰ
Li ^ $, n , ~ ᾿ ε » , ^ [4 ^ > ?, LJ
ἑωρῶμεν οὐκ àv ἐζητοῦμεν, ody ws εἰδότες TH ὁρᾶν, ἀλλ᾽ ὡς
ἔχοντες τὸ καθόλου ἐκ τοῦ ὁρᾶν. οἷον εἰ τὴν ὕαλον τετρυπη-
, € ^ ‘ ^ ~ , ^ ^ M ^ ,
μένην ἑωρῶμεν kai τὸ φῶς Sudv, δῆλον ἂν ἦν καὶ διὰ τί
καίει, τῷ ὁρᾶν μὲν χωρὶς ἐφ᾽ ἑκάστης, νοῆσαι δ᾽ ἅμα ὅτι
4 ~ 2
ἐπὶ πασῶν οὕτως.
b3r οὐδὲν νῦν nl 32 dv om. Ad ὃ yàp n! 36 δυοῖν ὀρθαῖν n
37 ὡς τινές φασιν n ἐπιστάμεθα B: fj ἐπιστάμεθα d: ἧ ἠπιοστάμεθα d?
48 τὸ Bet ut vid. P: τῷ 4 Β'άπ = ró om. πὶ 39 e om. An! 40
rj/^? om. n 8821 διότι nPS νῦν nP*: om. ABd 4 ἔχομεν n
6-7 τῆς αἰσθήσεως kai τῶν νοήσεων n 7 ὅσων ἕτερον ΒΡ ΡΤ: ὅσον
αἴτιον A Bd 9 rà] τὸ B! Io ἀποδεικτικῶν A Bd εἰ] ἢ πὶ τὸϊ
om. 5 13 ro B! 14 ἔχοντες om. d ὕελον A BdP 15 ἦν
A? B*nP : εἴην ABd 16 καίει B*d?PT : kai εἰ dn: καὶ A, fort. Β τῷ
Bekker: τὸ 484: διὰ τὸ π 17 ériom.n
30. 87*^26-32. 88°13
32 Tas δ᾽ αὐτὰς ἀρχὰς ἁπάντων εἶναι τῶν συλλογισμῶν
, , ~ x - ^ t X J >
ἀδύνατον, πρῶτον μὲν λογικῶς θεωροῦσιν. of μὲν yap ἀλη-
^ 3, ^ ~ « * ^ ‘ > LÀ
θεῖς εἰσι τῶν συλλογισμῶν, of δὲ ψευδεῖς. καὶ yàp εἰ ἔστιν 20
ἀληθὲς ἐκ ψευδῶν συλλογίσασθαι, ἀλλ᾽ ἅπαξ τοῦτο γίνεται,
οἷον εἰ τὸ A κατὰ τοῦ l' ἀληθές, τὸ δὲ μέσον τὸ B ψεῦ-
Sos: οὔτε γὰρ τὸ A τῷ B ὑπάρχει οὔτε τὸ B τῷ D. ἀλλ᾽
ἐὰν τούτων μέσα λαμβάνηται τῶν προτάσεων, ψευδεῖς
ἔσονται διὰ τὸ πᾶν συμπέρασμα ψεῦδος ἐκ ψευδῶν εἶναι, 25
a > ~ ^ ~
τὰ δ᾽ ἀληθῆ ἐξ ἀληθῶν, ἕτερα δὲ τὰ ψευδῆ xai τἀληθῆ.
Or 4 ^ > - a ^ * ^ LÀ ^ ~
εἶτα οὐδὲ τὰ ψευδῆ ἐκ τῶν αὐτῶν éavrois: ἔστι yap ψευδῆ
ἀλλήλοις καὶ ἐναντία καὶ ἀδύνατα ἅμα εἶναι, οἷον τὸ τὴν
δικαιοσύνην εἶναι ἀδικίαν ἢ δειλίαν, καὶ τὸν ἄνθρωπον ἵππον
3) βοῦν, ἢ τὸ ἴσον μεῖζον 7) ἔλαττον. 30
᾽Εκ δὲ τῶν κειμένων 3o
La $034 ^ ^ 2 - ε > x > ^ , b4
ὧδε: οὐδὲ yàp τῶν ἀληθῶν ai αὐταὶ ἀρχαὶ πάντων. ἕτεραι
γὰρ πολλῶν τῷ γένει ai ἀρχαί, καὶ οὐδ᾽ ἐφαρμόττουσαι,
οἷον ai μονάδες ταῖς στιγμαῖς οὐκ ἐφαρμόττουσιν: αἱ μὲν
γὰρ οὐκ ἔχουσι θέσιν, αἱ δὲ ἔχουσιν. ἀνάγκη δέ γε ἢ εἰς
μέσα ἁρμόττειν 7 ἄνωθεν T) κάτωθεν, ἢ τοὺς μὲν εἴσω ἔχειν 3;
Ἂς > ww ~ Ld > * Os ^ ~ > ~ , ,
τοὺς δ᾽ ἔξω τῶν ὅρων. add’ οὐδὲ τῶν κοινῶν ἀρχῶν οἷόν 7
, , E: L " , * ‘
εἶναί τινας ἐξ ὧν ἅπαντα δειχθήσεται: λέγω δὲ κοινὰς
οἷον τὸ πᾶν φάναι ἢ ἀποφάναι. τὰ γὰρ γένη τῶν ὄντων 88b
ἕτερα, καὶ τὰ μὲν τοῖς ποσοῖς τὰ δὲ τοῖς ποιοῖς ὑπάρχει
μόνοις, μεθ᾽ ὧν δείκνυται διὰ τῶν κοινῶν. ἔτι αἱ ἀρχαὶ οὐ
πολλῷ ἐλάττους τῶν συμπερασμάτων: ἀρχαὶ μὲν γὰρ αἱ
προτάσεις, ai δὲ προτάσεις ἢ προσλαμβανομένου ὅρου 3 ἐμ- 5
βαλλομένου εἰσίν. ἔτι τὰ συμπεράσματα ἄπειρα, οἱ δ᾽ ὅροι
πεπερασμένοι. ἔτι αἱ ἀρχαὶ αἱ μὲν ἐξ ἀνάγκης, αἱ δ᾽ ἐν-
δεχόμεναι.
OS 4 7 , 195i ‘ » x t
JUTw μὲν οὖν σκοπουμένοις ἀδύνατον τὰς αὐτὰς εἶναι
πεπερασμένας, ἀπείρων ὄντων τῶν συμπερασμάτων. εἰ δ᾽ το
L4 , Ld ene ^ Lj Li] *
ἄλλως πως λέγοι τις, olov ὅτι αἷδὶ μὲν γεωμετρίας aidi δὲ
~ «ον 4 ^ ^ , -^ " 4 , v
λογισμῶν aidi δὲ ἰατρικῆς, τί dv εἴη τὸ λεγόμενον ἄλλο
A L4 > ' > * ~ > ~ M * M | EN ,
πλὴν ὅτι εἰσὶν ἀρχαὶ τῶν ἐπιστημῶν; τὸ δὲ τὰς αὐτὰς φά-
8418 εἶναι om. d 2ολογισμῶν A κἂν 4282 eiom. ABd 21 γινό-
μενον A Bd 26 ra? om. d 27 ἑαυτῶν ἑαυτοῖς A Bin 31 o) n
2 αἱ om. n ἐφαρμόττουσιν n 35 ἐφαρμόττειν P 36 οἷόν om. n!
1 ofov om. st S λαμβανομένου" ἐκβαλλομένου d 9 εἶναι - ἢ πὶ
11 λέγοι nP: λέγει 484: λέγῃ d* 11 bis et 12 aide n I3 To-
σαύτας A
ANAAYTIKQN YETEPQN A
a Ld > M L4 ^ Li 2 yk , ^ σ
vat γελοῖον, ὅτι αὐταὶ αὑταῖς αἱ αὐταί: πάντα γὰρ οὕτω
a , £ > ^ ‘ or 4 3. € , ,
15 γίγνεται ταὐτά. ἀλλὰ μὴν οὐδὲ τὸ ἐξ ἁπάντων δείκνυσθαι
ὁτιοῦν, τοῦτ᾽ ἐστὶ τὸ ζητεῖν ἁπάντων εἶναι τὰς αὐτὰς ἀρχάς"
λίαν γὰρ εὔηθες. οὔτε γὰρ ἐν τοῖς φανεροῖς μαθήμασι τοῦτο
γίνεται, οὔτ᾽ ἐν τῇ ἀναλύσει δυνατόν: ai yap ἄμεσοι προ-
τάσεις ἀρχαί, ἕτερον δὲ συμπέρασμα προσληφθείσης γίνε-
20 ται προτάσεως ἀμέσου. εἰ δὲ λέγοι τις τὰς πρώτας ἀμέσους
προτάσεις, ταύτας εἶναι ἀρχάς, μία ἐν ἑκάστῳ γένει ἐστίν. εἰ
M sy 3 t ~ e , , Lj - ^o» -" T £f
δὲ μήτ᾽ ἐξ ἁπασῶν ws δέον δείκνυσθαι ὁτιοῦν μήθ οὕτως ἑτέ-
ρας wal? ἑκάστης ἐπιστήμης εἶναι ἑτέρας, λείπεται εἰ συγ-
γενεῖς αἱ ἀρχαὶ πάντων, ἀλλ᾽ ἐκ τωνδὶ μὲν ταδί, ἐκ δὲ
\
25 τωνδὶ ταδί. φανερὸν δὲ καὶ τοῦθ᾽ ὅτι οὐκ ἐνδέχεται: δέδει-
^ L4 » 3 Li ~ , 3 d ^ ,
κται yap ὅτι ἄλλαι ἀρχαὶ τῷ γένει εἰσὶν ai τῶν διαφό-
pov τῷ γένει. αἱ γὰρ ἀρχαὶ διτταί, ἐξ ὧν τε καὶ περὶ δ'
ε D 7 , v , ε * e 'o«^ > ,
αἱ μὲν οὖν ἐξ ὧν κοιναί, αἱ δὲ περὶ ὃ ἴδιαι, οἷον ἀριθμός,
μέγεθος.
LT > , hi A LU fg , ^ ^ M
30 Τὸ δ᾽ ἐπιστητὸν καὶ ἐπιστήμη διαφέρει τοῦ δοξαστοῦ xai
δόξης, ὅτι ἡ μὲν ἐπιστήμη καθόλου καὶ δι᾽ ἀναγκαίων, τὸ
δ᾽ ἀναγκαῖον οὐκ ἐνδέχεται ἄλλως ἔχειν. ἔστι δέ τινα ἀληθῆ
μὲν καὶ ὄντα, ἐνδεχόμενα δὲ καὶ ἄλλως ἔχειν. δῆλον οὖν
ὅτι περὶ μὲν ταῦτα ἐπιστήμη οὐκ ἔστιν" εἴη γὰρ ἂν ἀδύνατα
35 ἄλλως ἔχειν τὰ δυνατὰ ἄλλως ἔχειν. ἀλλὰ μὴν οὐδὲ νοῦς
(λέγω γὰρ νοῦν ἀρχὴν ἐπιστήμης) οὐδ᾽ ἐπιστήμη ἀναπόδεικτος"
~ , > «. L4 , - , , 4 > a >
τοῦτο δ᾽ ἐστὶν ὑπόληψις τῆς ἀμέσου προτάσεως. ἀληθὴς ὃ
8 «. M ^ M ? , M 86 Η M * , ,
O* ἐστὶ νοῦς καὶ ἐπιστήμη καὶ δόξα καὶ τὸ διὰ τούτων Aeyó-
oe , , + A * M 3, M ^ hal ~
μενον: wore λείπεται δόξαν εἶναι περὶ τὸ ἀληθὲς μὲν ἢ ψεῦ-
δος, ἐνδεχόμενον δὲ καὶ ἄλλως ἔχειν. τοῦτο δ᾽ ἐστὶν ὑπό-
ληψις τῆς ἀμέσου προτάσεως καὶ μὴ ἀναγκαίας. καὶ ὅμο-
, 2 L4 -^ , a ‘ 4 > ,
s λογούμενον δ᾽ οὕτω τοῖς φαινομένοις" 7j τε yap δόξα afé-
βαιον, καὶ ἡ φύσις ἡ τοιαύτη. πρὸς δὲ τούτοις οὐδεὶς οἴε-
ται δοξάζειν, ὅταν οἴηται ἀδύνατον ἄλλως ἔχειν, ἀλλ᾽ ἐπί-
στασθαι: ἀλλ᾽ ὅταν εἶναι μὲν οὕτως, οὐ μὴν ἀλλὰ καὶ ἄλλως
Or , / / € ^ M 4 , T
οὐδὲν κωλύειν, τότε δοξάζειν, ὡς τοῦ μὲν τοιούτου δόξαν οὖσαν,
10 τοῦ δ᾽ ἀναγκαίου ἐπιστήμην.
bi4 ὅτι αὗτιἩ "' 16 τούτων AB etut vid. d:roód?* τὸ δέξ B 21
τὰς αὐτὰς f et ut vid. P εἶναι- εἰ d 22 270 DM: μηδ᾽ ABdn
23 ὥσθ᾽ fecit n 24 τῶνδε d 26 yàp om. d 27 9] οὗ ABdP*
28 δ) οὗ Ad! ἴδιοι n 29 μέγεθος P: μεγέθους ABdn 30 καὶ 4-7)
n 34 μὲν et àv om. n 35 δυνατὰ - rà n! 36 yàp] δὲ n 37
τῆς Om. n 8922 μὲν ἢ] τε ἢ fecit n 9 κωλύει dn? ὡς τοῦ fecit B
33
b b
32. 88°14-33. 89°4
Πῶς οὖν ἔστι τὸ αὐτὸ δοξάσαι καὶ ἐπίστασθαι, καὶ διὰ
, > L4 € , , /, LÀ L4 Ld a >
τί οὐκ ἔσται ἡ δόξα ἐπιστήμη, et tis θήσει ἅπαν ὃ οἶδεν ἐν-
δέχεσθαι δοξάζειν; ἀκολουθήσει γὰρ ὁ μὲν εἰδὼς ὁ δὲ δοξά-
BS ~ , -΄ > Ἂς LÀ μὲ ν ΕΣ Γ
ζων διὰ τῶν μέσων, ἕως εἰς τὰ ἄμεσα ἔλθῃ, ὥστ᾽ εἴπερ
» ^ 7 x e 3 wo ^ M 4 -
ἐκεῖνος olde, καὶ ὁ δοξάζων οἶδεν. ὥσπερ yap Kat τὸ ὅτι
δοξάζειν ἔστι, καὶ τὸ διότι: τοῦτο δὲ τὸ μέσον. ἢ εἰ μὲν
er e L4 A ^ , » LÀ w LÀ
οὕτως ὑπολήψεται τὰ μὴ ἐνδεχόμενα ἄλλως ἔχειν ὥσπερ
[ἔχει] τοὺς ὁρισμοὺς δι᾽ ὧν αἱ ἀποδείξεις, οὐ δοξάσει ἀλλ᾽ ἐπι-
στησεται' εἰ δ᾽ ἀληθῆ μὲν εἶναι, οὐ μέντοι ταῦτά γε αὐτοῖς
ὑπάρχειν κατ᾽ οὐσίαν καὶ κατὰ τὸ εἶδος, δοξάσει καὶ οὐκ
, Ψ 3 ~ ' A 4 ‘ ‘ , 3A ^ ^
ἐπιστήσεται ἀληθῶς, καὶ τὸ ὅτι καὶ τὸ διότι, ἐὰν μὲν διὰ
~ > , , »* 4 Ay ^ ^ > Á, A a
τῶν ἀμέσων δοξάσῃ: ἐὰν δὲ μὴ διὰ τῶν ἀμέσων, τὸ ὅτι
‘ 3 ^ > ? ^ , M , ’ 3 4
μόνον δοξάσει; τοῦ δ᾽ αὐτοῦ δόξα καὶ ἐπιστήμη οὐ πάντως
ἐστίν, ἀλλ᾽ ὥσπερ καὶ ψευδὴς καὶ ἀληθὴς τοῦ αὐτοῦ Tpó-
πον τινά, οὕτω καὶ ἐπιστήμη καὶ δόξα τοῦ αὐτοῦ. καὶ γὰρ
δόξαν ἀληθῆ καὶ ψευδῆ ὡς μέν τινες λέγουσι τοῦ αὐτοῦ
εἶναι, ἄτοπα συμβαίνει αἱρεῖσθαι ἄλλα τε καὶ μὴ δοξά-
ζειν ὃ δοξάζει ψευδῶς- ἐπεὶ δὲ τὸ αὐτὸ πλεοναχῶς λέγε-
ται, ἔστιν ὡς ἐνδέχεται, ἔστι δ᾽ ὡς οὔ. τὸ μὲν γὰρ
, x 4 3 - , LÀ
σύμμετρον εἶναι τὴν διάμετρον ἀληθῶς δοξάζειν ἄτοπον"
ἀλλ᾽ ὅτι ἡ διάμετρος, περὶ ἣν αἱ δόξαι, τὸ αὐτό, οὕτω τοῦ
$, ^ A A é € Là ^ ^ , » * , a
αὐτοῦ, τὸ δὲ τί ἦν εἶναι ἑκατέρῳ κατὰ τὸν λόγον οὐ τὸ αὐτό.
ὁμοίως δὲ καὶ ἐπιστήμη καὶ δόξα τοῦ αὐτοῦ. ἡ μὲν γὰρ
σ A^ , σ 4 » , M ^ L4 >
οὕτως τοῦ ζῴου wore μὴ ἐνδέχεσθαι μὴ εἶναι ζῷον, ἡ ὃ
LÀ , > Ed > € a σ 3 , » , ε »
Gor ἐνδέχεσθαι, olov εἰ ἡ μὲν ὅπερ ἀνθρώπου ἐστίν, ἡ ὃ
> , , * L4 > 3 ’ ^ ΕἸ ^ MJ " Ld
ἀνθρώπου μέν, μὴ ὅπερ δ᾽ ἀνθρώπου. τὸ αὐτὸ yap ὅτι av-
θρωπος, τὸ δ᾽ ὡς οὐ τὸ αὐτό.
Φανερὸν δ᾽ ἐκ τούτων ὅτι οὐδὲ δοξάζειν ἅμα τὸ αὐτὸ
^ » , , , L4 x bal » [4 , ~
καὶ ἐπίστασθαι ἐνδέχεται. ἅμα yap av ἔχοι ὑπόληψιν τοῦ
ἄλλως ἔχειν καὶ μὴ ἄλλως τὸ αὐτό ὅπερ οὐκ ἐνδέχεται.
> L4 A ^ € , » H ~ , ^ € LÀ
ἐν ἄλλῳ μὲν yàp ἑκάτερον εἶναι ἐνδέχεται τοῦ αὐτοῦ ὡς εἴ-
, * ~ > ~ > - , L4 ^ € ,
pura, ἐν δὲ τῷ αὐτῷ οὐδ᾽ οὕτως οἷόν τε" ἕξει yàp ὑπόλη-
ψιν ἅμα, οἷον ὅτι ὁ ἄνθρωπος ὅπερ ζῷον (τοῦτο γὰρ ἦν τὸ
311 οὖν- οὐκ P 12 ἔστιν De 13 ἀκολουθήσει DP : ἀκολουθοῦσι
ABdn 14 εἰς τὰ μέσα πὶ 16 δοξάζειν... διότι om. πὶ 18 ἔχει
seclusi: habent ABdn: ἔχειν M δι᾽ οὗ B 21 τὸξ om. n 22 δοξάσῃ
«ον ἀμέσων om. nl 23 δοξάσῃ A δ᾽ αὖ n! 24 ψευδεῖς καὶ
ἀληθεῖς B! 27 ἄτοπον 4ΑΒάὰ εἰρῆσθαι A*3n* : ἐρεῖσθαι d 28 ἐπὶ πὶ
29 ἔστιν] ἔστι μὲν A?n? 30 ἀσύμμετρον A Bn} by τὸ] ταὐτὸ πὶ
3 αὐτῷ) οὕτως Ad 4¢éom.n
15
20
25
30
35
89^
ANAAYTIKON YETEPQN A
^ > , ^ ~ M x Ld ~ ^ A
s μὴ ἐνδέχεσθαι εἶναι μὴ ζῷον) καὶ μὴ ὅπερ ζῷον: τοῦτο yàp
ἔστω τὸ ἐνδέχεσθαι.
Τὰ δὲ λοιπὰ πῶς δεῖ διανεῖμαι ἐπί τε διανοίας καὶ
νοῦ καὶ ἐπιστήμης καὶ τέχνης καὶ φρονήσεως καὶ σοφίας,
A ‘A ^ ^ * 9 ^ , ^ , ,
τὰ μὲν φυσικῆς τὰ δὲ ἠθικῆς θεωρίας μᾶλλόν ἐστιν.
10 'H & dyyivoud ἐστιν εὐστοχία τις ἐν ἀσκέπτῳ χρόνῳ
Lj , * LÀ > ^ L4 € , M ^ 3. jJ
τοῦ μέσου, olov εἴ τις ἰδὼν ὅτι ἡ σελήνη TO λαμπρὸν ἀεὶ ἔχει
, ^ - ‘ , , J , ^ L4 A d ,
πρὸς τὸν ἥλιον, ταχὺ ἐνενόησε διὰ τί τοῦτο, ὅτι διὰ τὸ Adp-
3 M ^ [6 V4 -* , ΄ » ,
mew ἀπὸ τοῦ ἡλίου: ἢ διαλεγόμενον πλουσίῳ ἔγνω διότι 8a-
, hel , , L4 ᾽ M ^ > ~ , ^
vei(erav ἢ διότι φίλοι, ὅτι ἐχθροὶ τοῦ αὐτοῦ. πάντα yap
^ wv ^ , € » Lo A. » M "d M ‘
15 τὰ αἴτια τὰ μέσα [ὁ] ἰδὼν τὰ ἄκρα ἐγνώρισεν. τὸ λαμπρὸν
‘ Ἂς ‘ kid 3.4? L a ^ , > M ^ fef
εἶναι τὸ πρὸς τὸν ἥλιον ἐφ᾽ οὗ A, τὸ λάμπειν ἀπὸ τοῦ ἡλίου
B, σελήνη τὸ D'. ὑπάρχει δὴ τῇ μὲν σελήνῃ τῷ I' τὸ B,
‘ , > E] ^ eye ^ M M ^ * ^
τὸ λάμπειν ἀπὸ τοῦ ἡλίου: τῷ δὲ B τὸ A, τὸ πρὸς τοῦτ
εἶναι τὸ λαμπρόν, ἀφ᾽ οὗ λάμπει: dore καὶ τῷ I τὸ A
20 διὰ τοῦ B.
A , , > LÀ A > * μι M ,
Ta ζητούμενά ἐστιν ἴσα τὸν ἀριθμὸν ὅσαπερ émwrá-
~ xX , M μὲ * , M L4 ,
μεθα. ζητοῦμεν δὲ τέτταρα, τὸ ὅτι, τὸ διότι, εἰ ἔστι, τί
25 ἐστιν. ὅταν μὲν γὰρ πότερον τόδε ἢ τόδε ζητῶμεν, εἰς ἀρι-
A , * , > , e Ld ων L4 ^ oe
θμὸν θέντες, olov πότερον ἐκλείπει ὁ ἥλιος ἢ oU, τὸ ὅτι ζη-
τοῦμεν. σημεῖον δὲ τούτου" εὑρόντες γὰρ ὅτι ἐκλείπει πε-
, * »* $, > ~ 20. « - > , > ~
mavpeba: καὶ ἐὰν ἐξ ἀρχῆς εἰδῶμεν ὅτι ἐκλείπει, od ζητοῦ-
μεν πότερον. ὅταν δὲ εἰδῶμεν τὸ ὅτι, τὸ διότι ζητοῦμεν, οἷον
» , Ld , , * Ld ^ t - M ὃ , > ,
3o εἰδότες ὅτι ἐκλείπει καὶ ὅτι κινεῖται ἡ γῆ, TO διότι ἐκλείπει
- ὃ , a - ^ 1 ^ e ” δ᾽ ν
ἢ διότι κινεῖται ζητοῦμεν. ταῦτα μὲν οὖν οὕτως, ἔνια δ᾽ dA-
λον τρόπον ζητοῦμεν, οἷον εἰ ἔστιν ἢ μὴ ἔστι κένταυρος 7) θεός"
4 > > wv ^ ^ Li ~ , > » > > M ^ ,
TO δ᾽ εἰ ἔστιν ἢ μὴ ἁπλῶς λέγω, ἀλλ᾽ οὐκ εἰ λευκὸς 7] μή.
, , Ὁ w sf ^ LJ , 4 > , ^
γνόντες δὲ ὅτι ἔστι, τί ἐστι ζητοῦμεν, οἷον τί οὖν ἐστι θεός, ἢ
35 τί ἐστιν ἄνθρωπος;
« * τ ~ ' ^ € , w ^ *
‘A μὲν οὖν ζητοῦμεν καὶ à εὑρόντες ἴσμεν, ταῦτα καὶ
^ ^ ‘A [4
τοσαῦτά ἐστιν. ζητοῦμεν δέ, ὅταν μὲν ζητῶμεν τὸ ὅτι ἢ τὸ
,»» € ^ tT > δα , > LI] > L4 Ld M ,
εἰ ἔστιν ἁπλῶς, ἄρ᾽ ἔστι μέσον αὐτοῦ ἢ οὐκ ἔστιν" ὅταν δὲ yvóv-
b6 ἔσται A? 9 μᾶλλόν om. nt 14 ὅτι] ἢ ὅτι A? 15 rà? om. d
6 seclusi: om. ut vid. P 17 β- τὸ λαμπρὸν dei ἔχειν πρὸς τὸν ἥλιον n
τὸ Om. 9 τῷ] τὸ πῇ 24 εἰ οἴῃ. π 25 mérepovom, [2 : πρότερον A
ζητοῦμεν n 27 παυόμεθα n 28 ἴδωμεν A 29 70*] τότε
τὸ π 30713... κινεῖται om, πὶ 31 οὖν om. die 34 οὖν
om. d 37 μὲν om. d 38-9 Grav... εἰ fecit 2
34
I
b a
33. 89°5-B. 2. 90730
a * 4 Ral , L4 a ^ » * , - a Li ~ ,
τες ἣ τὸ ὅτι ἢ εἰ ἔστιν, ἣ τὸ ἐπὶ μέρους 7 τὸ ἁπλῶς, πάλιν
τὸ διὰ τί ζητῶμεν ἢ τὸ τί ἐστι, τότε ζητοῦμεν τί τὸ μέσον.
λέγω δὲ τὸ ὅτι ἔστιν ἐπὶ μέρους καὶ ἁπλῶς, ἐπὶ μέ-
, 722 > F L4 ta -* L4 > , > *
ρους μέν, dp’ ἐκλείπει ἡ σελήνη ἢ αὔξεται; εἰ γάρ ἐστι τὶ
nn -^ ^ ^
ἢ μὴ ἔστι ti, ἐν τοῖς τοιούτοις ζητοῦμεν: ἁπλῶς δ᾽, εἰ ἔστιν
^ ^ , ^ , , LÀ > € , ^
ἢ μὴ σελήνη ἢ νύξ. συμβαίνει dpa ἐν ἁπάσαις ταῖς ζη-
τήσεσι ζητεῖν ἢ εἰ ἔστι μέσον ἢ τί ἐστι τὸ μέσον. τὸ μὲν
^ ^ ^ T)? ,
yàp αἴτιον TO μέσον, ἐν ἅπασι δὲ τοῦτο ζητεῖται. dp’ éx-
, ^ -
λείπει; ἄρ᾽ ἔστι τι αἴτιον ἢ οὔ; μετὰ ταῦτα γνόντες ὅτι ἔστι
“- ^ A w ~
τι, τί οὖν τοῦτ᾽ ἔστι ζητοῦμεν. τὸ yap airov τοῦ εἶναι μὴ
τοδὲ ἢ τοδὶ GAN’ ἁπλῶς τὴν οὐσίαν, 7j τοῦ μὴ ἁπλῶς ἀλ-
λ / ~ 3 € ^ - ^ , ^ , > ,
d& τι τῶν καθ᾽ αὑτὸ 7) κατὰ συμβεβηκός, τὸ μέσον ἐστίν.
^ * EJ
λέγω δὲ τὸ μὲν ἁπλῶς τὸ ὑποκείμενον, olov σελήνην ἢ γῆν
^ 4 -^ , ^ * M L4 > , » ,
ἢ ἥλιον 1) τρίγωνον, τὸ δὲ τὶ ἔκλειψιν, ἰσότητα ἀνισότητα,
εἰ ἐν μέσῳ ἢ μή. ἐν ἅπασι γὰρ τούτοις φανερόν ἐστιν ὅτι
M » , > ^ , , Li 4 Lad ^ > »
τὸ αὐτό ἐστι τὸ τί ἐστι καὶ διὰ τί ἔστιν. τί ἐστιν ἔκλειψις;
στέρησις φωτὸς ἀπὸ σελήνης ὑπὸ γῆς ἀντιφράξεως. διὰ
, v L4 hol 3 , , rà € , ^ ^
τί ἔστιν ἔκλειψις, ἢ διὰ τί ἐκλείπει ἡ σελήνη; διὰ τὸ
ἀπολείπειν τὸ φῶς ἀντιφραττούσης τῆς γῆς. τί ἐστι συμ-
^ ^ ^ d
φωνία; λόγος ἀριθμῶν ἐν ὀξεῖ καὶ βαρεῖ. διὰ τί συμφω-
^ A » A ~ a A A , v > ~ M » *
vet τὸ ὀξὺ τῷ βαρεῖ; διὰ τὸ λόγον ἔχειν ἀριθμῶν τὸ ὀξὺ
καὶ τὸ βαρύ. ἄρ᾽ ἔστι συμφωνεῖν τὸ ὀξὺ καὶ τὸ βαρύ; ap’
, M H > θ ^ Lj , » ~ , δ᾽ - LA ,
ἐστὶν ἐν ἀριθμοῖς 6 λόγος αὐτῶν; λαβόντες δ᾽ ὅτι ἔστι, Tis
οὖν ἐστιν ὁ λόγος;
Ὅτι δ᾽ ἐστὶ τοῦ μέσου ἡ ζήτησις, δηλοῖ ὅσων τὸ μέ-
^ , ^
gov αἰσθητόν. ζητοῦμεν yàp μὴ ἠσθημένοι, olov τῆς ἐκλεί-
> w ^ , * | A. ud $ t ^ , , ^ "
ψεως, εἰ ἔστιν 1j μή. εἰ δ᾽ ἦμεν ἐπὶ τῆς σελήνης, οὐκ ἄν ἐζη-
^ ww» , , M εἶ * > » Ld ^ ^
τοῦμεν οὔτ᾽ εἰ γίνεται οὔτε διὰ τί, GAN’ ἅμα δῆλον dv ἦν.
, A ~ LJ M A , > é ^ € ^ , ,
ἐκ yap τοῦ αἴσθεσθαι καὶ τὸ καθόλου ἐγένετο àv ἡμῖν εἰδέ-
ναι. ἡ μὲν γὰρ αἴσθησις ὅτι νῦν ἀντιφράττει (καὶ γὰρ δῆ-
λον ὅτι νῦν ἐκλείπει): ἐκ δὲ τούτου τὸ καθόλου ἂν ἐγένετο.
go*r ἢ τὸ διότι η ζητοῦμεν A Bd 2 δὅτι- ἢ An®: -ἰ ἢ εἰ Bin ἔστιν
om. dAn¢ 43...rtom.d 5 # om. d 6 ἣ εἰ] ἢ π: εἰ πῇ
ἐστι-" μέσον ἣ τί ἐστι n 8 τι] τὸ d γνὼν A: γνῶναι d g mom.
ἔστιν - ὃ n! τοῦ] μὴ d IO τὴν... ἁπλῶς om. n! τοῦ coni. Bonitz :
τὸ codd. 11 κατὰ AD An*P*6: κατὰ τὸ d τὸ κατὰ rn 12 μὲν] μέσον d
I3 ἢ ἥλιον om. d ἰσότητα om. n! ἀνισότητα om. n* I4 ei] 5
Adn? 19 dpiÜu d ὀξεί " xainP:% ABd βαρείᾳ 20 ἀριθ-
pov d 21 συμφώνων d 23óo0m.d 24 ἡ οἵη. d ὅσων
B*nAnE: ὅσον ABd 27 οὔτε NET: οὔτ᾽ εἰ A Bdii* ἂν ἦν nP*:
ἦν ἂν ABd 28 αἰσθάνεσθαι nE PST ἐγίνετο B 30 ἐκ] εἰ A
90"
5
1το
15
20
30
ANAAYTIKON YZTEPON B
"0 - λέ * , > ἰδέ > , » ^
σπερ οὖν λέγομεν, TO τί ἐστιν εἰδέναι ταὐτό ἐστι xai
ow ^ ^ ^ H
διὰ τί ἔστιν, τοῦτο δ᾽ ἣ ἁπλῶς καὶ μὴ τῶν ὑπαρχόντων τι,
c* ~ [4 ty * σ΄ 4 > , ^ -* ^ ^
ἢ τῶν ὑπαρχόντων, οἷον ὅτι δύο ὀρθαί, ἢ ὅτι μεῖζον ἢ
ἔλαττον.
Ὅ * s / M ΄ , , ΄ >
35 T. μὲν οὖν πάντα τὰ ζητούμενα μέσου ζήτησίς ἐστι,
δῆλον: πῶς δὲ τὸ τί ἐστι δείκνυται, καὶ τίς 6 τρόπος τῆς
> ~ ^ , » e ,
ἀναγωγῆς, καὶ τί ἐστιν ὁρισμὸς καὶ τίνων, εἴπωμεν, διαπο-
^ ‘ “ > ~
püjcavres πρῶτον περὶ αὐτῶν. ἀρχὴ δ᾽ ἔστω τῶν μελλόντων
L4 , * > Fd ~
go> ἥπερ ἐστὶν οἰκειοτάτη τῶν ἐχομένων λόγων. ἀπορήσειε γὰρ
PR v i: ^ -^
dv tis, ἄρ᾽ ἔστι τὸ αὐτὸ Kal κατὰ τὸ αὐτὸ ὁρισμῷ εἰδέναι
M > , un > , Lj * Ἁ € * ^ , >
kai ἀποδείξει, 7 ἀδύνατον; ὁ μὲν yap ὁρισμὸς τοῦ τί ἐστιν
εἶναι δοκεῖ, τὸ δὲ τί ἐστιν ἅπαν καθόλου καὶ κατηγορικόν"
b > LEA] Li b , t » » ,
ς συλλογισμοὶ δ᾽ εἰσὶν of μὲν στερητικοί, οἱ δ᾽ οὐ καθόλου,
οἷον of μὲν ἐν τῷ δευτέρῳ σχήματι στερητικοὶ πάντες, oi δ᾽
ἐν τῷ τρίτῳ οὐ καθόλου. εἶτα οὐδὲ τῶν ἐν τῷ πρώτῳ σχή-
ματι κατηγορικῶν ἁπάντων ἔστιν ὁρισμός, οἷον ὅτι πᾶν τρί-
A » ^ »* μ᾿ Ld * , v * + ,
yovov δυσὶν ὀρθαῖς ἴσας ἔχει. τούτον δὲ λόγος, ὅτι τὸ ἐπί-
, » M > ^ ^ > , » σ , > *
10 στασθαί ἐστι τὸ ἀποδεικτὸν τὸ ἀπόδειξιν ἔχειν, ὥστ᾽ ἐπεὶ
“- r4 > , L4 - - u a LJ , ~ *
τῶν τοιούτων ἀπόδειξις ἔστι, δῆλον ὅτι οὐκ àv εἴη αὐτῶν καὶ
ὁρισμός: ἐπίσταιτο γὰρ ἄν τις καὶ κατὰ τὸν ὁρισμόν, οὐκ
LÀ a 3 , 3 * M Ld A L4 μι . &
ἔχων τὴν ἀπόδειξιν: οὐδὲν yap κωλύει μὴ dua ἔχειν. ἱκανὴ
δὲ πίστις καὶ ἐκ τῆς ἐπαγωγῆς: οὐδὲν γὰρ πώποτε ὁρισά-
15 μενοι ἔγνωμεν, οὔτε τῶν καθ᾽ αὑτὸ ὑπαρχόντων οὔτε τῶν συμ-
,
βεβηκότων. ἔτι ef 6 ὁρισμὸς οὐσίας τινὸς γνωρισμός, τά γε
τοιαῦτα φανερὸν ὅτι οὐκ οὐσίαι.
LÀ * + u L4 « ^ a T * , ,
Or. μὲν οὖν οὐκ ἔστιν ὁρισμὸς ἅπαντος οὗπερ καὶ amó-
δειξις, δῆλον. τί δαί, οὗ δρισμός, dpa παντὸς ἀπόδειξις ἔστιν
201) οὔ; εἷς μὲν δὴ λόγος καὶ περὶ τούτου ὁ αὐτός. τοῦ γὰρ
Li , μὰ , » , L4 , LÀ a + , A »
ἑνός, ἡ ἕν, μία ἐπιστήμη. wor εἴπερ TO ἐπίστασθαι τὸ ἀπο-
, , A 4 > , v ΄ , » [4
δεικτόν ἐστι τὸ τὴν ἀπόδειξιν ἔχειν, συμβήσεταί τι advva-
L] ~
TOv: ὃ yap τὸν ὁρισμὸν ἔχων ἄνευ τῆς ἀποδείξεως ἐπιστήσε-
v t ~ d
ται. ἔτι at ἀρχαὶ τῶν ἀποδείξεων ὁρισμοί, ὧν ὅτι οὐκ ἔσον-
> , a Li M >
25 ται ἀποδείξεις δέδεικται πρότερον---ἢ ἔσονται ai ἀρχαὶ dmo-
331 λέγωμεν tt 33 ἢ τῶν ὑπαρχόντων om, n! 35 ἐστι ante πάντα π'
by ἥπερ B*nEP : εἴπερ ABd 6 δευτέρῳ-: τῷ n 8 οἷον om. πὶ
Io τὸ AdP: om. Bn ἀποδεικτὸν OPS: ἀποδεικτικὸν Ad: ἀποδεικτικῶς Bn
ἐπεὶ] εἰ ἐπὶ Adn*Po: ἐπὶ n 12 τις οπι, 48 15 τῶνδ τ κατὰ d
16 εἰ οὔ. n. ὁ AnP:om. Bd τινὸς BnE: τις d: om. A γνωρισμάς
ME: γνώριμος ABdn δὲπ 18 μὲν τοίνυν n 198 AdnP of AE:
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22 τὴν οπ!. ἔχει πὶ 25 ἀπόδειξις An! ἢ) εἰ ἀ! ἀποδέδεικται πὶ
2. 90*31-4. 91°23
A b ^ > ^ > , * a? > LJ
8eucral kai τῶν ἀρχῶν ἀρχαί, καὶ τοῦτ᾽ εἰς ἄπειρον βαδι-
εἴται, 7) τὰ πρῶτα ὁρισμοὶ ἔσονται ἀναπόδεικτοι.
3 - ^ -^
Ἀλλ᾽ dpa, εἰ μὴ παντὸς τοῦ αὐτοῦ, ἀλλὰ τινὸς τοῦ
*, a Ww € * * > , ^ > 7 2 a L4
αὐτοῦ ἔστιν ὁρισμὸς καὶ ἀπόδειξις; ἢ ἀδύνατον; οὐ yàp ἔστιν
ἀπόδειξις οὗ ὁρισμός. ὁρισμὸς μὲν γὰρ τοῦ τί ἐστι καὶ οὐ- 30
, e » > , , ^ € , X
σίας" ai δ᾽ ἀποδείξεις φαίνονται πᾶσαι ὑποτιθέμεναι kai
t
λαμβάνουσαι τὸ Tí ἐστιν, οἷον at μαθηματικαὶ τί μονὰς xal
, ^ / ^ ¢ » Ld , μ᾿ ^ 3 ,
τί τὸ περιττόν, Kat al ἄλλαι ὁμοίως. ἔτι πᾶσα ἀπόδειξις
, ~
τὶ κατὰ τινὸς δείκνυσιν, οἷον ὅτι ἔστιν ἢ οὐκ ἔστιν: ἐν δὲ τῷ
¢ ^ ^ L4 M ^
ὁρισμῷ οὐδὲν ἕτερον ἑτέρου κατηγορεῖται, οἷον οὔτε TO ζῷον 35
X ^ ^ ^ ~ ^ τῶν X. ^ ^
κατὰ τοῦ δίποδος οὔτε τοῦτο κατὰ τοῦ ζῴου, οὐδὲ δὴ κατὰ τοῦ
ἐπιπέδου τὸ σχῆμα: οὐ γάρ ἐστι τὸ ἐπίπεδον σχῆμα, οὐδὲ
^ > M LÀ ^,
τὸ σχῆμα ἐπίπεδον. ἔτι ἕτερον τὸ Ti ἐστι καὶ ὅτι ἔστι δεῖξαι.
ὁ μὲν οὖν ὁρισμὸς τί ἐστι δηλοῖ, ἡ δὲ ἀπόδειξις ὅτι ἔστι Q1?
, ^ ^ a > L4 € L4 ^ € , , , oN
τόδε κατὰ τοῦδε ἢ οὐκ ἔστιν. ἑτέρου δὲ ἑτέρα ἀπόδειξις, ἐὰν
* e , ~ 6X ~ δὲ λέ Ed δέδ
μὴ ὡς μέρος ἦ τι τῆς ὅλης. τοῦτο δὲ λέγω, ὅτι δέδεικται
‘ », a , 3 , > =~ , Ly ,
τὸ ἰσοσκελὲς δύο ὀρθαί, εἰ πᾶν τρίγωνον δέδεικται: μέρος
, * , Ld ~ M ‘ ἄλλ , L4 L4
ydp, τὸ δ᾽ ὅλον. ταῦτα δὲ πρὸς λα οὐκ ἔχει οὕτως, ς
τὸ ὅτι ἔστι καὶ τί ἐστιν: οὐ γάρ ἐστι θατέρου θάτερον μέρος.
, > ,
Φανερὸν dpa ὅτι οὔτε ob ὁρισμός, τούτου παντὸς dmó-
M , Ld
δειξις, οὔτε οὗ ἀπόδειξις, τούτου παντὸς ὁρισμός, οὔτε ὅλως
~ » ^ * ^ > a » w σ ~ € ᾽ M
τοῦ αὐτοῦ οὐδενὸς ἐνδέχεται ἄμφω ἔχειν. ὥστε δῆλον ws οὐδὲ
L4 A ^ >? , L4 A » * - LJ w ΄ »
ὁρισμὸς kai ἀπόδειξις οὔτε TO αὐτὸ ἂν εἴη οὔτε θάτερον ἐν θα- 1o
τέρῳ- καὶ γὰρ ἂν τὰ ὑποκείμενα ὁμοίως εἶχεν.
^ ^ ,
4 Ταῦτα μὲν οὖν μέχρι τούτου διηπορήσθω: τοῦ δὲ τί
, , L4 ^ ^ > , n , v
ἐστι πότερον ἔστι συλλογισμὸς Kai ἀπόδειξις ἢ οὐκ ἔστι, Ka-
, ~ € , € , € ^ ^ 3 * *
θάπερ viv ὁ λόγος ὑπέθετο; ὁ μὲν yàp συλλογισμὸς τὶ κατὰ
^ LÀ M ?
τινὸς δείκνυσι διὰ τοῦ μέσου: τὸ δὲ τί ἐστιν ἴδιόν τε, Kal ἐν 15
~ ^ ~ , »
τῷ Ti ἐστι κατηγορεῖται. ταῦτα δ᾽ ἀνάγκη ἀντιστρέφειν. εἰ
γὰρ τὸ A τοῦ Γ ἴδιον, δῆλον ὅτι καὶ τοῦ B καὶ τοῦτο τοῦ I,
σ > ~ , H
ὥστε πάντα ἀλλήλων. ἀλλὰ μὴν kai εἰ τὸ A ἐν τῷ τί ἐστιν
€ , M ^ A] 06 A B ^ ^ I »
ὑπάρχει παντὶ τῷ B, καὶ καθόλου τὸ παντὸς τοῦ ἐν
~ , > , » , E! ^ > ~ i > ^
τῷ τί ἐστι λέγεται, ἀνάγκη καὶ τὸ A ἐν τῷ τί ἐστι τοῦ l'zo
, M * ' L4 ^ ΄ » LEA
λέγεσθαι. εἰ δὲ μὴ οὕτω τις λήψεται διπλώσας, οὐκ ἀνάγκη
ν Ν “- a » ^ ?o» » ‘ *
ἔσται τὸ A τοῦ Γ κατηγορεῖσθαι ἐν τῷ τί ἐστιν, εἰ τὸ μὲν A
~ » ~ LJ ^4 > Ld * ^ , ~ , »
τοῦ B ἐν τῷ τί ἐστι, μὴ καθ᾽ ὅσων δὲ τὸ B, ἐν τῷ τί ἐστιν.
b34 ὅτι ἢ m grat ὅτι nE* : --ἢ AB: +d 3 τι fecit d* : ὡς
τι À 4 ὀρθαῖς ABdn? 8 οὔτεξ Pacius: ὥστε codd. Ec 10 ἐν
om. ὦ 11 ἔχειν Ad 15 τινὸς -᾿ ἀεὶ ἢ 19 ὑπάρχειν n 23 6]
an τὸ B év?
4985 ΕἸ
ANAAYTIKQN YETEPQN B
τὸ δὲ τί ἐστιν ἄμφω ταῦτα eer ἔσται dpa καὶ τὸ B κατὰ
^ a Τ᾽." ᾽ 3 3 Fo» M M tt L4
as τοῦ Γ τὸ τί ἐστιν. εἰ δὴ τὸ τί ἐστι καὶ τὸ τί ἦν εἶναι ἄμφω
ἔχει, ἐπὶ τοῦ μέσου ἔσται πρότερον τὸ τί ἦν εἶναι. ὅλως τε,
»» ^ a , L4 ΝΜ M L4 4 4
εἰ ἔστι δεῖξαι τί ἐστιν ἄνθρωπος, ἔστω τὸ I ἄνθρωπος, τὸ δὲ
Α τὸ τί ἐστιν, εἴτε ζῷον δίπουν εἴτ᾽ ἄλλο τι. εἰ τοίνυν συλ-
λογιεῖται, ἀνάγκη κατὰ τοῦ Β τὸ Α παντὸς κατηγορεῖσθαι.
^ » L4 w ,ὔ , L4 ‘ ^ v H
3o τοῦτο δ᾽ ἔσται ἄλλος λόγος μέσος, ὥστε kai τοῦτο ἔσται Ti
> ^ ^
ἐστιν ἄνθρωπος. λαμβάνει οὖν ὃ Set δεῖξαι: kal yap τὸ B
᾿ !
ἔσται τί ἐστιν ἄνθρωπος.
^ ^ , ^
Act δ᾽ ἐν ταῖς δυσὶ προτάσεσι καὶ τοῖς πρώτοις καὶ
^ ,
dpéaow σκοπεῖν: μάλιστα yàp φανερὸν τὸ λεγόμενον γίνε-
45 ται. οἱ μὲν οὖν διὰ τοῦ ἀντιστρέφειν δεικνύντες τί ἐστι ψυχή,
^ , > L4 ^ LÀ LJ ~ ~ » M * > ~
ἢ τί ἐστιν ἄνθρωπος 7j ἄλλο ὁτιοῦν τῶν ὄντων, τὸ ἐξ ἀρχῆς
> ^ ” > n 1 $. ' ΠῚ to^
αἰτοῦνται, olov εἴ τις ἀξιώσειε ψυχὴν εἶναι τὸ αὐτὸ αὑτῷ
αἴτιον τοῦ ζῆν, τοῦτο δ᾽ ἀριθμὸν αὐτὸν αὑτὸν κινοῦντα: ἀνάγκη
γὰρ αἰτῆσαι τὴν ψυχὴν ὅπερ ἀριθμὸν εἶναι αὐτὸν αὑτὸν κι-
QI» νοῦντα, οὕτως ὡς τὸ αὐτὸ ὄν. οὐ γὰρ εἰ ἀκολουθεῖ τὸ A
τῷ B καὶ τοῦτο τῷ I, ἔσται τῷ Γ τὸ A τὸ τί ἦν εἶναι,
ἀλλ᾽ ἀλ θὲ > ^ M re Y: , L4 * A Ld
ηθὲς εἰπεῖν ἔσται μόνον: οὐδ᾽ εἰ ἔστι TO ὅπερ τι
καὶ κατὰ τοῦ B κατηγορεῖται παντός. καὶ γὰρ τὸ ζῴῳ «l-
s ναὶ κατηγορεῖται κατὰ τοῦ ἀνθρώπῳ εἶναι (ἀληθὲς γὰρ πᾶν
τὸ ἀνθρώπῳ εἶναι ζῴῳ εἶναι, ὥσπερ καὶ πάντα ἄνθρωπον
^ » 3 , " e a 3^ ^ 7. εἶ Ὁ
ζῷον), ἀλλ᾽ οὐχ οὕτως ὥστε ἕν εἶναι. ἐὰν μὲν οὖν μὴ οὕτω
λάβῃ, οὐ συλλογιεῖται ὅτι τὸ A ἐστὶ τῷ Γ τὸ τί ἣν εἶναι
M € ? , 35 x L4 , , L4 , 4 ^
καὶ ἡ ovata: ἐὰν δὲ οὕτω λάβῃ, πρότερον ἔσται εἰληφὼς τῷ
ID Ὁ ^ », “ A LA > > > ὃ ἐδ ^ ^
το T° τί ἐστι τὸ τί ἦν εἶναι [τὸ B]. ὥστ᾽ οὐκ ἀποδέδεικται" τὸ yàp
ἐν ἀρχῇ εἴληφεν.
~ ,
᾿Αλλὰ μὴν οὐδ᾽ ἡ διὰ τῶν διαιρέσεων ὁδὸς συλλογί-
ζεται, καθάπερ ἐν τῇ ἀναλύσει τῇ περὶ τὰ σχήματα εἴ-
ρηται. οὐδαμοῦ γὰρ ἀνάγκη γίνεται τὸ πρᾶγμα ἐκεῖνο εἶναι
^ ow > $ σ 50} * » 4 3 , , A
15 τωνδὶ ὄντων, GAN’ ὥσπερ οὐδ᾽ 6 ἐπάγων ἀποδείκνυσιν. o) yàp
^ M] ^ ^ ^ H »
δεῖ τὸ συμπέρασμα ἐρωτᾶν, οὐδὲ τῷ δοῦναι εἶναι, ἀλλ
824 δὴ B τὰ αὐτὰ d 25 δὲ n 26 τὸ om. n 30 τοῦτοϊ coni.
Bonitz: τούτου codd. AnE et ut vid. P 31 δεῖ om. n! : eee P 32
ἔσται coni. Bonitz: ἐστι codd. E 35 οὖν) δὴ n br οὐ yàp εἰ BnE: εἰ
yàp Ad 3 ἀληθὲς n et ut vid. E: ἀληθὲς ἦν A Bd: ἀληθὲς πᾶν coni.
Bywater : ὃ ἀληθὲς coni. Mure ἔσται] + ὅτι ἔστι (omisso ἦν) coni. Bonitz
4 ζῴῳ BnE: ζῷον Ad § πᾶν τὸ] mavrin 6 elvai? post 7 ζῷον d: om. n
dore n 1 ὦστε ἐνεῖναι nt 8 λάβῃ om. n 970m. 7” 1o τῷ]
ὅτι coni. Bywater τὸ B seclusi II εἰληφέναι d I5 τωνδὲ fecit
d* ó om. A
4. 91?24-6. 92710
3 , ? , Μ΄ nn M ~ e 3 ,
ἀνάγκη εἶναι ἐκείνων ὄντων, κἂν μὴ φῇ ὁ ἀποκρινόμενος.
ἄρ᾽ ó ἄνθρωπος ζῷον ἢ ἄψυχον; εἶτ᾽ ἔλαβε ζῷον, οὐ συλ-
λελόγισται. πάλιν ἅπαν ζῷον ἢ πεζὸν ἢ ἔνυδρον: ἔλαβε
, * A > * L4 * Ld ~ , ?
πεζόν. kai τὸ εἶναι τὸν ἄνθρωπον τὸ ὅλον, ζῷον πεζόν, οὐκ 20
» , , ^ ’ L4 > A , M ^
ἀνάγκη ἐκ τῶν εἰρημένων, ἀλλὰ λαμβάνει Kai τοῦτο. δια-
, , , A , * ^ nn LA WA Uu ^ ^ > 4
φέρει δ᾽ οὐδὲν ἐπὶ πολλῶν ἢ ὀλίγων οὕτω ποιεῖν: τὸ αὐτὸ
, », ~ ^
ydp ἐστιν. (ἀσυλλόγιστος μὲν οὖν kai ἡ χρῆσις γίνεται τοῖς
οὕτω μετιοῦσι καὶ τῶν ἐνδεχομένων συλλογισθῆναι.) τί γὰρ
, ^ ^ ^
κωλύει τοῦτο ἀληθὲς μὲν τὸ πᾶν εἶναι κατὰ τοῦ ἀνθρώπου, 25
M ΕἾ 5. -^
μὴ μέντοι τὸ τί ἐστι μηδὲ TO τί ἦν εἶναι δηλοῦν; ἔτι τί κω-
, - ~ , nn , ^ *» € , ^ > Lj
λύει ἢ προσθεῖναί τι ἢ ἀφελεῖν ἢ ὑπερβεβηκέναι τῆς οὐσίας;
Ταῦτα μὲν οὖν παρίεται μέν, ἐνδέχεται δὲ λῦσαι τῷ
£f * ^ , > , * * , ~ ^ ,
λαμβάνειν ἐν τῷ τί ἐστι πάντα, kai τὸ ἐφεξῆς τῇ διαιρέσει
ποιεῖν, αἰτούμενον τὸ πρῶτον, καὶ μηδὲν παραλείπειν. τοῦτο 30
δ᾽ ἀναγκαῖον, εἰ ἅπαν εἰς τὴν διαίρεσιν ἐμπίπτει καὶ μηδὲν
> , ~ > > -^ Ld ^ LÀ ^ T 2 *
ἐλλείπει" [τοῦτο δ᾽ avaykatov,] ἄτομον yàp ἤδη δεῖ εἶναι. ἀλλὰ
x Ld » μὴ * » w » ,
συλλογισμὸς ὅμως οὐκ ἔστι, ἀλλ᾽ εἴπερ, ἄλλον τρόπον
γνωρίζειν ποιεῖ. καὶ τοῦτο μὲν οὐδὲν ἄτοπον: οὐδὲ γὰρ ὃ
ἐπάγων ἴσως ἀποδείκνυσιν, ἀλλ᾽ ὅμως δηλοῖ τι. συλλογι- 45
kl 3 3 z, Ld , ~ , , M € *
cuóv δ᾽ ov λέγει ὁ ἐκ τῆς διαιρέσεως λέγων τὸν ὁρισμόν.
ὥσπερ γὰρ ἐν τοῖς συμπεράσμασι τοῖς ἄνευ τῶν μέσων,
ἐάν τις εἴπῃ ὅτι τούτων ὄντων ἀνάγκη τοδὶ εἶναι, ἐνδέχεται
ἐρωτῆσαι διὰ τί, οὕτως καὶ ἐν τοῖς διαιρετικοῖς ὅροις. τί ἐστιν
»ν ~ 4 € 4 » » ^ ,
ἄνθρωπος; ζῷον θνητόν, ὑπόπουν, δίπουν, ἅπτερον. διὰ τί, 925
παρ᾽ ἑκάστην πρόσθεσιν; ἐρεῖ γάρ, καὶ δείξει τῇ διαιρέσει,
e *w Ld ^ nn x bd » , « * ^ ,
ὡς οἴεται, ὅτι πᾶν ἢ θνητὸν ἢ ἀθάνατον. 6 δὲ τοιοῦτος Aó-
γος ἅπας οὐκ ἔστιν ὁρισμός, ὥστ᾽ εἰ καὶ ἀπεδείκνυτο τῇ διαι-
, > » » LÀ A , a ,
ρέσει, ἀλλ᾽ 6 γ᾽ ὁρισμὸς οὐ συλλογισμὸς γίνεται. 5
» , 7 L4 * 3 ^ A , > , , ,
6 ᾿Αλλ’ dpa ἔστι καὶ ἀποδεῖξαι τὸ τί ἐστι κατ᾽ οὐσίαν,
» (i 4 , H A ' HN 5. M , ^ ,
ἐξ ὑποθέσεως δέ, λαβόντα τὸ μὲν τί ἦν εἶναι TO ἐκ τῶν ἐν
^ P» v» LÀ * * > ^ , , , M om ^
TQ τέ ἐστιν ἴδιον, ταδὶ δὲ ἐν τῷ τί ἐστι μόνα, kai ἴδιον τὸ
^ ^ , , > > a ^ , Ww M /
πᾶν; τοῦτο ydp ἐστι τὸ εἶναι ἐκείνῳ. ἢ πάλιν εἴληφε τὸ τί
ἦν εἶναι καὶ ἐν τούτῳ; ἀνάγκη γὰρ διὰ τοῦ μέσου δεῖξαι. το
biB εἴτ᾽ AnET: εἴτ᾽ Bd λαβὼνη 25 εἶναι τὸ πᾶν n Án* 28 παρ-
€irai fi pe] dn δὲ om. n? 29 ἐν] rà ἐν n 30 παραλιπεῖν
ABdP 31-2 ef... ἐλλείπει codd. AnEP : secl. Sylburgiana 32 τοῦτο
δ᾽ ἀναγκαῖον codd. EP: secl. Waitz yap om. Ad ἤδη om. P*:
εἴδη B! δεῖ BnP : om. Ad 33 ὅμως] ye ὅμως n ἔστι nP : ἔνεστι
ABd 38 τοδὶ A Br? Pc, fecit d?: τόδε n 9243 3! om. n 4 οὐκ
ἔστιν dEP : οὐκέτι ABn 4 ὁρισμός codd. E°T : συλλογισμός coni. Bonitz
6 xai om, τ 8 tov! Pacius: ἐδέίων codd. AnEPT 9 ydp] ἄν n
15
20
25
39
35
ANAAYTIKQN YETEPQN B
ἔτι ὥσπερ οὐδ᾽ ἐν συλλογισμῷ λαμβάνεται τί ἐστι τὸ συλ-
λ , » ^ a un 7. € , , T t
ελογίσθαι (det yàp ὅλη ἢ μέρος ἡ πρότασις, ἐξ ὧν ὁ συλ-
, A »$* M ot > ^» ^ H ^
λογισμός), οὕτως οὐδὲ TO Ti ἦν εἶναι δεῖ ἐνεῖναι ἐν TH συλ-
~ * ^ ~
λογισμῷ, ἀλλὰ χωρὶς τοῦτο τῶν κειμένων εἶναι, καὶ πρὸς
> ^ LJ ~
τὸν ἀμφισβητοῦντα εἰ συλλελόγισται ἢ μή, τοῦτο ἀπαντᾶν
" € >
ὅτι “τοῦτο yap ἦν συλλογισμός᾽᾽, kai πρὸς τὸν ὅτι οὐ τὸ τί
- + , L4 [£i , ^ M » eo^ M
ἦν εἶναι συλλελόγισται, ὅτι "vat: τοῦτο yàp ἔκειτο ἡμῖν τὸ
, 2) - 3 / * v ^ , 4 M" d
τί ἦν elvan”. ὥστε ἀνάγκη kal ἄνευ τοῦ τί συλλογισμὸς ἢ τὸ
PT H
τί ἣν εἶναι συλλελογίσθαι τι.
hj , Li f * , > Α ^ , 4 *
Kav ἐξ ὑποθέσεως δὲ δεικνύῃ, olov εἰ τὸ κακῷ ἐστὶ τὸ
~ > Lj ~
διαιρετῷ εἶναι, τὸ δ᾽ ἐναντίῳ τὸ TH ἐναντίῳ «ἐναντίῳ» εἶναι, ὅσοις
ἔστι τι ἐναντίον" τὸ δ᾽ ἀγαθὸν τῷ κακῷ ἐναντίον καὶ τὸ ἀδιαίρε-
Tov τῷ OwuperQ: ἔστιν ἄρα τὸ ἀγαθῷ εἶναι τὸ ἀδιαιρέτῳ et-
M M » ~ s x L4 εν ,
var, καὶ yap ἐνταῦθα λαβὼν τὸ τί ἦν εἶναι δείκνυσι: Aap-
, , , ^ ^ M LN “ce , >? M
βάνει δ᾽ eis τὸ δεῖξαι τὸ τί ἦν εἶναι. "érepov μέντοι᾽᾽. ἔστω"
Xx ^ 3 ^ > , Ld > x [4 * ^! = M
καὶ yap ev ταῖς ἀποδείξεσιν, ὅτι ἐστὶ τόδε κατὰ τοῦδε: ἀλλὰ
^ 3 , * i ad « s ^ Tod M > , ‘ 2
μὴ αὐτό, μηδὲ οὗ 6 αὐτὸς λόγος, καὶ ἀντιστρέφει. πρὸς ἀμ-
φοτέρους δέ, τόν τε κατὰ διαίρεσιν δεικνύντα καὶ πρὸς τὸν
" Li A > A > 4 ^ POM e Ld
οὕτω συλλογισμόν, τὸ αὐτὸ ἀπόρημα- διὰ τί ἔσται ὁ ἄνθρω-
πος ζῷον πεζὸν δίπουν, ἀλλ᾽ οὐ ζῷον καὶ πεζόν «καὶ δίπουν»; ἐκ
x ^ , > rs > / > x a , A
yàp τῶν λαμβανομένων οὐδεμία ἀνάγκη ἐστὶν ἕν γίνεσθαι τὸ
, > > ὁ kJ L4 € 2 M » *
κατηγορούμενον, ἀλλ᾽ ὥσπερ av ἄνθρωπος ὁ αὐτὸς εἴη μουσικὸς
καὶ γραμματικός.
^ d bi © = , / M > , hl x. ,
Πῶς οὖν δὴ ὁ δριζόμενος δείξει τὴν οὐσίαν ἢ τὸ τί
, A ^ e > 4 > € fA ^
ἐστιν; οὔτε yàp ws ἀποδεικνὺς ἐξ ὁμολογουμένων εἶναι δῆ-
*7 > x
λον ποιήσει ὅτι ἀνάγκη ἐκείνων ὄντων ἕτερόν τι εἶναι (ἀπό-
Ν ~ »n € € , , ^ ~ > bÀ
δειξις yàp τοῦτο), οὔθ᾽ ὡς ὁ ἐπάγων διὰ τῶν Kal? ἕκαστα
ὃ , μ᾿ kd ^ e ^ δὲ L4 , ^ ;
ἥλων ὄντων, ὅτι πᾶν οὕτως TQ μηδὲν ἄλλως od yap τί
» , 2 , € LEA -^ , M , T M ,
ἐστι δείκνυσιν, ἀλλ᾽ ὅτι ἣ ἔστιν ἢ οὐκ ἔστιν. Tis οὖν ἄλλος Tpó-
art ἐν ΜΕΤ᾽ : om. ABd I2 ὧν-" ἐστιν d 13 οὕτως-- ἄρα E : +yap
Eve 15 εἰ] ἢ ἃ 17 vai] εἶναι n 1876 AdEPT: τοῦ Bn I9 συλ-
λελόγισται ἀ : συλλογεῖσθαι π. 20 δὲ οἵη. d. εἰ οἴη." τῷ “ἀπ τῷ ἃ
21 τὸϊ coni, Bonitz: rà codd. ΡΞ ἐναντίῳ adi. Bonitz, habet fort. E : om.
codd. PT 22 διαιρετὸν τῷ ἀδιαιρέτῳ d 23 τὸ om. Adn τὸ
ΒΑΕΤ: τῷ An 24 λαμβάνει B*T : λαμβάνειν ABdn 25 μέντοι Aldina:
μέν τι ABdnE: nn? 27 αὐτό dE: αὐτῷ ABA — óom.dn! — 288éom.d
29 συλλογιζόμενον n* 30 πεζὸν δίπουν EPC*T : δίπουν πεζὸν codd.
«at... δίπουν scripsi, habent ut vid. EP: καὶ πεζόν codd. E*: δίπουν καὶ
πεζὸν xai coni. Bonitz 31 ἕν γίνεσθαι B?E : ἐν γίνεο Jac 5: ἐγγίνεσθαι
A Bd 32 àv om. Bd: én εἴη] ἂν ἡ n: ἂν εἴη π΄ 34 δὴ om. ὦ
ó nECP*; om. ABd διοριζόμενος d 35 stun δεικνὺς n
37 60m. E 38 πάνθ᾽ n
6. g2711-7. 92°34
, ~ > x ~
mos Aourós; οὐ yap δὴ δείξει ye τῇ αἰσθήσει ἢ τῷ δα-
κτύλῳ.
» ~ LU a L4 > > , ^ M » , M
Ἔτι πῶς δείξει τὸ τί ἐστιν; ἀνάγκη yap τὸν εἰδότα τὸ
»» Ld bl L4 € ~ > L3 M Ld LÀ ^ ^
τί ἐστιν ἄνθρωπος 7) ἄλλο ὁτιοῦν, εἰδέναι καὶ ὅτι ἔστιν (τὸ yàp
M nn > M T Ld > , 3 a , A , € ,
μὴ ὃν οὐδεὶς οἶδεν ὅ τι ἐστίν, ἀλλὰ τί μὲν σημαίνει 6 λόγος
^ * LÀ LÀ LÀ Là , > 2 ^ ,
ἢ τὸ ὄνομα, Grav εἴπω τραγέλαφος, τί δ᾽ ἐστὶ rpayéAa-
> F4 5 , > LT M > ΄ , > " μὲ
gos ἀδύνατον εἰδέναι). ἀλλὰ μὴν εἰ δείξει τί ἐστι καὶ ὅτι
ν ~ ^ > ^ , LH kd M € M Ld
ἔστι, πῶς TQ αὐτῷ λόγῳ δείξει; 6 τε yap ὁρισμὸς ἕν τι
λ ^ M [4 3 "ὃ P ^ δὲ , , LÀ θ * ' Th
δηλοῖ kai ἡ ἀπόδειξις" τὸ δὲ τί ἐστιν ἄνθρωπος καὶ τὸ εἶναι
ἄνθρωπον ἄλλο.
3 ^ ,
Εἶτα xai Ov ἀποδείξεώς φαμεν ἀναγκαῖον εἶναι δεί-
L4 Ld 2 > ^ 3 ὅδ᾽ LJ M ? >
κνυσθαι ἅπαν 6 τι ἐστιν, ef μὴ οὐσία εἴη. τὸ δ᾽ εἶναι οὐκ
᾽ » , , , x , * » , Lá ww L4 Lg
οὐσία οὐδενί: οὐ yap γένος τὸ ὄν. ἀπόδειξις ap ἔσται ὅτι
ἔστιν. ὅπερ καὶ νῦν ποιοῦσιν αἱ ἐπιστῆμαι. τί μὲν γὰρ σημαί-
νει τὸ τρίγωνον, ἔλαβεν ὁ γεωμέτρης, ὅτι δ᾽ ἔστι, δείκνυσιν.
, T , e € , - J X M , H ^ Ld
Tí οὖν δείξει ὁ ὁριζόμενος ἢ τί ἐστι τὸ τρίγωνον; εἰδὼς ἄρα
τις ὁρισμῷ τί ἐστιν, εἰ ἔστιν οὐκ εἴσεται. ἀλλ᾽ ἀδύνατον.
Φανερὸν δὲ καὶ κατὰ τοὺς νῦν τρόπους τῶν ὅρων ὡς οὐ
e * ^
δεικνύουσιν οἱ ὁριζόμενοι ὅτι ἔστιν. εἰ yàp καὶ ἔστιν ἐκ τοῦ ué-
LÀ 3 M τ LJ A L4 M A , ^
σου τι ἴσον, ἀλλὰ διὰ τί ἔστι τὸ ὁρισθεν; καὶ διὰ τί τοῦτ
LÀ , LJ ^ bal M 3 , , ΕΣ ,
ἔστι κύκλος; εἴη yàp dv kai ópewdAkov φάναι εἶναι αὐτόν.
οὔτε γὰρ ὅτι δυνατὸν εἶναι τὸ λεγόμενον προσδηλοῦσιν οἱ
L4 » Ld > ^ T x 7T € , > » 7.4 L4
ὅροι, οὔτε ὅτι ἐκεῖνο οὗ φασὶν εἶναι ὁρισμοί, ἀλλ᾽ ἀεὶ ἔξεστι
λέγειν τὸ διὰ τί.
H » L4 Ld , , ^ , > hal , ,
Εἰ dpa 6 ὁριζόμενος δείκνυσιν ἢ τί ἐστιν ἢ τί σημαίνει
^ - M
τοὔνομα, εἰ μὴ ἔστι μηδαμῶς τοῦ τί ἐστιν, εἴη ἂν ὁ ὁρισμὸς
λόγος ὀνόματι τὸ αὐτὸ σημαίνων. ἀλλ᾽ ἄτοπον. πρῶτον
μὲν γὰρ καὶ μὴ οὐσιῶν dv εἴη καὶ τῶν μὴ ὄντων" σημαΐνειν
γὰρ ἔστι καὶ τὰ μὴ ὄντα. ἔτι πάντες οἱ λόγοι ὁρισμοὶ ἂν
we a μι LÀ , € ~ , " Ld hJ
elev: εἴη yàp ἂν ὄνομα θέσθαι ὁποιῳοῦν λόγῳ, ὥστε ὅρους àv
, , ^ [4 , ^ Ld ' ^ LJ L4 >
διαλεγοίμεθα πάντες καὶ ἡ ᾿Ιλιὰς δρισμὸς ἂν εἴη. ἔτι οὐδε-
,ὔ , , , ὃ , ^ μὲ ^ LÀ s λ ^
μία ἀπόδειξις ἀποδείξειεν ἂν ὅτι τοῦτο τοὔνομα τουτὶ δηλοῖ"
» ce ^ ^ ^
οὐδ᾽ of ὁρισμοὶ τοίνυν τοῦτο προσδηλοῦσιν.
ba ye om. d 4 762 BdnE*: om. AT 53 dnET: εἰ AB
ai... τραγέλαφος om. d 8 μὴν] μὴ Waitz 9 πῶς DANSE:
καὶ πῶς ABdn 13 ὅ τι ἐστι scripsi: ὅτι ἔστιν codd. εἰ] ἢ n! 14
οὐδενός πΖ᾽ γὰρ om. d 16 δεικνύουσιν n! 17 ἢ τί ἐστι scripsi,
fort. habent AnEP:7i ἐστιν 4 ABdn: τί ἐστιν f πὲ τὸ ABnE: om. ἀπῇ
21 τι] τὸ B 22 ἂν om. d 24 οὗ] οὐ A ἀλλ᾽ εἰ n! 26 à
om. πὶ $51) εἰ A 27 τοῦ] τὸ πὶ εἴη ἂν à nP*: ἦν ἂν ABd 32
ἡ οἵη. 2 33 ἀπόδειξις om. AB: ἐπιστήμη Ben ἀποδείξειεν] εἶεν d
Io
I5
20
25
39
ANAAYTIKQN YZTEPQN B
> b , , LÀ [4 M * M
35 "Ex μὲν τοίνυν τούτων οὔτε ὁρισμὸς καὶ συλλογισμὸς
φαίνεται ταὐτὸν ὄν, οὔτε ταὐτοῦ συλλογισμὸς καὶ ὁρισμός"
πρὸς δὲ τούτοις, ὅτι οὔτε ὁ ὁρισμὸς οὐδὲν οὔτε ἀποδείκνυσιν οὔτε
fA L4 € ? wor e ~ wo» » 7, LÀ ~
δείκνυσιν, οὔτε τὸ τί ἐστιν οὔθ᾽ ὁρισμῷ οὔτ᾽ ἀποδείξει ἔστι γνῶναι.
93* Πάλιν δὲ σκεπτέον τί τούτων λέγεται καλῶς καὶ τί οὐ
καλῶς, καὶ τί ἐστιν ὁ ὁρισμός, καὶ τοῦ τί ἐστιν ἄρά πως ἔστιν
> ‘ * € A] n , ~ > ^ > > , t L4
ἀπόδειξις καὶ ὁρισμὸς T] οὐδαμῶς. ἐπεὶ δ᾽ ἐστίν, ὡς ἔφαμεν,
x 4 > , b » M " ~ >
ταὐτὸν τὸ εἰδέναι τί ἐστι Kal τὸ εἰδέναι τὸ αἴτιον τοῦ εἰ ἔστι
, b , -" μὴ ‘ LJ M ^ bl ^ Uu roa
5 (λόγος δὲ τούτου, ὅτι ἔστι τι τὸ αἴτιον, καὶ τοῦτο 7] τὸ αὐτὸ 7
LÀ bal > μον ^ οἷα * n > , > ,
ἄλλο, κἂν ἦ ἄλλο, ἢ ἀποδεικτὸν ἢ ἀναπόδεικτον)----οΟΕἰ τοίνυν
, * Ld ^ > , > ^ > , ,
ἐστὶν ἄλλο καὶ ἐνδέχεται ἀποδεῖξαι, ἀνάγκη μέσον εἶναι
τὸ αἴτιον καὶ ἐν τῷ σχήματι τῷ πρώτῳ δείκνυσθαι" κα-
θόλου τε γὰρ καὶ κατηγορικὸν τὸ δεικνύμενον. εἷς μὲν δὴ
, ^ » L4 ^ ἐξ , 4 ὃ , LAA 4,3 ὃ ,
το Τρόπος ἂν εἴη ὃ viv ἐξητασμένος, τὸ δι᾿ ἄλλου του τί ἐστι δεί-
κνυσθαι. τῶν τε γὰρ τί ἐστιν ἀνάγκη τὸ μέσον εἶναι τί ἐστι,
καὶ τῶν ἰδίων ἴδιον. ὥστε τὸ μὲν δείξει, τὸ δ᾽ οὐ δείξει τῶν τί
ἦν εἶναι τῷ αὐτῷ πράγματι.
τ A T Lj , Ld , bal LÀ » , LÀ
Οὗτος μὲν οὖν 6 τρόπος ὅτι οὐκ dv εἴη ἀπόδειξις, εἴρηται
» n ? , μὴ λ * AX ^ ^ , , a δὲ
15 πρότερον: ἀλλ᾽ ἔστι λογικὸς συλλογισμὸς τοῦ τί ἐστιν. ὃν δὲ
, , , , > ca A , 3 ~ LÀ
τρόπον ἐνδέχεται, λέγωμεν, εἰπόντες πάλιν ἐξ ἀρχῆς. wo-
^ >
περ yàp τὸ διότι ζητοῦμεν ἔχοντες τὸ ὅτι, ἐνίοτε δὲ καὶ ἅμα
“- , > , w , ig M , 4: ,
δῆλα γίνεται, ἀλλ᾽ οὔτι πρότερόν ye τὸ διότι δυνατὸν γνωρί-
σαι τοῦ ὅτι, δῆλον ὅτι ὁμοίως καὶ τὸ τί ἦν εἶναι οὐκ ἄνευ τοῦ
3 ~
20 ὅτι ἔστιν: ἀδύνατον yap εἰδέναι τί ἐστιν, ἀγνοοῦντας εἰ ἔστιν.
A 3, , L4 ee. * M ^ LÀ € >
τὸ δ᾽ εἰ ἔστιν ὁτὲ μὲν κατὰ συμβεβηκὸς ἔχομεν, ὁτὲ ὃ
LÀ , ? -^ ^ , L4 Ld ,
ἔχοντές τι αὐτοῦ τοῦ πράγματος, olov βροντήν, ὅτι ψόφος
^ a LÀ Ld , , , M L4
τις νεφῶν, καὶ ἔκλευψιν, ὅτι στέρησίς tis φωτός, καὶ dvOpw-
πον, ὅτι ζῷόν τι, καὶ ψυχήν, ὅτι αὐτὸ αὑτὸ κινοῦν. ὅσα μὲν
7 M * L4 L4 L4 2 ^ ^
25 οὖν κατὰ συμβεβηκὸς οἴδαμεν ὅτι ἔστιν, ἀναγκαῖον μηδαμῶς
ἔχειν πρὸς τὸ τί ἐστιν: οὐδὲ γὰρ ὅτι ἔστιν ἴσμεν: τὸ δὲ ζητεῖν
)0 M LÀ LÀ L4 ^ ^ > » wc *,
τί ἐστι μὴ ἔχοντας ὅτι ἔστι, μηδὲν ζητεῖν ἐστιν. καθ᾽ ὅσων ὃ
ἔχομέν τι, ῥᾷον. ὥστε ὡς ἔχομεν ὅτι ἔστιν, οὕτως ἔχομεν καὶ
πρὸς τὸ τί ἐστιν. ὧν οὖν ἔχομέν τι τοῦ τί ἐστιν, ἔστω πρῶτον μὲν
b37 οὔτε! nP°: οὐδὲ ABd 9334 εἰ AB*dE*P : τί Bn Ane 5 τὸ
om. nE τὸ OM. π 6 καὶ εἰ fecit 2 ἢ] εἰ ΒΑΡ: εἴη E 8 τῷ"
om. d 9 89+ τοίνυν n τον 4 rovscripsi: τὸ codd. 16 λέγω-
μεν ABP: λέγομεν A*dnE εἰπόντες codd. An®: ἐπιόντες PC 17 yàp
om.B'! ὅτι] τί πὶ 20 ὅτιοτη. 4 ἀδύνατον... €orwom, d? 23 Tis?
om. d 24 ψυχήν P, Aldina: ψυχή Bn: om. Ad ὅτι om. Adn
23 ἄνθρωπος d 27 μηδὲ ζητεῖν A? κάθοσοον B! 28 ῥᾷδιον n
29 ὧν- μὲν n
b b
7. 9235-9. 93°23
ὧδε" ἔκλειψις ἐφ᾽ οὗ τὸ A, σελήνη ἐφ᾽ οὗ Γ᾽, ἀντίφραξις 30
^ γι» T A x 4 , 2 , ^ L4 4
γῆς ἐφ᾽ οὗ B. τὸ μὲν οὖν πότερον ἐκλείπει ἢ οὔ, τὸ B. ζη-
^ μ᾿ T» W - L4 ^ , , Α ,ὔ ^ M ,
τεῖν ἔστιν, dp’ ἔστιν 7 οὔ. τοῦτο δ᾽ οὐδὲν διαφέρει ζητεῖν ἢ εἰ
L7 ΄ , ^ EY 4 ^ , af E
ἔστι λόγος αὐτοῦ: Kai ἐὰν ἦ τοῦτο, κἀκεῖνό φαμεν εἶναι. ἢ
ποτέρας τῆς ἀντιφάσεώς ἐστιν 6 λόγος, πότερον τοῦ ἔχειν δύο
ὀρθὰς 7j τοῦ μὴ ἔχειν. ὅταν δ᾽ εὕρωμεν, ἅμα τὸ ὅτι καὶ τὸ 35
, LJ bal , » , A 3 > ^ , ‘ a * , >
διότι ἴσμεν, av δι’ ἀμέσων T: εἰ δὲ μή, TO ὅτι, TO διότι ὃ
οὔ. σελήνη I, ἔκλειψις A, τὸ πανσελήνου σκιὰν μὴ δύ-
^ : CoA S4 ^ » T
νασθαι ποιεῖν μηδενὸς ἡμῶν μεταξὺ ὄντος φανεροῦ, ἐφ᾽ οὗ
B. «i τοίνυν τῷ I ὑπάρχει τὸ B τὸ μὴ δύνασθαι ποιεῖν
σκιὰν μηδενὸς μεταξὺ ἡμῶν ὄντος, τούτῳ δὲ τὸ A τὸ ἐκλε- 93>
»* σ M > , ~ , > L4 M "
λοιπέναι, ὅτι μὲν ἐκλείπει δῆλον, διότι δ᾽ οὔπω, καὶ ὅτι
^ v μὴ LÀ , ΕΣ , M > LÀ , > »
μὲν ἔστιν ἔκλειψις ἴσμεν, τί δ᾽ ἐστὶν οὐκ ἴσμεν. δήλου δ᾽ ὄν-
τος ὅτι τὸ A τῷ l' ὑπάρχει, ἀλλὰ διὰ τί ὑπάρχει, τὸ ζη-
^ ^ , > , > , -^ M ~ LA
τεῖν τὸ B τί ἐστι, πότερον ἀντίφραξις ἢ στροφὴ τῆς σελήνης 5
ἢ ἀπόσβεσις. τοῦτο δ᾽ ἐστὶν ὁ λόγος τοῦ ἑτέρου ἄκρου, οἷον ἐν
P4 ~ μ᾿ ij tc L4 > , € Li ~ ,
τούτοις τοῦ A: ἔστι yàp ἡ ἔκλειψις ἀντίφραξις ὑπὸ γῆς. τί
> , ^ Ej , > , ^ ,ὔ ~ b.
ἐστι βροντή; πυρὸς ἀπόσβεσις ἐν νέφει. διὰ τί βροντᾶ; διὰ
τὸ ἀποσβέννυσθαι τὸ πῦρ ἐν τῷ νέφει. νέφος Γ᾽, βροντὴ A,
> , a x ~ * - , L4 , ‘
ἀπόσβεσις πυρὸς τὸ B. τῷ δὴ I τῷ νέφει ὑπάρχει τὸ Bi
> » ‘ , > ~ ^ ~ Li M M ,
(ἀποσβέννυται yàp ἐν αὐτῷ τὸ πῦρ), τούτῳ δὲ τὸ A, ψό-
pos καὶ ἔστι γε λόγος τὸ B τοῦ A τοῦ πρώτου ἄκρου. ἂν
δὲ πάλιν τούτου ἄλλο μέσον 4, ἐκ τῶν παραλοίπων ἔσται
λόγων.
Ὥ * , , * , , ‘ , ?
s μὲν τοίνυν λαμβάνεται τὸ Ti ἐστι καὶ γίνεται γνώ-
ριμον, εἴρηται, ὥστε συλλογισμὸς μὲν τοῦ τί ἐστιν οὐ γίνεται
οὐδ᾽ ἀπόδειξις, δῆλον μέντοι διὰ συλλογισμοῦ καὶ δι’ ἀπο-
δείξεως: ὥστ᾽ οὔτ᾽ ἄνευ ἀποδείξεως ἔστι γνῶναι τὸ τί ἐστιν,
ew LÀ LJ LÀ w » w E ? ΕΣ -^ e 4
οὗ ἔστιν αἴτιον ἄλλο, οὔτ᾽ ἔστιν ἀπόδειξις αὐτοῦ, ὥσπερ Kal
ἐν τοῖς διαπορήμασιν εἴπομεν.
LÀ , ^ M σ , LJ ^ > > LÀ L4
9 “Hor δὲ τῶν μὲν ἕτερόν τι αἴτιον, τῶν δ᾽ οὐκ ἔστιν. ὥστε
δῆλον ὅτι καὶ τῶν τί ἐστι τὰ μὲν ἄμεσα καὶ ἀρχαί εἰσιν,
ἃ καὶ εἶναι καὶ τί ἐστιν ὑποθέσθαι δεῖ ἢ ἄλλον τρόπον
15
20
330r60m.5n Γ[Γ]τὸγ Β 31 οὖν αἀ πότερον B?nEP : πρότερον
ABd 32 εἰ om. A 34-5 TÓTepov . . . ἔχειν om. mi 35 τοῦ
nE: τὸ 484 36 διὰ μέσων ABdAnEPS 3] πασσελήνου Α
39 εἰ] à πὶ by τοῦτο n! 3 ἔκλειψίς ἐστιν A Bd 7 τί ἐστι om. d
8 νέφη A! 1ο δὲ n 11 τοῦτο ABd 12 ro a ró Bn 13 ἢ]
εἴη ABd 18 ὥστ᾽... ἀποδείξεως om. n! 19 οὗ ἔστιν om. ril
21 τὸν nt τῶν om. n! 23 τρόπον B'dnPT : τόπον AB
25
30
94°
IO
15
ANAAYTIKQN YETEPQN B
4 ^ L4 ia 3 * ^ M & ,
φανερὰ ποιῆσαι (ὅπερ ὃ ἀριθμητικὸς ποιεῖ: Kai yap τί
a 4 , € J, 4 Ld L4 ~ ᾽ > Hi
ἐστι τὴν μονάδα ὑποτίθεται, kai ὅτι ἔστιν): τῶν δ᾽ ἐχόν-
των μέσον, καὶ ὧν ἔστι τι ἕτερον αἴτιον τῆς οὐσίας, ἔστι δι᾽
ἀποδείξεως, ὥσπερ εἴπομεν, δηλῶσαι, μὴ τὸ τί ἐστιν ἀπο-
δεικνύντας.
“Ορισμὸς δ᾽ ἐπειδὴ λέγεται εἶναι λόγος τοῦ τί ἐστι, φα-
νερὸν ὅτι ὁ μέν τις ἔσται λόγος τοῦ τί σημαίνει τὸ ὄνομα ἢ λό-
γος ἕτερος ὀνοματώδης, οἷον τί σημαίνει [τί ἐστι] τρί-
γωνον. ὅπερ ἔχοντες ὅτι ἔστι, ζητοῦμεν διὰ τί ἔστιν: χαλε-
* , L4 > * ^ a A LÀ Ld L4 € > > 7
mov δ᾽ οὕτως ἐστὶ λαβεῖν ἃ μὴ ἴσμεν ὅτι ἔστιν. ἡ δ᾽ αἰτία
εἴρηται πρότερον τῆς χαλεπότητος, ὅτι οὐδ᾽ εἰ ἔστιν ἢ μὴ
LÀ 5 3 ^ ^ , , » > M ~
ἴσμεν, ἀλλ᾽ ἣ κατὰ συμβεβηκός. (λόγος δ᾽ εἷς ἐστὶ διχῶς,
© A , a t 3 , L4 ^ ^ ^ > € *
ὁ μὲν συνδέσμῳ, ὥσπερ ἡ "IMs, ὁ δὲ τῷ ἕν καθ᾽ ἑνὸς δη-
λοῦν μὴ κατὰ συμβεβηκός.)
τ 4 M - » * " € > , L4 5 *, A
Εἷς μὲν δὴ ὅρος ἐοτὶν ὅρου ὁ εἰρημένος, ἄλλος δ᾽ ἐστὶν
Ld a e ~ ^A tow o € M , ,
ὅρος λόγος ὃ δηλῶν διὰ τί ἔστιν. ὥστε ὁ μὲν πρότερος σημαί-
Ls ; > L4 t > o0 ^ - Ld
ve. μέν, δείκνυσι δ᾽ οὔ, 6 δ᾽ ὕστερος φανερὸν ὅτι ἔσται οἷον
ἀποδειξις τοῦ τί ἐστι, τῇ θέσει διαφέρων τῆς ἀποδείξεως.
, ki » ^ x s -^ b] , » , > ~
διαφέρει yap εἰπεῖν διὰ τί βροντᾷ καὶ τί ἐστι βροντή" ἐρεῖ
^ L4 * ee , > ,ὔ * ~ 2 ^ ,
yàp οὕτω μὲν “'διότι ἀποσβέννυται TO πῦρ ἐν τοῖς védeov"-
,ὔ , , M if L4 2 4 * 2 ,
τί δ᾽ ἐστὶ βροντή; ψόφος ἀποσβεννυμένου πυρὸς ἐν νέφεσιν.
σ « 3 a , Mw ΄ * M εςι 3 3 ,
ὥστε 6 αὐτὸς λόγος ἄλλον τρόπον λέγεται, Kal «0i μὲν ἀπό-
’ egos ^ e -* w > * Ld ^ ,
δειξις συνεχής, wot δὲ ὁρισμός. (ἔτι ἐστὶν ὅρος βροντῆς ψό-
dos ἐν νέφεσι: τοῦτο δ᾽ ἐστὶ τῆς τοῦ τί ἐστιν ἀποδείξεως συμ-
πέρασμα.) 6 δὲ τῶν ἀμέσων ὁριομὸς θέσις ἐστὶ τοῦ τί ἐστιν
ἀναπόδεικτος.
Ν Ld ¢ M] Lu A , ~ , bg > L4
Ἔστιν dpa ὁρισμὸς εἷς μὲν λόγος τοῦ τί ἐστιν ἀναπό-
* A ^ , > a ,
9eucros, εἷς δὲ συλλογισμὸς τοῦ τί ἐστι, πτώσει διαφέρων
^ 3 , , A ^ ^ H0» 3 Hu
τῆς ἀποδείξεως, τρίτος δὲ τῆς τοῦ τί ἐστιν ἀποδείξεως συμ-
^ M ~ ^
πέρασμα. φανερὸν οὖν ἐκ τῶν εἰρημένων Kal πῶς ἔστι τοῦ τί
, ~
ἐστιν ἀπόδειξις kai πῶς οὐκ ἔστι, καὶ τίνων ἔστι καὶ τίνων οὐκ
» LÀ ~ ΤᾺ ^
ἔστιν, ἔτι δ᾽ ὁρισμὸς ποσαχῶς Te λέγεται καὶ πῶς τὸ τί
, x ~ 2 L4 M [a
ἐστι δείκνυσι kai πῶς ov, kai τίνων ἔστι kai τίνων ov, ἔτι δὲ
b26 μέσων 4 οὐσίας -ἰ- καὶ τοῦ εἶναι ti 31 τί] τὸ τί ABdn® τί ἐστι
seclusi, om. ut vid. P: habet Bu: τί ἐστιν ἣ Ad 32 χαλεπὸς A
33 οὗτος Ad 355 om. B 36 rà πάῃ: τὸ ABd δηλῶν n?
38 προειρημένος n 9432 διαφέρον πὶ 3 ἐρεῖ D: --ἰ uév ABdn
4 οὕτω pevom. d: οὕτω τὸ μὲν n! 7 ἔτι] ἔτι εἰ Β : ὅτι ἀϊπὶ 10 ἀποδει-
κτικός A II dpa om. n! : +6 A ἀναπόδεικτον A 13 τί om. B
16 ἔστι δ᾽ ἃ 17 καὶ τίνων ἔστι Bn ÁnP Co: om. ἃ καὶ τίνων οὔ om. d
IO
II
b b
9. 93 24-11. 94°9
A 3 , ~ w o. ~ > , - > ~
πρὸς ἀπόδειξιν πῶς ἔχει, kai πῶς ἐνδέχεται τοῦ αὐτοῦ εἶναι
καὶ πῶς οὐκ ἐνδέχεται.
E. A δὲ > ; f L4 Y^ M AME 3
met δὲ ἐπίστασθαι οἰόμεθα Grav εἰδῶμεν τὴν αἰτίαν,
» 5 4 , 4, ^ * it T ig a M ,
αἰτίαι δὲ τέτταρες, pia μὲν τὸ τί ἦν εἶναι, μία δὲ TO τίνων
ὄντων ἀνάγκη τοῦτ᾽ εἶναι, ἑτέρα δὲ ἡ τί πρῶτον ἐκίνησε, τε-
τάρτη δὲ τὸ τίνος ἕνεκα, πᾶσαι αὗται διὰ τοῦ μέσου δεί-
κνυνται. τό τε γὰρ οὗ ὄντος τοδὶ ἀνάγκη εἶναι μιᾶς μὲν
, , > LÀ ^ M , /
προτάσεως ληφθείσης οὐκ ἔστι, δυοῖν δὲ τοὐλάχιστον"
^ *,
τοῦτο δ᾽ ἐστίν, ὅταν ἕν μέσον ἔχωσιν. τούτου οὖν ἑνὸς λη-
φθέντος τὸ συμπέρασμα ἀνάγκη εἶναι. δῆλον δὲ καὶ ὧδε.
ὃ ^ 9 07; t > e A Ἢ ^ " > 05: LÀ δὴ , £7,
ιὰ τί ὀρθὴ ἡ ἐν ἡμικυκλίῳ; Tivos ὄντος ὀρθή; ἔστω δὴ ὀρθὴ
ἐφ’ ἧς A, ἡμίσεια δυοῖν ὀρθαῖν ἐφ᾽ ἧς B, ἡ ἐν ἡμικυ-
κλίῳ ἐφ᾽ ἧς D. τοῦ δὴ τὸ A τὴν ὀρθὴν ὑπάρχειν τῷ D τῇ
H ^ € , LÀ 4 L4 ^ ^ ~ LÀ t
ἐν τῷ ἡμικυκλίῳ αἴτιον τὸ B. αὕτη μὲν yàp τῇ A ion, ἡ
δὲ τὸ Γ τῇ Β' δύο γὰρ ὀρθῶν ἡμίσεια. τοῦ Β οὖν ὄντος
t , δύ, >? θῶ M ^ I L4 , ^ δ᾽ εν M >
ἡμίσεος δύο ὀρθῶν τὸ A τῷ I ὑπάρχει (τοῦτο δ᾽ ἦν τὸ ἐν
€ , , x ~ * > , > ^ δ᾽ * 4
ἡμικυκλίῳ ὀρθὴν εἶναι). τοῦτο δὲ ταὐτόν ἐστι τῷ τί ἦν εἶναι,
^ ~ , * , > M b * ^ , E νὴ
τῷ τοῦτο σημαίνειν τὸν λόγον. ἀλλὰ μὴν kai τὸ Tí ἦν εἶναι
αἴτιον δέδεικται τὸ μέσον «ὄν».
Τὸ δὲ διὰ τί ὁ Μηδικὸς πόλεμος
, , » L4 , * ^ ^ * L4 o
ἐγένετο ᾿Αθηναίοις; τίς αἰτία τοῦ πολεμεῖσθαι ᾿Αθηναίους; ὅτι
Σ , , , , > /, ^ M LIC 1
εἰς Σάρδεις pet 'Eperpiéov ἐνέβαλον: τοῦτο yap ἐκίνησε
πρῶτον. πόλεμος ἐφ᾽ οὗ A, προτέρους εἰσβαλεῖν B, ᾿4θη-
vaio. τὸ Γ΄. ὑπάρχει δὴ τὸ B τῷ I, τὸ προτέροις ἐμβαλεῖν
^ 3 ,ὔ A * ^ ^ M ^ ,
τοῖς ᾿Αθηναίοις, τὸ δὲ A τῷ B- πολεμοῦσι yap τοῖς πρό-
2 , € a L4 ^ x M A1
τερον ἀδικήσασιν. ὑπάρχει dpa τῷ μὲν B τὸ A, τὸ πολε-
μεῖσθαι τοῖς προτέροις ἄρξασι:- τοῦτο δὲ τὸ B τοῖς
3 θ 7 / ^ > f LÀ ‘ > 00
᾿Αθηναίοις: πρότεροι yap ἦρξαν. μέσον apa καὶ ἐνταῦθα
τὸ αἴτιον, τὸ πρῶτον κινῆσαν.
LÀ > LÀ M LÀ Uu
Οσων δ᾽ αἴτιον τὸ ἕνεκα tivos—
^ , ^ - € ^ ^ , > , LÀ
οἷον διὰ τί περιπατεῖ; ὅπως ὑγιαίνῃ: διὰ τί οἰκία ἔστιν;
21 ἦν om. πὶ 22 4 τι ÁABn 24 οὗ om. 5 25 δυσὶ B
27 δὲ om. d καὶ om. 5 28 τίνος) ἢ rivos D 29 δυοῖν ABE:
δυσὶν d : δυεῖν n 33 ἡμίσεως ABdn! τοῦ] τῷ A 34 τοῦτο ΒΑΡ:
τούτῳ AnE τῷ CP, Aldina: τὸ A BdnE 35 τῷ τοῦτο) τούτῳ τὸ
ni τὸ DP: τοῦ ABdn?: rovroun 36 óv om. ABdn! ὁ om. ἢ
37 τί) ἡ ἃ ᾿Αθηναίους) ᾿Αθηναίοις B by ἐκινήθη Adn? 2 εἰσβάλ-
Aew dn! 3 προτέρους n: πρότερον Bekker ἐμβάλλειν dn 4 τοὺς
᾿Αθηναίους n 5 ἀδικήμασιν A 6 πρότερον D τοῦτο] τοῦ Ald
βιτῷγ D?f 4-76 y fecit n 7 πρότερον ABdm 8 αἴτιον! + ἐν ols
τὸ αἴτιον B:+ ἐν οἷς αἴτιον n ἕνεκα τίνος SCTipSi: ἕνεκά τινος codd.
20
25
3o
35
36
36
94>
8
8
ANAAYTIKON YZTEPON B
Ld , A ;, A * μ᾿ ^ [4 , x 3
ro ὅπως σῴζηται τὰ σκεύη--τὸ μὲν ἕνεκα τοῦ ὑγιαίνειν, τὸ ὃ
-- m ^ a , * > * , ^ ^
ἕνεκα τοῦ σῴζεσθαι. διὰ τί δὲ ἀπὸ δείπνου δεῖ περιπατεῖν,
Α L4 , ^ ort , , > ^ ,
καὶ ἕνεκα τίνος δεῖ, οὐδὲν διαφέρει. περίπατος ἀπὸ δείπνου
I A A , Ad 4 , Leal T B * t a » 1»
, TO μὴ ἐπιπολάζειν τὰ σιτία ἐφ᾽ οὗ B, τὸ ὑγιαίνειν ἐφ
οὗ A. ἔστω δὴ τῷ ἀπὸ δείπνου περιπατεῖν ὑπάρχον τὸ ποι-
^ , ^ ^
15 ety μὴ ἐπιπολάζειν τὰ σιτία πρὸς TH στόματι τῆς κοιλίας,
b] ^ ^ ^ ^ ^
καὶ τοῦτο ὑγιεινόν. δοκεῖ yàp ὑπάρχειν τῷ περιπατεῖν τῷ D
A ‘ A > , ‘ , 4 * ‘ M t
TO B τὸ μὴ ἐπιπολάζειν τὰ σιτία, τούτῳ δὲ τὸ A τὸ ὑγι-
, , T LÀ ^ ^ ^ [4 , ‘ ^ &
ewov. τί οὖν αἴτιον τῷ Γ τοῦ τὸ A ὑπάρχειν τὸ οὗ ἕνεκα;
4 * A , , ~ > , M " H , ,
τὸ B τὸ μὴ ἐπιπολάζειν. τοῦτο δ᾽ ἐστὶν ὥσπερ ἐκείνου Aó-
20 yos: τὸ yap A οὕτως ἀποδοθήσεται. διὰ τί δὲ τὸ B τῷ Γ
LÀ " - 3 L4 Ai € te M ov LÀ ^ 4
ἔστιν; ὅτι τοῦτ᾽ ἔστι τὸ ὑγιαίνειν, τὸ οὕτως ἔχειν. δεῖ δὲ
μεταλαμβάνειν τοὺς λόγους, καὶ οὕτως μᾶλλον ἕκαστα
^ * ^ -
φανεῖται. αἱ δὲ γενέσεις ἀνάπαλιν ἐνταῦθα καὶ ἐπὶ τῶν
κατὰ κίνησιν αἰτίων: ἐκεῖ μὲν γὰρ τὸ μέσον δεῖ γενέσθαι
25 πρῶτον, ἐνταῦθα δὲ τὸ I, τὸ ἔσχατον, τελευταῖον δὲ τὸ
οὗ ἕνεκα.
> δέ: δὲ 4 J M * e , A »
Ἐνδέχεται δὲ τὸ αὐτὸ καὶ ἕνεκά τινος εἶναι καὶ ἐξ
3 ,ὔ ἴο ὃ X ^ À ^ A a eae ‘ 4 , > ,
ἀνάγκης, οἷον διὰ τοῦ λαμπτῆρος τὸ φῶς" καὶ yàp ἐξ áváy-
κηῆς διέρχεται τὸ μικρομερέστερον διὰ τῶν μειζόνων πόρων, .
^ , ~
30 εἴπερ φῶς γίνεται TH διιέναι, καὶ ἕνεκά τινος, ὅπως μὴ
, T) 5 , $ > , * , > 7
πταίωμεν. ἄρ᾽ οὖν εἰ εἶναι ἐνδέχεται, kai γίνεσθαι ἐνδέχε-
^ ^ ,
ται" ὥσπερ εἰ βροντᾷ «ὅτι» ἀποσβεννυμένου re τοῦ πυρὸς ἀνάγκη
, M ^ , > « € , rg 2
σίζειν καὶ ψοφεῖν καί, εἰ ws οἱ Πυθαγόρειοί φασιν, ἀπει-
λῆς ἕνεκα τοῖς ἐν τῷ ταρτάρῳ, ὅπως φοβῶνται; πλεῖστα
* ay w * , > ^ X 5 ,
45 δὲ τοιαῦτ᾽ ἔστι, kai μάλιστα ἐν rois κατὰ φύσιν συνισταμέ-
* = € a €
νοις Kai συνεστῶσιν: ἡ μὲν yap ἕνεκά Tov ποιεῖ φύσις, ἡ
» . > , v 3 * , , € M M Ἂν 4
δ᾽ ἐξ ἀνάγκης. ἡ δ᾽ ἀνάγκη διττή: ἡ μὲν yàp κατὰ φύ-
a * A € a € ' , € A Ἂν, ς L4 e ,
95? σιν καὶ τὴν ὁρμήν, ἡ δὲ Bia ἡ παρὰ τὴν ὁρμήν, ὥσπερ λί-
> > , ‘ L4 ^ , , > > ? ‘A
Bos ἐξ ἀνάγκης καὶ ἄνω καὶ κάτω φέρεται, ἀλλ᾽ οὐ διὰ
^ , A , , > b ^ > 4 , M * ᾽ ,
τὴν αὐτὴν ἀνάγκην. ev δὲ τοῖς ἀπὸ διανοίας rà μὲν οὐδέποτε
, M ~ *, , [4 4 , f hal 2 , 505 >
ἀπὸ τοῦ αὐτομάτου ὑπάρχει, olov οἰκία ἢ ἀνδριάς, οὐδ᾽ ἐξ
bio τὸ] ἢ d μὲν om. Ald 11 διὰ τί δὲ] διὰ τί d: τὸ δὲ διὰ τί π
I2 δεῖ -Ἐ περιπατεῖν n 14 τῷ Adn?E: τὸ Bn ποιεῖν om. d 15 τὸ
στόμα n 16 ὑπάρχει An? : ὑπάρχει δὴ Bn τῷϊ B*, fecit n: ro ABd
17 τοῦτο B! Toa Á 18 τοῦ om. n? 20 τί om, πὶ δὲ om. D
τῷ] τὸ πὶ 21 ὅτι] ἥλιος d 25 τὸξ om. πὶ 29 μικρομερέστατον d
30 τὸ πὶ διιέναι Bn* EP : διεῖναι Adn 32 εἰ om. n! ὅτι adieci,
habent ut vid. ET τε om. 23 34 rois BnP : τῆς A: τινος τοῖς d
35 ἐν] ἅμα ἐν Ad: ἃ ἅμα ἐν n 36 συνιστῶσιν 4 ποιεῖν AL Bd 9541 7
H
ον ὁρμήν om. d ἡ om. πὶ ὥσπερ-ἰ- ὁ ἀπ 4 oix d
1I. 94*?10-12. 95°38
2 , 3 > L4 ἣν * X " > M , Φ € ,
ἀνάγκης, ἀλλ᾽ ἕνεκά Tov, rà δὲ xai ἀπὸ τύχης, olov ὑγί- 5
X , , x > Ld > , b] T
ea καὶ σωτηρία. μάλιστα δὲ ἐν ὅσοις ἐνδέχεται καὶ ὧδε
M LÀ L4 ^ > * 4, « , T7 L4 x ,
καὶ ἄλλως, Grav, μὴ ἀπὸ τύχης, ἡ γένεσις ἦ ὥστε τὸ τέλος
Ἃς , LÀ , , ΠῚ a , a , > a »
ἀγαθόν, ἕνεκά Tov γίνεται, καὶ ἢ φύσει ἢ τέχνῃ. ἀπὸ τύ-
^ , > M Ld $ ,
χῆς δ᾽ οὐδὲν ἕνεκά rov γίνεται.
4 , > 4 " , , - , ^ ^
12 Τὸ δ᾽ αὐτὸ αἴτιόν ἐστι τοῖς γινομένοις καὶ τοῖς yeyevn- to
Li ^ > , ^
μένοις Kal τοῖς ἐσομένοις ὅπερ Kal τοῖς οὖσι (τὸ yap μέ-
" jJ - ^ ^
cov αἴτιον), πλὴν τοῖς μὲν οὖσιν ὄν, τοῖς δὲ γινομένοις ywó-
^ , L4 M >
μενον, τοῖς δὲ γεγενημένοις γεγενημένον kai ἐσομένοις ἐσό-
τ ^ , , >
μενον. olov διὰ Tí γέγονεν ἔκλεωμις; διότι ἐν μέσῳ γέγονεν
«- ~ , δὲ Jf , » ^ , wv » ,
ἡ γῆ" γίνεται δὲ διότι γίνεται, ἔσται δὲ διότι ἔσται ev μέσῳ, 15
καὶ ἔστι διότι ἔστιν. τί ἐστι κρύσταλλος; εἰλήφθω δὴ ὅτι ὕδωρ
, e 41} T κέ hM ,»15 e ad LJ *
πεπηγός. ὕδωρ ef οὗ I, πεπηγὸς ἐφ᾽ οὗ A, αἴτιον τὸ
μέσον ἐφ᾽ οὗ B, ἔκλεωμις θερμοῦ παντελής. ὑπάρχει δὴ
~ x L4 A * , 4. > 3 Φ ,
TQ Γ τὸ B, rovro δὲ τὸ πεπηγέναι τὸ ἐφ᾽ ob A. γίνεται
, » -
δὲ κρύσταλλος γινομένου τοῦ B, γεγένηται δὲ γεγενημένου, 20
ἔσται δ᾽ ἐσομένου.
4 ' ^ e" ” 4 * LÀ ,
To μὲν οὖν οὕτως αἴτιον xai οὗ αἴτιον ἅμα yiverat,
ὅταν γίνηται, καὶ ἔστιν, Grav jy καὶ ἐπὶ τοῦ. γεγονέναι καὶ
ἔσεσθαι ὡσαύτως. ἐπὶ δὲ τῶν μὴ ἅμα ἄρ᾽ ἔστιν ἐν τῷ συ-
-^ , LÀ ^ L4 ^ LÀ LÀ LÀ
νεχεῖ χρόνῳ, ὥσπερ δοκεῖ ἡμῖν, ἄλλα ἄλλων αἴτια εἶναι, 25
^ 3 ^
τοῦ τόδε γενέσθαι ἕτερον γενόμενον, καὶ τοῦ ἔσεσθαι ἕτερον ἐσό-
^ ^ L4 , LÀ v > , LÀ M
μενον, xai τοῦ γίνεσθαι δέ, εἴ τι ἔμπροσθεν ἐγένετο; ἔστι δὴ
ἀπὸ τοῦ ὕστερον γεγονότος 6 συλλογισμός (ἀρχὴ δὲ καὶ
τούτων τὰ γεγονότα): διὸ καὶ ἐπὶ τῶν γινομένων ὡσαύτως.
ἀπὸ δὲ τοῦ προτέρου οὐκ ἔστιν, οἷον ἐπεὶ τόδε γέγονεν, ὅτι 30
τόδ᾽ ὕστερον yéyovev: καὶ ἐπὶ τοῦ ἔσεσθαι ὡσαύτως. οὔτε
γὰρ ἀορίστου οὔθ᾽ ὁρισθέντος ἔσται τοῦ χρόνου ὥστ᾽ ἐπεὶ τοῦτ᾽
3 b 3 ^ A 7» » M *, ^ , ^
ἀληθὲς εἰπεῖν γεγονέναι, τόδ᾽ ἀληθὲς εἰπεῖν γεγονέναι τὸ
ὕστερον. ἐν γὰρ τῷ μεταξὺ ψεῦδος ἔσται τὸ εἰπεῖν τοῦτο,
LÀ , , e > ΕΣ A , ‘ LEAL] ~ ’
ἤδη θατέρου γεγονότος. ὁ δ᾽ αὐτὸς λόγος καὶ ἐπὶ τοῦ ἐσο- 35
> * LAU L4 ^
μένου, οὐδ᾽ ἐπεὶ τόδε γέγονε, τόδ᾽ ἔσται. τὸ yap μέσον
^ ~ - 3
ὁμόγονον δεῖ εἶναι, τῶν γενομένων γενόμενον, τῶν ἐσομένων
^ , ^ » μὰ ~
ἐσόμενον, τῶν γινομένων γινόμενον, τῶν ὄντων ὄν" τοῦ δὲ yé-
a7 wore] ὧν δὲ εἰ ὥστ᾽ εἰ Ev? 14 γέγονεν ἐν μέσῳ n τό καί-Ἐ τι πὶ
διότι om. d: δὲ ὅτι AB 23 τοῦ] τούτων fort. Bi 26 τοῦ τόδε
AB*n AnEP : τοῦτο δὲ B: τοῦ d 27 δέ... ἐγένετο) τὸ τοῦτο γεγονέναι
An* 29 rà om. Ad διὸ BE: δύο Ad: διότι n 30 πρότερον d
30, 32 ἐπεὶ] ἐπὶ πὶ 33 τόδ᾽... γεγονέναι om. A 34 τούτου d
35 ἤδη] εἴδη Bn! : δὴ d
ANAAYTIKQN YETEPQN B
M ~ Ld % , , « Li L4 L4
yove καὶ τοῦ ἔσται οὐκ ἐνδέχεται εἶναι ὁμόγονον. ἔτι οὔτε
4o ἀόριστον ἐνδέχεται εἶναι τὸν χρόνον τὸν μεταξὺ οὔθ᾽ wpt-
95" σμένον: ψεῦδος γὰρ ἔσται τὸ εἰπεῖν ἐν τῷ μεταξύ. ἐπισκε-
πτέον δὲ τί τὸ συνέχον dore μετὰ τὸ γεγονέναι τὸ γίνεσθαι
ὑπάρχειν ἐν τοῖς πράγμασιν. ἢ δῆλον ὅτι οὐκ ἔστιν ἐχόμε-
νον γεγονότος γινόμενον; οὐδὲ γὰρ γενόμενον γενομένου" πέ-
s para γὰρ καὶ ἄτομα: ὥσπερ οὖν οὐδὲ στιγμαί εἰσιν ἀλλή-
ν» φ9φφ᾽." , » A > , ANS
λων ἐχόμεναι, οὐδὲ γενόμενα: ἄμφω yap ἀδιαίρετα. οὐδὲ
, X 4
δὴ γινόμενον γεγενημένου διὰ τὸ αὐτό" τὸ μὲν yàp γινόμε-
> ^
vov διαιρετόν, TO δὲ γεγονὸς ἀδιαίρετον. ὥσπερ οὖν γραμμὴ
πρὸς στιγμὴν ἔχει, οὕτω τὸ γινόμενον πρὸς τὸ γεγονός- ἐν-
το ὑπάρχει γὰρ ἄπειρα γεγονότα ἐν τῷ γινομένῳ. μᾶλλον δὲ
φανερῶς ἐν τοῖς καθόλου περὶ κινήσεως δεῖ λεχθῆναι περὶ
τούτων.
4 E T ^ a n > a ΄, - ’
Περὶ μὲν οὖν τοῦ πῶς av ἐφεξῆς γινομένης τῆς yeve-
Μ ἣν , ^ LJ LEN ^ , , » ,
σεως ἔχοι TO μέσον τὸ αἴτιον ἐπὶ τοσοῦτον εἰλήφθω. ἀνάγκη
1s γὰρ καὶ ἐν τούτοις τὸ μέσον καὶ τὸ πρῶτον ἄμεσα εἶναι.
e ^ , , * & , Ld ^ ^ ,
otov τὸ A γέγονεν, ἐπεὶ τὸ I’ γέγονεν (ὕστερον δὲ τὸ I' yé-
Μ ^ * > M ‘ x M A > Ld
yovev, ἔμπροσθεν δὲ τὸ A- ἀρχὴ δὲ τὸ Γ᾽ διὰ τὸ ἐγγύτερον
τοῦ νῦν εἶναι, 6 ἐστιν ἀρχὴ τοῦ χρόνου). τὸ δὲ Γ᾽ γέγονεν, εἰ
τὸ 4 γέγονεν. τοῦ δὴ 4 γενομένου ἀνάγκη τὸ Α γεγονέναι.
w * 1 ~ ^ , M , ,
zo αἴτιον δὲ τὸ I τοῦ yàp A γενομένου τὸ l' ἀνάγκη yeyo-
νέναι, τοῦ δὲ I γεγονότος ἀνάγκη πρότερον τὸ A γεγονέναι.
οὕτω δὲ λαμβάνοντι τὸ μέσον στήσεταί που εἰς ἄμεσον, ἢ
ἀεὶ παρεμπεσεῖται διὰ τὸ ἄπειρον; οὐ γάρ ἐστιν ἐχόμενον
* , LÀ » , ? » ν , LÀ
γεγονὸς γεγονότος, ὥσπερ ἐλέχθη. ἀλλ᾽ ἄρξασθαί ye ὅμως
es ἀνάγκη ἀπ᾽ ἀμέσου καὶ ἀπὸ τοῦ νῦν πρώτου. ὁμοίως δὲ
M ᾽ M ~ μὲ , ^ > M » ^ Ld LÀ 1
Kal ἐπὶ τοῦ ἔσται. εἰ yap ἀληθὲς εἰπεῖν ὅτι ἔσται τὸ A,
> 7 , dX θὲ > ^ L4 x A μη , δ᾽
ἀνάγκη πρότερον ἀληθὲς εἰπεῖν ὅτι τὸ ἔσται. τούτου
LJ À » b A ^ w L4 ^ v
αἴτιον τὸ l^ εἰ μὲν yap τὸ A ἔσται, πρότερον τὸ I’ ἔσται"
> M A » , 4 L4 ε , > LÀ
et δὲ τὸ l' ἔσται, πρότερον τὸ A ἔσται. ὁμοίως δ᾽ ἄπειρος
€ * > td M ,
307) τομὴ καὶ ἐν τούτοις" o) yap ἔστιν ἐσόμενα ἐχόμενα ἀλ-
AA > ‘ δὲ M > , L4 À , L4 M
λήλων. ἀρχὴ δὲ xai ἐν τούτοις ἄμεσος ληπτέα. ἔχει δὲ
3 ἐν ^ > > , ^
οὕτως ἐπὶ τῶν ἔργων. εἰ γέγονεν οἰκία, ἀνάγκη τετμῆσθαι
by τὸ] τῷ A 4 γενόμενον om. 73 γινομένου n* 5 ἅπερ d
6 γενόμενα ABE: γινόμενα d: γινόμεναι n ἀδιαίρετα B*nEP : διαιρετά
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τὸ BnP: μέσον E°: μὲν Ad 17 y] a 4! 19 δὶ BnE: a Ad
23 παραπεσεῖται d 24 ὁμοίως n 25 ἀπὸ μέσου 4 BdEY? : ἀπὸ τοῦ
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H * , ^ x , Ld > d H
λίθους καὶ γεγονέναι. τοῦτο διὰ τί; ὅτι ἀνάγκη θεμέλιον
A
γεγονέναι, εἴπερ καὶ οἰκία γέγονεν: εἰ δὲ θεμέλιον, mpó-
if , > L4 7 > LÀ *, , ε ,
τερον λίθους γεγονέναι ἀνάγκη. πάλιν εἰ ἔσται οἰκία, ὡσαύ-
, » ^
Tws πρότερον ἔσονται λίθοι. δείκνυται δὲ διὰ τοῦ μέσου
,ὔ
ὁμοίως: ἔσται γὰρ θεμέλιος πρότερον.
3 M 2 € ^ , ^ , 4 ‘ ,
Ἐπεὶ δ᾽ ὁρῶμεν ἐν τοῖς γινομένοις κύκλῳ τινὰ γένεσιν
+ , , ^ LJ L4 » la ' ,
οὖσαν, ἐνδέχεται τοῦτο εἶναι, εἴπερ ἕποιντο ἀλλήλοις τὸ μέ-
" Li > ^ >
gov καὶ oi ἄκροι" ἐν yap τούτοις τὸ ἀντιστρέφειν ἐστίν. δέ-
N * ^ , ^ L4
δεικται δὲ τοῦτο ἐν τοῖς πρώτοις, ὅτι ἀντιστρέφει τὰ avp-
A ~ > » X ^
περάσματα: τὸ δὲ κύκλῳ τοῦτό ἐστιν. ἐπὶ δὲ τῶν ἔργων
T ^ ^ H
φαίνεται de: βεβρεγμένης τῆς γῆς ἀνάγκη ἀτμίδα yevé-
σθαι, τούτου δὲ γενομένου νέφος, τούτου δὲ γενομένου ὕδωρ"
) b ’ > , , ^ ^ ^ * M
τούτου δὲ γενομένου ἀνάγκη βεβρέχθαι τὴν "yv: τοῦτο δ᾽ ἦν τὸ
, » ~ " , , ey M » ^ e ~
ἐξ ἀρχῆς, ὥστε κύκλῳ περιελήλυθεν- ἑνὸς yàp αὐτῶν ὁτουοῦν
ha ~
ὄντος ἕτερον ἔστι, κἀκείνου ἄλλο, καὶ τούτου TO πρῶτον.
"E 9, » * , , 5 rd ^ M
στι ἔνια μὲν γινόμενα καθόλου (ἀεί τε γὰρ καὶ
74 4 Ld ων Li ^ vA hd ^ > s M L4 t
ἐπὶ παντὸς οὕτως ἢ ἔχει ἣ γίνεται), rà δὲ ἀεὶ μὲν ov, ὡς
ay * M / f ? 2 L4 L4 M L4
ἐπὶ τὸ πολὺ δέ, olov od πᾶς ἄνθρωπος ἄρρην TO γένειον τρι-
~ E, > [4 $ »" 4 , ~ * , > , *
χοῦται, ἀλλ᾽ ὡς ἐπὶ τὸ πολύ. τῶν δὴ τοιούτων ἀνάγκη kai
A , « 3. * a , M * M ^
τὸ μέσον ws ἐπὶ τὸ πολὺ εἶναι. εἰ yàp τὸ A κατὰ τοῦ B
καθόλου κατηγορεῖται, καὶ τοῦτο κατὰ τοῦ Γ᾽ καθόλου, ἀνάγκη
^ 4 > M ^
καὶ TO A κατὰ τοῦ l' ἀεὶ kai ἐπὶ παντὸς κατηγορεῖσθαι:
~ , , hi , x > * M M ὦ ἢ > 2 € ,
τοῦτο ydp ἐστι τὸ καθόλου, τὸ ἐπὶ παντὶ καὶ ἀεί. ἀλλ᾽ ὑπέ-
kevro ὡς ἐπὶ τὸ πολύ: ἀνάγκη ἄρα καὶ τὸ μέσον ὡς ἐπὶ
^ J L3 * >4? T ^ L4 , M ^ [4
τὸ πολὺ εἶναι τὸ ἐφ᾽ οὗ τὸ B. ἔσονται τοίνυν kal τῶν ws
oN ‘ A >? M L4 Ld © y. 4 ^ * L4 L4
ἐπὶ τὸ πολὺ ἀρχαὶ ἄμεσοι, ὅσα ὡς ἐπὶ τὸ πολὺ οὕτως ἔστιν
^
ἢ γίνεται.
13 Πῶς μὲν οὖν τὸ τί ἐστιν εἰς τοὺς ὅρους ἀποδίδοται, καὶ
, ’ , , ^ t * LÀ > aN > LÀ »
τίνα τρόπον ἀπόδειξις ἢ ὁρισμὸς ἔστιν αὐτοῦ ἢ οὐκ ἔστιν, εἴρη-
ται πρότερον: πῶς δὲ δεῖ θηρεύειν τὰ ἐν τῷ τί ἐστι κατη-
γορούμενα, νῦν λέγωμεν.
~ ^ L4 , » L4 , L4 > L , M
Τῶν δὴ ὑπαρχόντων ἀεὶ ἑκάστῳ ἔνια ἐπεκτείνει ἐπὶ
, *, , L4 ^ LA , M , N , t ,
πλέον, od μέντοι ἔξω τοῦ γένους. λέγω δὲ ἐπὶ πλέον ὑπάρ-
Uv . , M « , , *, A » ^ M
xew ὅσα ὑπάρχει μὲν ἑκάστῳ καθόλου, od μὴν ἀλλὰ καὶ
b34 γεγονέναιϊ .. . θεμέλιον om. πὶ οἰκία γέγονεν scripsi, habet E : οἰκίαν
γεγονέναι A Bd 37 θεμέλιος nE: θεμέλιον A Bd 38 ἐν om. n!
39 €mowro] οἴονται d 40 ἄκροι Bn An^: ὅροι Ad 9673 γίνεσθαι
Aldina 4 τούτου... νέφος om. d 5 βρέχεσθαι d τὸ om. d
6 αὐτῶν om. n! 15 r0? n πο: καὶ ABd 18moM-Fatd ὡς ABE:
om. dn 23 λέγομεν d!n
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ἄλλῳ. οἷον ἔστι τι ὃ πάσῃ τριάδι ὑπάρχει, ἀλλὰ καὶ μὴ
, LÀ * a [4 , ~ , > M M 3
τριάδι, ὥσπερ TO Ov ὑπάρχει τῇ τριάδι, ἀλλὰ καὶ μὴ
2 ~ , ^ * ‘ * e , , ,
ἀριθμῷ, ἀλλὰ καὶ τὸ περιττὸν ὑπάρχει τε πάσῃ τριάδι
^ , X , « , M ^ ^ , € * , 2
καὶ ἐπὶ πλέον ὑπάρχει (καὶ γὰρ τῇ πεντάδι ὑπάρχει), ἀλλ
* L4 ^ , € 4 ^ ^ ? , ΕΣ 3 ἣν. M
οὐκ ἔξω τοῦ γένους" ἡ μὲν yap πεντὰς ἀριθμός, οὐδὲν δὲ ἔξω
ἀριθμοῦ περιττόν. τὰ δὴ τοιαῦτα ληπτέον μέχρι τούτου, ἕως
τοσαῦτα ληφθῇ πρῶτον ὧν ἕκαστον μὲν ἐπὶ πλέον ὑπάρξει,
-
ἅπαντα δὲ μὴ ἐπὶ πλέον: ταύτην yap ἀνάγκη οὐσίαν εἶναι
^ ‘
τοῦ πράγματος. olov τριάδι ὑπάρχει πάσῃ ἀριθμός, τὸ me-
^ ‘ ^
ριττόν, TO πρῶτον ἀμφοτέρως, kai ὡς μὴ μετρεῖσθαι ἀρι-
θμῷ καὶ ὡς μὴ συγκεῖσθαι ἐξ ἀριθμῶν. τοῦτο τοίνυν ἤδη
ἐστὶν ἡ τριάς, ἀριθμὸς περιττὸς πρῶτος καὶ ὡδὶ πρῶτος. τού-
των γὰρ ἕκαστον, τὰ μὲν καὶ τοῖς περιττοῖς πᾶσιν ὑπάρχει,
A L! ^ M ^ 4 id ‘ , , 2 M *
τὸ δὲ τελευταῖον καὶ τῇ δυάδι, πάντα δὲ οὐδενί. ἐπεὶ δὲ
δεδήλωται ἡμῖν ἐν τοῖς ἄνω ὅτι καθόλου μέν ἐστι τὰ ἐν
τῷ τί ἐστι κατηγορούμενα (τὰ καθόλου δὲ ἀναγκαῖα), τῇ δὲ
, * , » T L4 L4 , > ~ ff. 2 *
τριάδι, kal ἐφ᾽ οὗ ἄλλου οὕτω λαμβάνεται, ἐν τῷ τί ἐστι τὰ
λαμβανόμενα, οὕτως ἐξ ἀνάγκης μὲν ἂν εἴη τριὰς ταῦτα.
L4 , , H > ~ ~ > , , 2 ^ ^
ὅτι δ᾽ οὐσία, ἐκ τῶνδε δῆλον. ἀνάγκη ydp, εἰ μὴ τοῦτο jv
τριάδι εἶναι, οἷον γένος τι εἶναι τοῦτο, } ὠνομασμένον ἢ ἀνώ-
νυμον. ἔσται τοίνυν ἐπὶ πλέον ἢ τῇ τριάδι ὑπάρχον. ὑπο-
κείσθω γὰρ τοιοῦτον εἶναι τὸ γένος ὥστε ὑπάρχειν κατὰ δύ-
>, * , , , Ἂς « 4 * ^ ^
γαμιν ἐπὶ πλέον. εἰ τοίνυν μηδενὶ ὑπάρχει ἄλλῳ 7) ταῖς
ἀτόμοις τριάσι, τοῦτ᾽ ἂν εἴη τὸ τριάδι εἶναι (ὑποκείσθω γὰρ
καὶ τοῦτο, ἡ οὐσία ἡ ἑκάστου εἶναι ἡ ἐπὶ τοῖς ἀτόμοις ἔσχα-
τος τοιαύτη κατηγορία): ὥστε ὁμοίως καὶ ἄλλῳ ὁτῳοῦν τῶν
οὕτω δειχθέντων τὸ αὐτῷ εἶναι ἔσται.
Χρὴ δέ, ὅταν ὅλον τι πραγματεύηταί τις, διελεῖν τὸ
γένος εἰς τὰ ἄτομα τῷ εἴδει τὰ πρῶτα, οἷον ἀριθμὸν εἰς
, ^ (à » σ > , t A ^
τριάδα Kai δυάδα, εἶθ᾽ οὕτως ἐκείνων ὁρισμοὺς πειρᾶσθαι
, 4 , ^ M ^ M > ~
λαμβάνειν, olov εὐθείας γραμμῆς kai κύκλου, Kal ὀρθῆς yw-
νίας, μετὰ δὲ τοῦτο λαβόντα τί τὸ γένος, οἷον πότερον τῶν
~ na ^ ~ A , ^ ^ ~ ~
ποσῶν ἢ τῶν ποιῶν, rà ἴδια πάθη θεωρεῖν διὰ τῶν κοινῶν
427 τι Om. 5 28 καὶ μὴ BnT : μὴ A: μὴ καὶ d 31 οὐκ] οὐδὲ πὶ
33 ληφθῇ dnET : ληφθείη AB πλέον dnET: πλεῖον AB 30 πᾶσιν
om. n 1 ἐπὶ πὶ δὲ om. n3: δὲ καὶ d 2 ὅτι om, A καθόλον
scripsi: ἀναγκαῖα codd. AnEP 5 οὕτως om. B? 8 πλέον nE:
πλεῖον ABd 10 ὑπάρχει om. nt 12 καὶ] » n! rois Scripsi,
habet ut vid. E: rais codd. ἐσχάτοις n 14 δειχθέντων codd. P:
ληφθέντων Pre αὐτὸ An I7 καὶ δυάδα om. A 19 τῷ
ποσῷ B!
13. 96*27-97°13
πρώτων. τοῖς yàp συντιθεμένοις ἐκ τῶν ἀτόμων τὰ συμ-
Batvovra ἐκ τῶν ὁρισμῶν ἔσται δῆλα, διὰ τὸ ἀρχὴν εἶναι
πάντων τὸν ὁρισμὸν καὶ τὸ ἁπλοῦν καὶ τοῖς ἁπλοῖς καθ᾽
e ^ e , x , , -^ > w »
αὑτὰ ὑπάρχειν τὰ συμβαίνοντα μόνοις, rois δ᾽ ἄλλοις xar
> - e ^ , € ^ ^ ^ , ,
ἐκεῖνα. αἱ δὲ διαιρέσεις ai κατὰ tas διαφορὰς χρήσιμοί
εἰσιν εἰς τὸ οὕτω μετιέναι: ὡς μέντοι δεικνύουσιν, εἴρηται ἐν
τοῖς πρότερον. χρήσιμοι δ᾽ ἂν εἶεν ὧδε μόνον πρὸς τὸ συλ-
λογίζεσθαι τὸ τί ἐστιν. καίτοι δόξειέν γ᾽ ἂν οὐδέν, ἀλλ᾽ εὐ-
θὺ λ , a σ hl > > > ^ ἐλ, , ,
bs λαμβάνειν ἅπαντα, ὥσπερ av εἰ ἐξ ἀρχῆς ἐλάμβανέ
τις ἄνευ τῆς διαιρέσεως. διαφέρει δέ τι τὸ πρῶτον καὶ ὕστε-
ρον τῶν κατηγορουμένων κατηγορεῖσθαι, οἷον εἰπεῖν ζῷον ἥμε-
ρον δίπουν ἢ δίπουν ζῷον ἥμερον. εἰ γὰρ ἅπαν ἐκ δύο ἐστί,
καὶ ἕν τι τὸ ζῷον ἥμερον, καὶ πάλιν ἐκ τούτου καὶ τῆς δια-
φορᾶς 6 ἄνθρωπος ἢ 6 τι δήποτ᾽ ἐστὶ τὸ ἕν γινόμενον, ἀναγ-
καῖον διελόμενον αἰτεῖσθαι.
Ἔτι πρὸς τὸ μηδὲν παραλιπεῖν
ἐν τῷ τί ἐστιν οὕτω μόνως ἐνδέχεται. ὅταν γὰρ τὸ πρῶτον
ληφθῇ γένος, ἂν μὲν τῶν κάτωθέν τινα διαιρέσεων λαμ-
βάνῃ, οὐκ ἐμπεσεῖται ἅπαν εἰς τοῦτο, οἷον οὐ πᾶν ζῷον ἢ
ε , "^ , > A ^ ~ v ,
ὁλόπτερον ἢ σχιζόπτερον, ἀλλὰ πτήνον ζῷον ἅπαν' τούτου
γὰρ διαφορὰ αὕτη. πρώτη δὲ διαφορά ἐστι ζῴον εἰς ἣν
΄ ^ ? , Li , Ν A ~ L4 e ,
ἅπαν ζῷον ἐμπίπτει. ὁμοίως δὲ Kai τῶν ἄλλων ἑκάστου,
A ^ LÀ ~ a ~ e > > , T Ld , a
καὶ τῶν ἔξω γενῶν kai τῶν ὑπ᾽ αὐτό, olov ὄρνιθος, εἰς ἣν
" Ld M » , 3 a Ld , , L4 Α T
ἅπας ὄρνις, kai ἰχθύος, eis ἣν ἅπας ἰχθύς. οὕτω μὲν οὖν
βαδίζοντι ἔστιν εἰδέναι ὅτι οὐδὲν παραλέλειπται: ἄλλως δὲ
a ^ > ^ * * ΕΣ ^ , * b ^ A
καὶ παραλιπεῖν ἀναγκαῖον kai μὴ εἰδέναι. οὐδὲν δὲ δεῖ τὸν
ὁριζόμενον καὶ διαιρούμενον ἅπαντα εἰδέναι τὰ ὄντα. καί-
> , , L ^ A » fA ^ ^
To. ἀδύνατόν φασί τινες εἶναι τὰς διαφορὰς εἰδέναι τὰς πρὸς
ἕκαστον μὴ εἰδότα ἕκαστον: ἄνευ δὲ τῶν διαφορῶν οὐκ εἶναι
LÀ » ’ T * ^ ; à > M , Ld *
ἕκαστον εἰδέναι: ob yap μὴ διαφέρει, ταὐτὸν εἶναι τούτῳ, οὗ δὲ
διαφέρει, ἕτερον τούτου. πρῶτον μὲν οὖν τοῦτο ψεῦδος- οὐ γὰρ
* ^ ^ LÀ M ^ M € ,
κατὰ πᾶσαν διαφορὰν ἕτερον: πολλαὶ yap διαφοραὶ ὑπάρ-
χουσι τοῖς αὐτοῖς τῷ εἴδει, ἀλλ᾽ οὐ κατ᾽ οὐσίαν οὐδὲ καθ᾽
b21 πρῶτον A*nEP 23 róv BEP: om. Adn ὁρισμὸν A? BnEP:
ὁρισμῶν Ad 24 ὑπάρχει n 25 χρήσιμοί Cdn AnEPT : χρήσιμαί AB
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L4 , 7 [2 , 3 , * ^ A X
αὑτά. εἶτα ὅταν λάβῃ τἀντικείμενα καὶ τὴν διαφορὰν καὶ
μὲ ~ , , > ^ μὴ > ^, ^4 d , ,
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^ a ^ ~ ^ > i3 * » ,ὔ
τὸ ζητούμενον εἶναι, καὶ τοῦτο γινώσκῃ, οὐδὲν διαφέρει εἰδέ-
n ^ > tA , > Ld ~ Là €
vat ἢ μὴ εἰδέναι ἐφ᾽ ὅσων κατηγοροῦνται ἄλλων αἱ δια-
f * 4 σ *-^ «“ cA MU , Lj
φοραί. φανερὸν yàp ὅτι dv οὕτω βαδίζων ἔλθῃ εἰς ταῦτα
Φ L4 LÀ ft Ll a p ^ *, , ^A »
ὧν μηκέτι ἔστι διαφορά, ἕξει τὸν λόγον τῆς οὐσίας. τὸ ὃ
20 ἅπαν ἐμπίπτειν εἰς τὴν διαίρεσιν, ἂν ἦ ἀντικείμενα ὧν μὴ
Ἔ
ἔστι μεταξύ, οὐκ αἴτημα: ἀνάγκη γὰρ ἅπαν ἐν θατέρῳ
αὐτῶν εἶναι, εἴπερ ἐκείνου διαφορά ἐστι.
» ^ ^ ^
Eis δὲ τὸ κατασκευάζειν ὅρον διὰ τῶν . διαιρέσεων τριῶν
^ ~ ^ ^ ^
δεῖ στοχάζεσθαι, τοῦ λαβεῖν τὰ κατηγορούμενα ἐν τῷ τί
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πάντα. ἔστι δὲ τούτων ἕν πρῶτον διὰ τοῦ δύνασθαι, ὥσπερ
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πρὸς συμβεβηκὸς συλλογίσασθαι ὅτι ὑπάρχει, καὶ διὰ τοῦ
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πρῶτον λάβῃ. τοῦτο δ᾽ ἔσται, ἐὰν ληφθῇ ὃ πᾶσιν ἀκολου-
30 θεῖ, ἐκεῳ δὲ μὴ πάντα: ἀνάγκη γὰρ εἶναί τι τοιοῦτον.
F4 ^ , LÀ > ^ ^ J € , ^ "d
ληφθέντος δὲ τούτου ἤδη ἐπὶ τῶν κάτω ὁ αὐτὸς τρόπος"
δεύτερον γὰρ τὸ τῶν ἄλλων πρῶτον ἔσται, καὶ τρίτον τὸ
τῶν ἐχομένων: ἀφαιρεθέντος γὰρ τοῦ ἄνωθεν τὸ ἐχόμενον
^ » ~ » Lj , b M Lj Mi ~ L4
τῶν ἄλλων πρῶτον ἔσται. ὁμοίως δὲ kai ἐπὶ τῶν ἄλλων.
oe 3 Ld ^ ki > ~ ~ , m
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^ , * Ld μὴ , a a ^ € ,
Tov κατὰ διαίρεσιν, ὅτι ἅπαν ἢ τόδε ἢ τόδε ζῷον, ὑπάρ-
χει δὲ τόδε, καὶ πάλιν τούτου ὅλου τὴν διαφοράν, τοῦ δὲ
τελευταίου μηκέτι εἶναι διαφοράν, ἢ καὶ εὐθὺς μετὰ τῆς
, ^ ^ ^ * £F ΜΙ Ν ~
τελευταίας διαφορᾶς τοῦ avvóAov μὴ διαφέρειν εἴδει ἔτι τοῦτο.
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> μὰ , L4 * , > r2 -* M , wa
ἐστιν εἴληπται τούτων) οὔτε ἀπολείπει οὐδέν: ἢ yàp γένος ἢ
διαφορὰ ἂν εἴη. γένος μὲν οὖν τό τε πρῶτον, καὶ μετὰ
^ ^ ~ , € M A ~
τῶν διαφορῶν τοῦτο προσλαμβανόμενον: ai διαφοραὶ δὲ πᾶ-
w ΕΣ x LÀ L4 [4 rd to X n 8 d
s σαι Éxyovrav οὐ yap ἔτι ἔστιν ὑστέρα: εἴδει yàp ἂν διέφερε
^ ^ ~
τὸ τελευταῖον, τοῦτο δ᾽ εἴρηται μὴ διαφέρειν.
^ ^ ^ » a » '* M LÀ A > Li
Ζητεῖν δὲ Set ἐπιβλέποντα ἐπὶ τὰ ὅμοια καὶ ἀδιά-
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~ a L4 » 1 w , 21}
$opa, πρῶτον τί ἅπαντα ταὐτὸν ἔχουσιν, εἶτα πάλιν ἐφ
ἑτέροις, ἃ ἐν ταὐτῷ μὲν γένει ἐκείνοις, εἰσὶ δὲ αὑτοῖς μὲν
, MJ ~ , a > ΄ - > > τ ,
ταὐτὰ τῷ εἴδει, ἐκείνων δ᾽ ἕτερα. ὅταν δ᾽ ἐπὶ τούτων λη- τὸ
^ , , , , M x, * ~ Lá e , > M ~
$04 τί πάντα ταὐτόν, Kai ἐπὶ τῶν ἄλλων ὁμοίως, ἐπὶ τῶν
> , , ^ *, > ,’ -΄ ^ > σ΄ Là
εἰλημμένων πάλιν σκοπεῖν εἰ ταὐτόν, ἕως dv eis ἕνα ἔλθῃ
λόγον: οὗτος γὰρ ἔσται τοῦ πράγματος ὁρισμός. ἐὰν δὲ μὴ
, , LÀ > , > , - , ~ c , Ἅ LÀ
βαδίζῃ εἰς ἕνα ἀλλ᾽ eis δύο ἢ πλείους, δῆλον ὅτι οὐκ ἂν εἴη
μὰ M ^ > ^ , , , ,
ἕν τι εἶναι τὸ ζητούμενον, ἀλλὰ πλείω. olov λέγω, εἰ Tits
ἐστι μεγαλοψυχία ζητοῖμεν, σκεπτέον ἐπί τινων μεγαλο-
ψύχων, οὖς ἴσμεν, τί ἔχουσιν ἕν πάντες jj τοιοῦτοι. οἷον εἰ
Ἀλκιβιάδης μεγαλόψυχος ἢ 6 ᾿Αχιλλεὺς καὶ ὁ Αἴας, τί
ἕν ἅπαντες; τὸ μὴ ἀνέχεσθαι ὑβριζόμενοι: ὁ μὲν γὰρ ἐπο-
λέμησεν, ὁ δ᾽ ἐμήνισεν, 6 δ᾽ ἀπέκτεινεν ἑαυτόν. πάλιν ἐφ᾽ 2o
ἑτέρων, οἷον Λυσάνδρου ἢ Σωκράτους. εἰ δὴ τὸ ἀδιάφοροι el-
ναι εὐτυχοῦντες καὶ ἀτυχοῦντες, ταῦτα δύο λαβὼν σκοπῶ
τί τὸ αὐτὸ ἔχουσιν 1j τε ἀπάθεια ἡ περὶ τὰς τύχας καὶ
e i] L4 * > L4 » 8 x 8 LA ὃ , . ἴδ bel w
ἡ μὴ ὑπομονὴ ἀτιμαζομένων. εἰ δὲ μηδέν, δύο εἴδη ἂν εἴη
^ , : M , , , ~ 4 06A » ,
τῆς μεγαλοψυχίας. αἰεὶ δ᾽ ἐστί πᾶς ὅρος καθόλου- οὐ γάρ τινι 25, 26
ὀφθαλμῷ λέγει τὸ ὑγιεινὸν ὁ ἰατρός, ἀλλ᾽ ἢ παντὶ ἢ εἴδει ἀφ-
, «nat A to e A had ^ 06 A ~
ορίσας. ῥᾷόν re τὸ καθ᾽ ἕκαστον ὁρίσασθαι 7 τὸ καθόλου, διὸ δεῖ
> ^ ~ > 4 »—* A Ls , M
ἀπὸ τῶν Kal? ἕκαστα ἐπὶ rà καθόλου μεταβαίνειν: Kai
γὰρ αἱ ὁμωνυμίαι λανθάνουσι μᾶλλον ἐν τοῖς καθόλου ἢ ἐν 30
^ > H e 375 L^ 2 H ^ H
τοῖς ἀδιαφόροις. ὥσπερ δὲ ἐν ταῖς ἀποδείξεσι δεῖ τό ye
Ἂ e , L4 M ? ^ Ld * ,
συλλελογίσθαι ὑπάρχειν, οὕτω καὶ ἐν τοῖς ὅροις τὸ σαφές.
~ » LÀ »* A ~ > c > ,ὔ ^ >
τοῦτο δ᾽ ἔσται, ἐὰν διὰ τῶν καθ᾽ ἕκαστον εἰλημμένων ἣ τὸ ἐν
Li , , € 7 , M Ed x ^ 2 A
ἑκάστῳ γένει ὁρίζεσθαι χωρίς, οἷον τὸ ὅμοιον μὴ πᾶν ἀλλὰ
τὸ ἐν χρώμασι καὶ σχήμασι, καὶ ὀξὺ τὸ ἐν φωνῇ, καὶ 35
| NS ^ M - > s M ig ,
οὕτως ἐπὶ τὸ κοινὸν βαδίζειν, εὐλαβούμενον μὴ ὁμωνυμίᾳ
ἐντύχῃ. εἰ δὲ μὴ διαλέγεσθαι δεῖ μεταφοραῖς, δῆλον ὅτι
οὐδ᾽ ὁρίζεσθαι οὔτε μεταφοραῖς οὔτε ὅσα λέγεται μεταφοραῖς"
διαλέγεσθαι γὰρ ἀνάγκη ἔσται μεταφοραῖς.
I4 Πρὸς δὲ τὸ ἔχειν τὰ προβλήματα ἐκλέγειν δεῖ τάς 985
b9 d om. A αὑτοῖς A*E: αὐτοῖς ABdn 11 τί Trendelenburg : τι
codd. ἅπαν n émi? om. n 12 πάλιν] πάνυ d εἰ A! B'dnEP:
ἡ 4:9 B 13 οὕτως d 14 πλείους EP : πλείω codd. 17 εἰ
om. 5 18 xai] ἢ d 23 «ire ἀπάθειαν ἣ d 31 ἀδιαφόροις A BP
dnEP: διαφόροις BAn* δὲ) τε d 32 συλλογίσασθαι Ad An‘
33 διὰ -Ὁ τὸ πὶ εἰλημμένων coni. Mure, habet ut vid. E : εἰρημένων codd. P*
36 ὁμωνυμία d 3] μηδὲ A:uájren διαφοραῖς ἃ ὅτι οὐδὲν πὶ 30 ἔστι
ἀ 9831 ἐκλέγειν B?n* E : λέγειν ABdnP
4985 T
ANAAYTIKQN YETEPQN B
2 M * ^ , -" x > * € ,
τε ἀνατομὰς καὶ Tas διαιρέσεις, οὕτω δὲ ἐκλέγειν, ὑποθέμε-
νον τὸ γένος τὸ κοινὸν ἁπάντων, οἷον εἰ ζῷα εἴη τὰ τεθεω-
, ^ ^ 4 € Ed L4 ^ ,
ρημένα, ποῖα παντὶ ζῴῳ ὑπάρχει, ληφθέντων δὲ τούτων,
ς πάλιν τῶν λοιπῶν τῷ πρώτῳ ποῖα παντὶ ἕπεται, οἷον εἰ
τοῦτο ὄρνις, ποῖα παντὶ ἕπεται ὄρνιθι, καὶ οὕτως αἰεὶ τῷ ἐγ-
[à ~ A L4 μὲ » , ^ ἣν , € L4
yurata: δῆλον yàp ὅτι ἕξομεν ἤδη λέγειν τὸ διὰ τί ὑπάρ-
χει τὰ ἑπόμενα τοῖς ὑπὸ τὸ κοινόν, οἷον διὰ τί ἀνθρώπῳ
ἢ ἵππῳ ὑπάρχει. ἔστω δὲ ζῷον ἐφ᾽ od A, τὸ δὲ B τὰ
^ ^ ^
10 ἑπόμενα παντὶ ζῴῳ, ef ὧν δὲ Γ A E rà τινὰ ζῷα. δῆ-
M ^ , ^ Li , ~ ^ ^ M € x
λον δὴ διὰ τί τὸ B ὑπάρχει τῷ 4: διὰ yàp τὸ A. ὁμοίως
b ‘A ~ » $23 8 FN ^ L4 € , X, ,
δὲ καὶ rots ἄλλοις: Kal ἀεὶ ἐπὶ τῶν κάτω ὁ αὐτὸς λόγος.
Νῦν μὲν οὖν κατὰ τὰ παραδεδομένα κοινὰ ὀνόματα
λέγομεν, δεῖ δὲ μὴ μόνον ἐπὶ τούτων σκοπεῖν, ἀλλὰ καὶ
γομεέν, Ded ,
, ~ ,
τς ἂν ἄλλο τι ὀφθῇ ὑπάρχον κοινόν, ἐκλαμβάνοντα, εἶτα τίσι
τοῦτ᾽ ἀκολουθεῖ καὶ ποῖα τούτῳ ἕπεται, οἷον τοῖς κέρατα
LÀ = 4 * ^ ^ * > ^ > , ^
ἔχουσι τὸ ἔχειν ἐχῖνον, τὸ μὴ ἀμφώδοντ᾽ εἶναι' πάλιν τὸ
, ᾽ LÀ Ἂ - “ x A , > , [4 ,
κέρατ᾽ ἔχειν τίσιν ἕπεται. δῆλον γὰρ διὰ τί ἐκείνοις ὑπάρ-
ἔξει τὸ εἰρημένον: διὰ γὰρ τὸ κέρατ᾽ ἔχειν ὑπάρξει.
20 “Ere δ᾽ ἄλλος τρόπος ἐστὶ κατὰ τὸ ἀνάλογον ἐκλέγειν.
a M ^ ΕἸ 4 ^ , , a ^ L4 , M
ἕν yap λαβεῖν οὐκ ἔστι τὸ αὐτό, ὃ δεῖ καλέσαι σήπιον Kai
ἄκανθαν καὶ ὀστοῦν: ἔσται δ᾽ ἑπόμενα καὶ τούτοις ὥσπερ
μιᾶς τινος φύσεως τῆς τοιαύτης οὔσης.
x Li 3 A , , , X * ~ X. , A
Ta δ᾽ αὐτὰ προβλήματά - ἐστι τὰ μὲν τῷ τὸ αὐτὸ
25 μέσον ἔχειν, οἷον ὅτι πάντα ἀντιπερίστασις. τούτων δ᾽ ena
τῷ γένει ταὐτά, ὅσα ἔχει διαφορὰς τῷ ἄλλων ἢ ἄλλως
εἶναι, οἷον διὰ τί ἠχεῖ, ἢ διὰ τί ἐμφαίνεται, καὶ διὰ τί
ἶρις. ἅπαντα γὰρ ταῦτα τὸ αὐτὸ πρόβλημά ἐστι γένει
, A > , 3 2 LI μὲ A A ^ M
(πάντα yàp ἀνάκλασις), ἀλλ᾽ εἴδει érepa. τὰ δὲ TH τὸ
, ¥ ^ A a , , ~ d
30 μέσον ὑπὸ τὸ ἕτερον μέσον εἶναι διαφέρει τῶν προβλημά-
των, οἷον διὰ τί ὁ Νεῖλος φθίνοντος τοῦ μηνὸς μᾶλλον ῥεῖ;
διότι χειμεριώτερος φθίνων 6 pels. διὰ τί δὲ χειμεριώτερος
€ ^
φθίνων; διότι ἡ σελήνη ἀπολείπει. ταῦτα yap οὕτως ἔχει
πρὸς ἀλληλα.
a2 δὲ om, Ad ἐκλέγειν B2, fecit n: διαλέγειν ABd 5 ποίῳ B
ἡ τῷ ἃ 8 τὸ om. n nid]yn ronk: τοῦ ABd 12 κάτω)
ἄλλων ABE 15 ἄλλῳ d 16 ποίῳ d 17 ἀμφόδοντ᾽ A?
21 καλεῖσθαι n σήπιον nE: ajmeov Ad: σηπεῖον BT 22 ἔστι ABE:
ἔσται dn Pc 24 τῷ omn. d 25 ἔνια BnE: om. Ad 26 7a?
B*nE*P: τῶν A Bdn*Pc 27 οἷον om. n 3273 ὁ... φθίνων
ΠΕΡΤ : om. ABd 32 ὁ μὴν ABdET
15
14. 98*2— τό. 98529
16 Περὶ δ᾽ αἰτίου καὶ οὗ αἴτιον ἀπορήσειε μὲν ἄν τις, 35
ἄρα ὅτε ὑπάρχει τὸ αἰτιατόν, καὶ τὸ αἴτιον ὑπάρχει (ὥσ-
, -^ bl * Li A x LÀ ~ , Li
περ εἰ φυλλορροεῖ ἢ ἐκλείπει, Kal τὸ αἴτιον τοῦ ἐκλείπειν
D ^ ν Lj , a> 4 " » 1
ἢ φυλλορροεῖν ἔσται: οἷον εἰ τοῦτ᾽ ἔστι τὸ πλατέα ἔχειν τὰ
* ~ 9, 3 , N) A ~ > , 7 * ^ b
φύλλα, τοῦ ἐκλείπειν τὸ τὴν γῆν ἐν μέσῳ εἶναι" εἰ γὰρ 98
^ € , LJ L4 A LÀ > ~ LÀ 4 w
μὴ ὑπάρχει, ἄλλο τι ἔσται τὸ αἴτιον αὐτῶν), εἴ τε TO αἴτιον
ὑπάρχει, ἅμα καὶ τὸ αἰτιατόν (οἷον εἰ ἐν μέσῳ ἡ γῆ, ἐκ-
λείπει, ἢ εἰ πλατύφυλλον, φυλλορροεῖ). εἰ δ᾽ οὕτως, ἅμ᾽
ἂν εἴη καὶ δεικνύοιτο δι’ ἀλλήλων. ἔστω γὰρ τὸ φυλλορ- ς
ροεῖν ἐφ᾽ οὗ A, τὸ δὲ πλατύφυλλον ἐφ᾽ οὗ B, ἄμπελος
δὲ ἐφ᾽ οὗ Γ. εἰ δὴ τῷ Β ὑπάρχει τὸ A (πᾶν γὰρ πλατύφυλ-
λον φυλλορροεῖ), τῷ δὲ I' ὑπάρχει τὸ B (πᾶσα γὰρ ἄμπε-
dos πλατύφυλλος), τῷ I ὑπάρχει τὸ A, καὶ πᾶσα ἀμ-
πελος φυλλορροεῖ. αἴτιον δὲ τὸ B τὸ μέσον. ἀλλὰ καὶ το
ὅτι πλατύφυλλον ἡ ἄμπελος, ἔστι διὰ τοῦ φυλλορροεῖν ἀπο-
δεῖξαι. ἔστω γὰρ τὸ μὲν A πλατύφυλλον, τὸ δὲ E τὸ
φυλλορροεῖν, ἄμπελος δὲ ἐφ᾽ οὗ Ζ. τῷ δὴ Z ὑπάρχει τὸ
E (φυλλορροεῖ γὰρ πᾶσα ἄμπελος), τῷ δὲ E τὸ 4 (ἅπαν
γὰρ τὸ φυλλορροοῦν πλατύφυλλον) πᾶσα ἄρα ἀμπελος 15
πλατύφυλλον. αἴτιον δὲ τὸ φυλλορροεῖν. εἰ δὲ μὴ ἐνδέχεται
LÀ T > , * * w , - M * ~
αἴτια εἶναι ἀλλήλων (τὸ yàp αἴτιον πρότερον οὗ αἴτιον, καὶ τοῦ
μὲν ἐκλείπειν αἴτιον τὸ ἐν μέσῳ τὴν γῆν εἶναι, τοῦ δ᾽ ἐν μέσῳ
τὴν γῆν εἶναι οὐκ αἴτιον τὸ ἐκλείπειν)---εἰ οὖν ἡ μὲν διὰ τοῦ αἰτίου
» , ~ A , £ M * M ~ > , ~ LÀ "
ἀπόδειξις τοῦ διὰ τί, ἡ δὲ μὴ διὰ τοῦ αἰτίου τοῦ ὅτι, ὅτι 20
Α > ra bu , | Ww Ld > > M » , LÀ
μὲν ἐν μέσῳ, olde, διότι δ᾽ οὔ. ὅτι δ᾽ od τὸ ἐκλείπειν αἴτιον
~ > , > * ~ ^ > 4, , > * ~
τοῦ ἐν μέσῳ, ἀλλὰ τοῦτο τοῦ ἐκλείπειν, φανερόν: ἐν yap τῷ
λόγῳ τῷ τοῦ ἐκλείπειν ἐνυπάρχει τὸ ἐν μέσῳ, ὥστε οῆλον ὅτι
διὰ τούτου ἐκεῖνο γνωρίζεται, ἀλλ᾽ οὐ τοῦτο δι᾽ ἐκείνου.
Ἄ ?» , L4 a y LÀ T M A > LÀ
H ἐνδέχεται ἑνὸς πλείω αἴτια εἶναι; καὶ yap εἰ ἔστι 25
τὸ αὐτὸ πλειόνων πρώτων κατηγορεῖσθαι, ἔστω τὸ A τῷ B
πρώτῳ ὑπάρχον, καὶ τῷ I ἄλλῳ πρώτῳ, καὶ ταῦτα τοῖς
4 E. ὑπάρξει ἄρα τὸ A τοῖς 4 Ε' αἴτιον δὲ τῷ μὲν A τὸ
Β, τῷ δὲ Ε τὸ Γ' ὥστε τοῦ μὲν αἰτίου ὑπάρχοντος ἀνάγκη
436 αἴτιον d τὸς οὗ d ὡς ἃ 37 φυλλοροεῖ Bd, qui ita solent
38 τὸ fecit Β rà om. AE Ὁ2 imdpynn εἴτε AB: et ye 3
αἴτιον 71! 4 δ᾽ +s d 6obróan ἄμπελος n*E : ἄμπελοι
ABdn 12 Ε]Β A 13 δὴ] δὲ n I4 ἅπασα n 20 ἡ
A*B?n AnE: € ABdAn* pat+hid δι᾽ αἰτίον π τοῦ ὅτι] τοῦτό τι n!
ὅτι") ὁ ὅτι Al 21-2 αἴτιον... ἐκλείπειν om, A} 23 τῷ om. d
τὸ A? B*d*n EPT : τῷ ABd 24 δι᾽ ἐκεῖνο A} 26 πρῶτον Adn:
πρώτως E
ANAAYTIKQN YZTEPON B
3o TÓ πρᾶγμα ὑπάρχειν, τοῦ δὲ πράγματος ὑπάρχοντος οὐκ
» ) - ^ n 7T LÀ » LI LJ L4 , , ^
ἀνάγκη πᾶν ὃ ἂν 7 αἴτιον, ἀλλ᾽ αἴτιον μέν, od μέντοι πᾶν.
nn , a4 , ^ , td > ^ ^ LÀ LÀ
ἢ εἰ dei καθόλου τὸ πρόβλημά ἐστι, Kal TO αἴτιον ὅλον τι,
* t d »" , A ~ v A» *
καὶ οὗ αἴτιον, καθόλου; olov τὸ φυλλορροεῖν ὅλῳ τινὶ ἀφωρισμέ-
~ LÀ > ^T M 3 , ^ ^ ^ x
vov, κἂν εἴδη αὐτοῦ 7, καὶ τοισδὶ καθόλου, ἢ φυτοῖς ἢ τοιοιοδὶ
a e Von ᾽ " “τ D ΄ OT ON
35 φυτοῖς" WOTE και TO μέσον LOOV δεῖ εἰναι ἐπι τουτων και OU αιτιον,
995
IO
15
16
16
20
kai ἀντιστρέφειν. οἷον διὰ τί τὰ δένδρα φυλλορροεῖ; εἰ δὴ διὰ
a ^4 ^ LÀ ^ , -^ © 4 ~
πῆξιν τοῦ ὑγροῦ, etre φυλλορροεῖ δένδρον, δεῖ ὑπάρχειν πῆξιν,
ἴτε πῆξις ὑπάρχει, μὴ ὁτῳοῦν ἀλλὰ δένδρῳ, φυλλ ü
etre πῆξις ὑπάρχει, μὴ ὁτῳοῦν ἀλλὰ δένδρῳ, φυλλορροεῖν.
> > ^ LJ ^
Πότερον δ᾽ ἐνδέχεται μὴ τὸ αὐτὸ αἴτιον εἶναι τοῦ αὐτοῦ
^ 3 > LÀ "^ » ^ 3. ^ > φ΄. ἃ > ,
πᾶσιν ἀλλ᾽ ἕτερον, 7 οὔ; ἢ εἰ μὲν καθ᾽ αὑτὸ ἀποδέδεικται
* X ^ ^ -^ ^ , T/ e ^ ,
Kal μὴ κατὰ σημεῖον ἢ συμβεβηκός, οὐχ οἷόν re: ὁ yàp Aó-
yos τοῦ ἄκρου τὸ μέσον ἐστίν᾽ εἰ δὲ μὴ οὕτως, ἐνδέχεται. ἔστι
δὲ καὶ οὗ αἴτιον καὶ ᾧ σκοπεῖν κατὰ συμβεβηκός: οὐ μὴν
δοκεῖ προβλήματα εἶναι. εἰ δὲ μή, ὁμοίως ἕξειν τὸ μέσον"
εἰ μὲν ὁμώνυμα, ὁμώνυμον τὸ μέσον, εἰ δ᾽ ὡς ἐν γένει,
ὁμοίως ἕξει. οἷον διὰ τί καὶ ἐναλλὰξ ἀνάλογον; ἄλλο γὰρ
αἴτιον ἐν γραμμαῖς καὶ ἀριθμοῖς καὶ τὸ αὐτό ye, ἦ μὲν
, LAX 5 »v L4 δί a > , Ld
γραμμή, ἄλλο, ἧ δ᾽ ἔχον αὔξησιν τοιανδί, τὸ αὐτό. ov-
τως ἐπὶ πάντων. τοῦ δ᾽ ὅμοιον εἶναι χρῶμα χρώματι καὶ
~ , ν᾿ Ld * P4 * ^ Ed
σχῆμα σχήματι ἄλλο ἄλλῳ. ὁμώνυμον yap τὸ ὅμοιον
$. 2 t4 L4 x ^ LÀ M > , » M
ἐπὶ τούτων: ἔνθα μὲν yàp ἴσως τὸ ἀνάλογον ἔχειν τὰς mÀev-
ρὰς καὶ ἴσας τὰς γωνίας, ἐπὶ δὲ χρωμάτων τὸ τὴν αἴσθη-
, Ww w ^ ^ x 3 > , ^
ow μίαν εἶναι ἢ τι ἄλλο τοιοῦτον. rà δὲ κατ᾽ ἀναλογίαν τὰ
, ^ M ^ 4 @ > 5 ,
αὐτὰ kai τὸ μέσον ἕξει κατ᾽ ἀναλογίαν.
LJ » LÀ ^
ἔχει δ᾽ οὕτω τὸ
παρακολουθεῖν τὸ αἴτιον ἀλλήλοις καὶ οὗ αἴτιον καὶ ᾧ ai-
θ᾽ - a 5, ‘ T LJ ? ,
τιον: καθ᾽ ἕκαστον μὲν λαμβάνοντι τὸ οὗ αἴτιον ἐπὶ πλέον,
ἵ 1 , LÀ M L4 $; κι / ^ , ^
olov τὸ τέτταρσιν ἴσας τὰς ἔξω ἐπὶ πλέον ἢ τρίγωνον ἢ re-
τράγωνον, ἅπασι δὲ én’ ἴσον (ὅσα γὰρ τέτταρσιν ὀρθαῖς
LÀ ^ L4 * 4 r4 € , w * ^ , ,
ἴσας τὰς ἔξω): kai τὸ μέσον ὁμοίως. ἔστι δὲ τὸ μέσον Ad-
b32 ἢ εἰ] εἴη fecit d? 33 08] οὐκ πὶ ἄλλῳ d 34 εἴδη] en δη n!
τοισδὶ A? P* : τοῖσδι Β: τοῖς δ᾽ εἰ Al: τοῖς δεῖ ἀ τοιοῖσδε ABdE 35 δεῖ
fecit B 37 δὴ ὑπάρχει B! 38 ὁτιοῦν B δένδρῳ A? B?nE : δένδρων
A: δένδρον Bd 9943 οἴονται 1i 4 τοῦ om. A τῷ ATBInEP:
ὃ ABd 7 ἐν BdnP*: om. AB*: ἕν coni, Mure γένει ABdnP*:
γένη A? B? 9 xai?] κατὰ n γε) γένος n? 10 γραμμαί A BdE PS
ἔχομεν d τοιανδί BAE SPS: τοιανδή A: τοιανδέ A? II xe@paom. A
I3 yàp om. d 14 δὲ- καὶ d 16 τὸξ] τοῦ n 17 & fecit A
19 3] xai n 20 ἐπ᾿ ἴσον AnE: eniowy Bd ὀρθὰς εἶναι ἴσας d
21 τὰς A*duE: rà AB μέσον" E τὸ πρῶτον n
r7
16. 98°30— 18. 99^r1
^ ^ > ~ ^
yos τοῦ πρώτου axpov, διὸ πᾶσαι αἱ ἐπιστῆμαι δι᾽ ὁρισμοῦ
, H * - Ld > ri 6. ^ ~ > Là
γίγνονται. οἷον τὸ φυλλορροεῖν ἅμα ἀκολουθεῖ τῇ ἀμπέλῳ
καὶ ὑπερέχει, καὶ συκῇ, καὶ ὑπερέχει: ἀλλ᾽ οὐ πάντων,
ἀλλ᾽ ἴσον. εἰ δὴ λάβοις τὸ πρῶτον μέσον, λόγος τοῦ φυλ- 25
λορροεῖν ἐστιν. ἔσται γὰρ πρῶτον μὲν ἐπὶ θάτερα μέσον, ὅτι
τοιαδὶ ἅπαντα: εἶτα τούτου μέσον, ὅτι ὀπὸς πήγνυται ἤ τι
» ~ , > > M ‘ ^ ^ , M
ἄλλο τοιοῦτον. τί δ᾽ ἐστὶ τὸ φυλλορροεῖν; τὸ πήγνυσθαι τὸν
ἐν τῇ συνάψει τοῦ σπέρματος ὁπόν.
- > ^ ‘
'Emi δὲ τῶν σχημάτων ὧδε ἀποδώσει ζητοῦσι τὴν παρ- 3°
Li ~ , 7 M * LJ w ^ ^ € ,
ακολούθησιν τοῦ αἰτίου καὶ οὗ αἴτιον. ἔστω τὸ A τῷ B ὑπάρ-
, M 4 Li , ~ A $3 , δέ M *
xew παντί, τὸ δὲ B ἑκάστῳ τῶν A, ἐπὶ πλέον δέ. τὸ μὲν
δὴ B καθόλου ἂν εἴη τοῖς A: τοῦτο γὰρ λέγω καθόλου ᾧ
Ἂς 3 , ~ δὲ θόλι T ^ M A >
μὴ ἀντιστρέφει, πρῶτον δὲ καθόλου d ἕκαστον μὲν μὴ ἀντι-
, σ A > , A , ^ *
στρέφει, ἅπαντα δὲ ἀντιστρέφει καὶ παρεκτείνει. τοῖς δὴ 35
4 αἴτιον τοῦ Α τὸ Β. δεῖ ἄρα τὸ Α ἐπὶ πλέον τοῦ Β ἐπεκ-
, * A , r4 ^ LJ » ^ x , »
τείνειν" εἰ δὲ μή, τί μᾶλλον αἴτιον ἔσται τοῦτο ἐκείνου; εἰ
a Ll Li , ^ * L4 , ^ ^ L4
δὴ πᾶσιν ὑπάρχει τοῖς E τὸ A, ἔσται τι ἐκεῖνα ἕν ἅπαντα
L4 ^ , ^ , ~ L4 , ~ - T A A
ἄλλο τοῦ B. εἰ yàp μή, πῶς ἔσται εἰπεῖν ὅτι ᾧ τὸ E, τὸ
A παντί, ᾧ δὲ τὸ A, οὐ παντὶ τὸ E; διὰ τί γὰρ οὐκ ἔσται ggb
τι αἴτιον olov [τὸ A] ὑπάρχει πᾶσι τοῖς 4; ἀλλ᾽ dpa καὶ
A L4 σ 3 , ^ ~ * L4 A
τὰ E ἔσται τι ἕν; ἐπισκέψασθαι δεῖ τοῦτο, καὶ ἔστω τὸ I’.
» ,ὔ * ^ > - , LJ > , > ~ >
ἐνδέχεται δὴ τοῦ αὐτοῦ πλείω αἴτια εἶναι, ἀλλ᾽ οὐ τοῖς ad-
τοῖς τῷ εἴδει, οἷον τοῦ μακρόβια εἶναι τὰ μὲν τετράποδα 5
a x: w , A * x A A bl L4 ,
τὸ μὴ ἔχειν χολήν, rà δὲ πτηνὰ τὸ ξηρὰ εἶναι ἢ ἕτερόν
τι. 1
γ A , A Ψ ἧς Or L4 * b ,
Εἰ δὲ εἰς τὸ ἄτομον μὴ εὐθὺς ἔρχονται, Kat μὴ μόνον 7
a ‘A , , * L4 M M » , , » LÀ
ἕν τὸ μέσον ἀλλὰ πλείω, καὶ τὰ αἴτια πλείω. | πότερον δ᾽ αἴτιον 8,9
τῶν μέσων, τὸ πρὸς τὸ καθόλου πρῶ]τον ἢ τὸ πρὸς τὸ καθ᾽ o, 10
ἕκαστον, τοῖς καθ᾽ ἕκαστον; δῆλον δὴ ὅτι | τὸ ἐγγύτατα ἑκάστῳ 10,1
822 αἱ om. n 24 ὑπερέχει) ὑπάρχει n? 25 ἴσον Α435Ὲ : ἴσων
ABd 27 τοιαδὶ A*BEPS: τοιαδὴ Ad: rowedén πάντα π τούτου]
τοῦ πὶ ὅὄὅτι- ὁ 30 ἀποδόσει At 32 πλεῖον A BdEP* 330
BE:6 AB'dn 34 ἀντιστρέφει A? Bn An* : ἀντιστρέφῃ Ad ἀντιστρέφει
A*3 BnE : ἀντιστρέφειν Ad 35 xai A BdnEP : καὶ μὴ Pacius 36 a μὴ
ἐπὶ B! B AB'dP: β τῷ ὃ n, fort. B ἐπεκτείνειν scripsi : παρεκ-
τείνειν codd. P: an ὑπερεκτείνειν 38 55] δὲ δὴ n bara
ὑπάρχει ABA AnP: τὸ a τῷ ὃ ὑπάρχει yap n: τοῦ A ὑπάρχει vel τὸ B ὑπάρχει
coni. Hayduck: τοῦ τὸ A ὑπάρχειν coni. Mure: τὸ A seclusi 3 τὰ
BdAn*:ró An: τῷ B? ΕἸ εἴπερ ΒΞ δεῖ) δὴ AB dnl E 676...
τὸ AnE: rà .. . τῷ B: τοῦ... τὸ d 8 ἀλλ᾽ --εἰς Ald: +alei n
9 ro! om. n! 10 rois καθ᾽ ἕκαστον om. 4 δὴ om. & 11 τὸ A™ An:
τὰ BAEP: om. A
11,12
12, 13
13, 14
15
20
25
3e
35
loo*
ANAAYTIKQN YZTEPON B
- rj - * ‘ ^ εν * , e 7 ^
ᾧ αἴτιον. τοῦ yàp TO πρῶτον ὑπὸ τὸ καθόλου ὑπάρχειν τοῦτο
“ T ^ A ~ 4 t , LJ ~ M
αἴτιον, otov τῷ A τὸ Γ τοῦ τὸ B | ὑπάρχειν αἴτιον. τῷ μὲν
οὖν 4 τὸ Γ αἴτιον τοῦ A, τῷ δὲ Γ | τὸ B, τούτῳ δὲ αὐτό.
IK * * Ls ^ " > 8 L , t ,
epi μὲν οὖν συλλογισμοῦ Kai ἀποδείξεως, τί τε éká-
Tepóv ἐστι καὶ πῶς γίνεται, φανερόν, ἅμα δὲ καὶ περὶ ἐπι-
στήμης ἀποδεικτικῆς" ταὐτὸν γάρ ἐστιν. περὶ δὲ τῶν ἀρχῶν,
^ y [4 ^
πῶς T€ γίνονται γνώριμοι Kal Tis ἡ γνωρίζουσα ἕξις, ἐντεῦ-
θεν ἔσται δῆλον προαπορήσασι πρῶτον.
Ὅτι μὲν οὖν οὐκ ἐνδέχεται ἐπίστασθαι δι’ ἀποδείξεως
* * ^ » LJ
μὴ γιγνώσκοντι τὰς πρώτας ἀρχὰς Tas ἀμέσους, εἴρηται
~ ^ ,
πρότερον. τῶν δ᾽ ἀμέσων τὴν γνῶσιν, Kal πότερον ἡ αὐτή
ἐστιν ἣ οὐχ ἡ αὐτή, διαπορήσειεν dv τις, καὶ πότερον ἐπι-
, ¥. , hd L4 ^ ^ * γ᾽ , -^ δ᾽ μι , ,
στήμη ἑκατέρου [7 ov], ἢ τοῦ μὲν ἐπιστήμη ToU δ᾽ ἕτερόν τι yé-
vos, καὶ πότερον οὐκ ἐνοῦσαι αἱ ἕξεις ἐγγίνονται T) ἐνοῦσαι
, , * M μὴ , , L4 ,
λελήθασιν. εἰ μὲν δὴ ἔχομεν αὐτάς, ἄτοπον: cupBatver
γὰρ ἀκριβεστέρας ἔχοντας γνώσεις ἀποδείξεως λανθάνειν.
εἰ δὲ λαμβάνομεν μὴ ἔχοντες πρότερον, πῶς av γνωρίζοι-
μεν καὶ μανθάνοιμεν ἐκ μὴ προὔπαρχούσης γνώσεως; ἀδύ-
P» o x δ᾽... ~ > , » ,
varov ydp, ὥσπερ Kal ἐπὶ τῆς ἀποδείξεως ἐλέγομεν. φα-
νερὸν τοίνυν ὅτι οὔτ᾽ ἔχειν οἷόν τε, οὔτ᾽ ἀγνοοῦσι καὶ μηδεμίαν
ἔχουσιν ἕξιν ἐγγίγνεσθαι. ἀνάγκη ἄρα ἔχειν μέν τινα δύνα-
μιν, μὴ τοιαύτην δ᾽ ἔχειν ἣ ἔσται τούτων τιμιωτέρα κατ᾽
ἀκρίβειαν. φαίνεται δὲ τοῦτό γε πᾶσιν ὑπάρχον τοῖς ζῴοις.
LÀ a , , , ^ ^ LÀ
ἔχει yàp δύναμιν σύμφυτον κριτικήν, ἣν καλοῦσιν αἴσθησιν"
ἐνούσης δ᾽ αἰσθήσεως τοῖς μὲν τῶν ζῴων ἐγγίγνεται μονὴ τοῦ
αἰσθήματος, τοῖς δ᾽ οὐκ ἐγγίγνεται. ὅσοις μὲν οὖν μὴ ἐγγί-
γνεται, ἢ ὅλως ἣ περὶ ἃ μὴ ἐγγίγνεται, οὐκ ἔστι τούτοις γνῶ-
ΜΝ ~ , , » Ld » μὰ > , »
ats ἔξω ToU αἰσθάνεσθαι: ἐν οἷς δ᾽ ἔνεστιν αἰσθομένοις ἔχειν
ἔτι ἐν τῇ ψυχῇ. πολλῶν δὲ τοιούτων γινομένων ἤδη διαφορά
^ > ~ ~
τις γίνεται, ὥστε Tots μὲν γίνεσθαι λόγον ἐκ τῆς τῶν τοιού-
bir d ΑΒάμξερ : om. n Ane τὸξ A’nP: τοῦ ABd 12 τῷ
fecit B B]a A? 13 τῷ fecit B τὸ y] roo B! τῷ fecit B
14 y B! αὐτὸ ABnEP: αὐτῷ d: τὸ αὐτὸ Ane 15 τῇ ὅ τι ἢ
19 ἐστι ABA 22 διὰ μέσων A} 23 dv om. A 24 ἣ οὔ
seclusi, om. fort. EP 25 ἣ ἐνουσίαι A! 27 ἔχοντες -ἰ τὰς d
30 λέγομεν A 31 ἀγνοοῦμεν οὖσιν καὶ n 32 τι η 34 yeom. n
ἃς ἔχει om. n! 37 ἐγγίνηται A} 38 ὅλοις d ἐγγινηται Αἱ
39 ἔστιν B?Pc αἰσθομένοις coni. Ueberweg, habet ut vid. An: aloBavo-
μένοις codd. : μὴ αἰσθομένοις coni. Trendelenburg 10081 ἔτι AE PS
et ut vid. TZ: ἔν τι dn, fecit B: τι An poxitev nm P γινομένων
dn Pe
19
18. g9^1r1— 19. 100517
TOV μονῆς, Tots δὲ μή. 3
E * - ? , , ,
k μὲν οὖν αἰσθήσεως γίνεται μνήμη, 3
ὥσπερ λέγομεν, ἐκ δὲ μνήμης πολλάκις τοῦ αὐτοῦ γινομέ-
νης ἐμπειρία: ai γὰρ πολλαὶ μνῆμαι τῷ ἀριθμῷ ἐμπειρίας
μία ἐστίν. ἐκ δ᾽ ἐμπειρίας 7j ἐκ παντὸς ἠρεμήσαντος τοῦ κα-
θόλου ἐν τῇ ψυχῇ, τοῦ ἑνὸς παρὰ τὰ πολλά, ὃ ἂν ἐν ἅπα-
σιν ἕν ἐνῇ ἐκείνοις τὸ αὐτό, τέχνης ἀρχὴ καὶ ἐπιστήμης,
ἐὰν μὲν περὶ γένεσιν, τέχνης, ἐὰν δὲ περὶ τὸ Ov, ἐπιστήμης.
οὔτε δὴ ἐνυπάρχουσιν ἀφωρισμέναι αἱ ἕξεις, οὔτ᾽ am’ dÀ- 10
λων ἕξεων γίνονται γνωστικωτέρων, ἀλλ᾽ ἀπὸ αἰσθήσεως,
οἷον ἐν μάχῃ τροπῆς γενομένης ἑνὸς στάντος ἕτερος ἔστη, εἶθ᾽
b4 b4 *» * Li ^ « A M € "d ,
ἕτερος, ἕως ἐπὶ ἀρχὴν ἦλθεν. ἡ δὲ ψυχὴ ὑπάρχει τοιαύτη
T7 . , , ^ ^ , 3 7 x ,
οὖσα ola δύνασθαι πάσχειν τοῦτο. ὃ δ᾽ ἐλέχθη μὲν πάλαι,
> ^ A > , , LJ »* A ~
od σαφῶς δὲ ἐλέχθη, πάλιν εἴπωμεν. στάντος yap τῶν 15
> , e ~ * *, ^ ~ , * x
ἀδιαφόρων ἑνός, πρῶτον μὲν ev τῇ ψυχῇ καθόλου (καὶ yap
» θ id A x p L4 e δ᾽ " θ ^ ,
αἰσθάνεται μὲν τὸ καθ᾽ ἕκαστον, ἡ δ᾽ αἴσθησις τοῦ καθόλου
ἐστίν, οἷον ἀνθρώπου, ἀλλ᾽ οὐ Καλλίου ἀνθρώπου): πάλιν ἐν τού- 100?
τοις ἵσταται, ἕως ἂν τὰ ἀμερῆ στῇ καὶ τὰ καθόλου, οἷον τοι-
M ~ - ~ * > , e , ~ A Ld
ονδὶ ζῷον, ἕως ζῷον, καὶ ἐν τούτῳ ὡσαύτως. δῆλον δὴ ὅτι
ἡμῖν τὰ πρῶτα ἐπαγωγῇ γνωρίζειν ἀναγκαῖον: καὶ γὰρ
ἡ αἴσθησις οὕτω τὸ καθόλου ἐμποιεῖ. 5
E, M * ~ M A
Tei δὲ τῶν περὶ τὴν 5
διάνοιαν ἕξεων αἷς ἀληθεύομεν ai μὲν ἀεὶ ἀληθεῖς εἰσιν,
αἱ δὲ ἐπιδέχονται τὸ ψεῦδος, οἷον δόξα καὶ λογισμός, ἀληθῆ
δ᾽ ἀεὶ ἐπιστήμη καὶ νοῦς, καὶ οὐδὲν ἐπιστήμης ἀκριβέστερον
» n ^ - e > > 4 ‘ea , " n
ἄλλο γένος ἢ νοῦς, αἱ δ᾽ ἀρχαὶ τῶν ἀποδείξεων γνωριμώ-
Tepdi, ἐπιστήμη δ᾽ ἅπασα μετὰ λόγου ἐστί, τῶν ἀρχῶν ἐπι-
P4 ^ % -^ LJ > * δ᾽ δὲ ar 8 , * ὃ δ H
στήμη μὲν οὐκ ἂν εἴη, ἐπεὶ δ᾽ οὐδὲν ἀληθέστερον ἐνδέχεται el-
-
o
vat ἐπιστήμης ἢ νοῦν, νοῦς ἂν εἴη τῶν ἀρχῶν, ἔκ re τούτων
“- 4 e , ’ > * » > , L4 > 10.»
σκοποῦσι καὶ ὅτι ἀποδείξεως ἀρχὴ οὐκ ἀπόδειξις, ὥστ᾽ οὐδ
? , , , , T. A LÀ » > , ,
ἐπιστήμης ἐπιστήμη. εἰ οὖν μηδὲν ἄλλο παρ᾽ ἐπιστήμην yé-
νος ἔχομεν ἀληθές, νοῦς ἂν εἴη ἐπιστήμης ἀρχή. καὶ ἡ μὲν τς
ἀρχὴ τῆς ἀρχῆς εἴη ἄν, ἡ δὲ πᾶσα ὁμοίως ἔχει πρὸς τὸ
πᾶν πρᾶγμα.
a6 δ᾽ codd. 4555: δὲ τῆς ΡΞ ἣ ἐκ παντὸς AB, fecitn: ἢ ἐκτὸς d: om. An
ἠρεμήσαντος A3 Bn An: ἠρεμίσαντος A: ἀριθμήσαντος d 8 ἐν ἐνῇ] fn:
evan? 11 αἰσθήσεων-" ws ft 16 διαφορῶν Al = uévom.m br ἐν
codd. E«P*: δ᾽ ἐν coni. Trendelenburg 2 τοιονδὶ A? Bn AncE : τοιονδὴ
A: τοιονδὲ d: τοιόνδε PC 4 ἡμῖν) ἡ μὲν ALB 5 ἡ 5“: καὶ
ABd ἐπὶ πὶ ἡ ἐνδέχονται d: δέχονται n II μὲν- ἐπιστήμης d
16 ἅπασα n 17 ἅπαν AB: om. d
CONSPECTUS OF THE CONTENTS
ANALYTICA PRIORA
BOOK I
A. STRUCTURE OF THE SYLLOGISM
1. Preliminary discussions
1 Subject and scope of the Analytics. Definitions of funda-
mental terms.
2 Conversion of pure propositions.
3 Conversion of modal propositions.
2. Exposition of the three figures
4-6 Assertoric syllogisms, in the three figures.
7 Common properties of the three figures.
8 Syllogisms with two apodeictic premisses.
9-11 Syllogisms with one apodeictic and one assertoric premiss,
in the three figures.
12 The modality of the premisses leading to assertoric or
apodeictic conclusions.
13 Preliminary discussion of contingency.
14-16 Syllogisms with two problematic premisses, with one
problematic and one assertoric premiss, with one prob-
lematic and one apodeictic premiss, in the first figure.
17-19 The same, in the second figure.
20-2: The same, in the third figure.
3. Supplementary discussions
23 Every syllogism is in one of the three figures, and reducible
to a universal mood of the first figure.
24 Quality and quantity of the premisses.
25 Number of the terms, premisses, and conclusions.
26 The kinds of proposition to be proved or disproved in each
figure.
B. MODE OF DISCOVERY OF ARGUMENTS
1. General
27 Rules for categorical syllogisms, applicable to all problems.
28 Rules for categorical syllogisms, peculiar to different prob-
lems.
29
30
m
39
I
CONSPECTUS OF THE CONTENTS 281
Rules for reductio ad impossibile, hypothetical syllogisms, and
modal syllogisms.
2. Proper to the several sciences and arts
Division.
C. RESOLUTION OF ARGUMENTS
. Resolution of arguments into figures and moods of syllogism
Rules for the choice of premisses, middle term, and figure.
Error of supposing that what is true of a subject in one respect
is true of it without qualification.
Error due to confusion between abstract and concrete terms.
Expressions for which there is no one word.
The nominative and the oblique cases.
The various kinds of attribution.
The difference between proving that a thing can be known,
and proving that it can be known to be so-and-so.
Substitution of equivalent expressions.
The difference between proving that B is A and proving that
Bis the A.
The difference between ‘A belongs to all of that to which B
belongs’ and ‘A belongs to all of that to all of which B
belongs’. The ‘setting out’ of terms is merely illustrative.
Analysis of composite syllogisms.
In discussing definitions, we must attend to the precise
point at issue.
Hypothetical arguments are not reducible to the figures.
2. Resolution of syllogisms in one figure into another
3. Resolution of arguments involving the expressions
‘ts not A’ and ‘ts a not- A'
BOOK II
A. PROPERTIES OF SYLLOGISM
More than one conclusion can sometimes be drawn from the
same premisses.
2-4 True conclusions from false premisses, in the three figures.
5-7 Reciprocal proof (i.e. inference of one premiss from the
conclusion and the converse of the other premiss), applied
to the three figures.
8-10 Conversion (i.e. inference of the opposite of one premiss
from the other premiss and the opposite of the conclusion),
applied to the three figures.
282 CONSPECTUS OF THE CONTENTS
11-13 Reductio ad impossibile in the three figures.
14 The relations between ostensive proof and reductio ad 1m-
possibile.
15 Reasoning from a pair of opposite premisses.
B. FALLACIES, ETC.
16 Fallacy of petitio principa.
17-18 Fallacy of false cause.
19-20 Devices to be used against an opponent in argument.
21 How ignorance of a conclusion can coexist with knowledge of
the premisses.
22 Rules for the use of convertible terms and of alternative
terms, and for the comparison of desirable and undesirable
objects.
C. DIALECTICAL MODES OF ARGUMENT REDUCIBLE TO THE THREE
FIGURES OF SYLLOGISM
23 Induction.
24 Argument from an example.
25 Reduction of one problem to another.
26 Objection.
27 Inference from signs.
ANALYTICA POSTERIORA
BOOK I
A. THE ESSENTIAL NATURE OF DEMONSTRATIVE SCIENCE
The student's need of pre-existent knowledge. Its nature.
The nature of scientific knowledge and of its premisses.
3 Two errors—the view that knowledge is impossible because
it involves an infinite regress, and the view that circular
demonstration is satisfactory.
4 The premisses of demonstration must be such that the
predicate is true of every instance of the subject, true of
the subject fer se, and true of it precisely qua itself.
5 How we fall into, and how we can avoid, the error of thinking
our conclusion a strict universal proposition when it is not.
6 The premisses of demonstration must state necessary con-
nexions.
hom
-
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
CONSPECTUS OF THE CONTENTS 283
B. PROPERTIES OF DEMONSTRATIVE SCIENCE
The premisses of demonstration must state essential attri-
butes of the same genus of which a property is to be proved.
Only eternal connexions can be demonstrated.
The premisses of demonstration must be peculiar to the
science in question, except in the case of subaltern sciences.
The different kinds of ultimate premiss required by a science.
The function of the most general axioms in demonstration.
Error due to assuming answers to questions inappropriate to
the science distinguished from that due to assuming wrong
answers to appropriate questions, or to reasoning wrongly
from true and appropriate assumptions. How a science
grows.
Knowledge of fact and knowledge of reasoned fact.
The first figure is the figure of scientific reasoning.
There are negative as well as affirmative propositions that
are immediate and indemonstrable.
C. ERROR AND IGNORANCE
Error as inference of conclusions whose opposites are im-
mediately true.
Error as inference of conclusions whose opposites can be
proved to be true.
Lack of a sense must involve ignorance of certain universal
propositions which can only be reached by induction from
particular facts.
D. FURTHER PROPERTIES OF DEMONSTRATIVE SCIENCE
Can there be an infinite chain of premisses in a demonstra-
tion, (1) if the primary attribute is fixed, (2) if the ultimate
subject is fixed, (3) if both terms are fixed?
There cannot be an infinite chain of premisses if both ex-
tremes are fixed.
If there cannot be an infinite chain of premisses in affirmative
demonstration, there cannot in negative.
There cannot be an infinite chain of premisses in affirmative
demonstration if either extreme is fixed.
Corollaries from the foregoing propositions.
Universal demonstration is superior to particular.
Affirmative demonstration is superior to negative.
Ostensive demonstration is superior to reductto ad impossibile.
The more abstract science is superior to the less abstract.
284 CONSPECTUS OF THE CONTENTS
28 What constitutes the unity of a science.
29 How there may be several demonstrations of one connexion.
30 Chance conjunctions are not demonstrable.
31 There can be no demonstration through sense-perception.
32 All syllogisms cannot have the same first principles.
E. STATES OF MIND TO BE DISTINGUISHED FROM SCIENTIFIC
KNOWLEDGE
33 Opinion.
34 Quick wit.
BOOK II
A. THE RELATION OF DEMONSTRATION TO DEFINITION
1. The possible types of inquiry
1 There are four types.
2 They are all concerned with a middle term.
2. Aporematic consideration of the relation of demonstration to
definition
3 There is nothing that can be both demonstrated and defined.
4 It cannot be demonstrated that a certain phrase is the defini-
tion of a certain term.
5 It cannot be shown by division that a certain phrase is the
definition of a certain term.
6 Attempts to prove the definition of a term by assuming the
definition either of definition or of the contrary term beg the
question.
7 Neither definition and syllogism nor their objects are the
same ; definition proves nothing ; knowledge of essence can-
not be got either by definition or by demonstration.
3. Positive consideration of the question
8 The essence of a thing that has a cause distinct from itself
cannot be demonstrated, but can become known by the
help of demonstration.
g What essences can and what cannot be made known by
demonstration.
το The types of definition.
B. CAUSES, AND THE METHOD OF DISCOVERY OF DEFINITIONS
1. Inference applied to cause and effect
11 Each of four types of cause can function as middle term.
12 The inference of past and future events.
CONSPECTUS OF THE CONTENTS 285
2. The uses of division
13 The use of division (a) for the finding of definitions.
14 The use of division (δ) for the orderly discussion of problems.
3. Further questions about cause and effect
ts One middle term will often explain several properties.
16 Where there is an attribute commensurate with a certain
subject, there must be a cause commensurate with the
attribute.
17-18 Different causes may produce the same effect, but not in
things specifically the same.
19 D. How wE COME BY THE APPREHENSION OF FIRST
PRINCIPLES
TABLE OF THE VALID MOODS
THE following table is taken in the main, but with certain altera-
tions and additions, from A. Becker’s Die arist. Theorie der
Móglichkeitsschlüsse. A stands for a universal affirmative pro-
position, E for a universal negative, I for a particular affirmative,
O for a particular negative. A", Ac, AP stand for propositions of
the form That all S be P is necessary, contingent (neither impos-
sible nor necessary), possible, E^, Ee, Ep for those of the form
That no S be P is necessary, contingent, possible, I^, Iv, IP for
those of the form That some S be P is necessary, contingent,
possible, O^, Oc, OP for those of the form That some S be not P
is necessary, contingent, possible.
P.S. = perfect (self-evident) syllogism. C. = reduce by con-
version. R. = reduce by reductio ad impossibile. C.C. = reduce
by complementary conversion (i.e. by converting ‘For all S, not
being P is contingent’ into ‘For all S, being P is contingent’, or
"For some S, not being P is contingent’ into ‘For some S, being P
is contingent’. Ec. = prove by ἔκθεσις.
Whenever an apodeictic and a problematic premiss yield an
assertoric conclusion, they yield a fortiori a conclusion of the form
It is possible that . . ., and Aristotle sometimes but not always
points this out.
Apart from certain syllogisms which are easily seen to be
validated by complementary conversion, and which for that
reason Aristotle does not trouble to mention, the only valid
syllogism he omits is EI^O in the second figure.
COMMENTARY
ANALYTICA PRIORA
BOOK I
CHAPTER 1
Subject and scope of the Analytics. Definitions of fundamental
terms
24°10. Our first task is to state our subject, which ts demonstra-
tion; next we must define certain terms.
16. A premiss is an affirmative or negative statement of some-
thing about something. A universal statement is one which says
that something belongs to every, or to no, so-and-so; a particular
statement says that something belongs to some, or does not
belong to some (or does not belong to every), so-and-so; an
indefinite statement says that something belongs to so-and-so,
without specifying whether it is to all or to some.
22. A demonstrative premiss differs from a dialectical one, in
that the former is the assumption of one of two contradictories,
while the latter asks which of the two the opponent admits; but
this makes no difference to the conclusion’s being drawn, since in
either case something is assumed to belong, or not to belong, to
something.
28. Thus a syllogistic premiss is just the affirmation or denial
of something about something ; a demonstrative premiss must in
addition be true, and derived from the original assumptions; a
dialectical premiss is, when one is inquiring, the asking of a pair
of contradictories, and when one is inferring, the assumption of
what is apparent and probable.
516. A term is that into which a premiss is analysed (i.e. a
subject or predicate), 'is' or 'is not' being tacked on to the terms.
18. A syllogism is a form of speech in which, certain things
being laid down, something follows of necessity from them, i.e.
because of them, i.e. without any further term being needed to
justify the conclusion.
22. A perfect syllogism is one that needs nothing other than the
premisses to make the conclusion evident ; an imperfect syllogism
needs one or more other statements which are necessitated by the
given terms but have not been assumed by way of premisses.
26. For B to be in A as in a whole is the same as for A to be
288 COMMENTARY
predicated ot all B. A is predicated of all B when there is no B
of which A will not be stated; ‘predicated of no B’ has a corre-
sponding meaning.
24*10-11. Πρῶτον... ἀποδεικτικῆς. A. here treats the Prior and
the Posterior Analytics as forming one continuous lecture-course
or treatise ; for it is not till he reaches the Posterior Analytics that
he discusses demonstration; in the Prior Analytics he discusses
syllogism, the form common to demonstration and dialectic.
τίνος . . . σκέψις might mean either ‘what the study is a study of’
(τίνος being practically a repetition of περὶ τί), or ‘to what science
the study belongs. Maier (2 a. 1 n.), taking τίνος, and therefore
also ἐπιστήμης ἀποδεικτικῆς, in the latter way, as subjective
genitives, renders the latter phrase ‘the demonstrative science’.
But to name logic by this name would be quite foreign to A.'s
usage; ἐπιστήμη ἀποδεικτική is demonstrative science in general
(cf. An. Post. 99't5-17), and the genitives must be objective.
εἰπεῖν... διορίσαι. A. not infrequently uses the infinitive
thus, to indicate a programme he is setting before himself, the
infinitive taking the place of a gerund; cf. Top. 106210, ^13, 21, etc.
The imperatival use of the infinitive is explained by Kühner,
Gr. Gramm. ii. 2. 19-20.
16. Πρότασις. The word apparently does not occur before A.
In A. it is found already in De Int. 20623, 24, Top. 101515-37,
1043-37, etc. A πρότασις is defined, as here, as one of a pair of
contradictory statements (ἀντιφάσεως μιᾶς μόριον, De Int. 20b24).
That is its form, and as for its function, it is something to which
one party in a discussion asks the other whether he assents (De
Int. z0b22-3). Strictly, it differs from a πρόβλημα in that it is
stated in the form ‘Is A B?', while a πρόβλημα is in the form
‘Is A B, or not?’ (Top. 101528-34); but in some of the other
passages of the Topics προτάσεις are stated in the form said to be
proper to προβλήματα. Further, it appears that the function of
προτάσεις is to serve as starting-points for argument. Thus the
Aristotelian usage of the term πρότασις is already to be found in
works probably earlier than the Prior Amalytics, though it is
only now that constant use begins to be made of the term.
The usage is derived from a usage of προτείνειν as meaning
*put forward for acceptance'; but of this again as applied to
statements we have no evidence earlier than A. In A. it is not
uncommon, especially in the Topics; προτείνεσθαι occurs once in
the same sense (16454). The only other usage of πρότασις which
it is worth while to compare (and contrast) with this is the use
I. 1. 24310— 514 289
of it in the astronomer Autolycus 2. 6 (c. 310 B.C.) and in later
writers, to denote the enunciation of a proposition to be proved.
17. οὗτος δὲ ἢ καθόλου ἢ ἐν μέρει ἢ ἀδιόριστος. In De Int. 7a
different classification of propositions in respect of quantity is
given. Entities (rà πράγματα) are divided into rà καθόλου and
τὰ καθ᾽ ἕκαστον, and propositions are divided into (1) those about
universals; (2) predicated universally, (b) predicated non-univer-
sally ; (2) those about individuals. This is the basis of the common
doctrine of formal logic, that judgements are universal, parti-
cular, or singular. The treatment of the matter in the Prior
Analytics is by comparison more formal. It ignores the question
whether the subject of the judgement is a universal or an indivi-
dual, and classifies judgements according as the word ‘all’, or the
word ‘some’, or neither, is attached to the subject ; and the judge-
ments in which neither ‘all’ nor ‘some’ appears are not, as might
perhaps be expected, those about individuals, but judgements
like ‘pleasure is not good’, where the subject is a universal. In
fact the Prior Analytics entirely ignores judgements about indi-
viduals, and the example of a syllogism which later was treated
as typical—Man is mortal, Socrates is a man, Therefore Socrates
is mortal—is quite different from those used in the Prior Analytics,
which are all about universals, the minor term being a species.
A.’s reason for confining himself to arguments about universals
probably lies in the fact mentioned in 43242-3, that ‘discussions
and inquiries are mostly about species’.
21. τὸ τῶν évavriov . . . ἐπιστήμην. The Greek commentators
rightly treat not 'the same science' but 'contraries' as the logical
subject of the statement, which is ἀδιόριστος because it says τῶν
ἐναντίων and not πάντων τῶν (or τινῶν) ἐναντίων (Am. 18. 28-33,
P. 2o. 25).
22-5. διαφέρει... ἐστιν. Demonstration firmly assumes the
truth of one of two contradictories as self-evident (or following
from something self-evident); in dialectic the person who is
trying to prove something asks the other party ‘Is A B?’, and
is prepared to argue from ‘A is B’ or from ‘A is not B’, according
as the interlocutor is willing to admit one or the other.
26. ἑκατέρου, i.e. τοῦ τε ἀποδεικνύοντος καὶ τοῦ ἐρωτῶντος.
bx2. ἐν τοῖς Τοπικοῖς εἴρηται, i.e. in 100227—30, το458.
13-14. τί διαφέρει... διαλεκτική. συλλογιστικὴ πρότασις is the
genus of which the other two are species.
14. Bv ἀκριβείας... ῥηθήσεται. What distinguishes demon-
strative from dialectical premisses is discussed in the Posterior
Analytics (especially 1. 4-12).
4985 U
290 COMMENTARY
16. "Opov. dpos in the sense of ‘term of a proposition’ seems not
to occur before A., nor, in A., before the Analytics. It was
probably used in this sense by an extension from its use to
signify the terms of a ratio, as in Archytas 2 éxxa ἔωντι τρεῖς ὅροι
κατὰ τὰν τοίαν ὑπεροχὰν ava λόγον. This arithmetical usage may
itself have developed from the use of ópos for the notes which
form the boundaries of musical intervals, as in Pl. Rep. 443d
ὥσπερ ὅρους τρεῖς ἁρμονίας. . ., veárgs τε kai ὑπάτης Kal μέσης,
Phileb. 1; ἃ τοὺς ὅρους τῶν διαστημάτων. The arithmetical usage
is found in A. (e.g. ΕΝ. 113155 ἔσται ἄρα ὡς 6 a ὅρος πρὸς τὸν
B, οὕτως 6 y πρὸς τὸν δ, cf. ib. 9, 16). It also occurs in Euclid
(e.g. V, Def. 8), and if we had more of the early Greek mathematical
writings we might find it established before A.'s time. His log?cal
usage of the word is no doubt original, as, indeed, ὅρον δὲ καλῶ
suggests. It belongs to the same way of thinking as his use of
ἄκρα for the terms and of διάστημα for the proposition, of ἐμπίπτειν,
παρεμπίπτειν, ἐμβάλλεσθαι, and καταπυκνοῦσθαι, of μείζων and
ἐλάττων (ὅρος), of πρῶτον, μέσον, and ἔσχατον.
The probable development of the logical usage of these
words from a mathematical usage as applied to progressions
is discussed at length by B. Einarson in 4./.P. lvii (1936),
155—64.
16-17. olov . . . κατηγορεῖται, The technical sense of κατη-
yopetv is already common in the Categories and in the Tofics.
It does not occur before A., but is an easy development from the
use of κατηγορεῖν τί τινος (κατά τινος, περί τινος), ‘to accuse some-
one of something’.
17-18. προστιθεμένου... μὴ εἶναι. The vulgate reading ἢ
προστιθεμένου ἢ διαιρουμένου τοῦ εἶναι xai μὴ εἶναι betrays its
incorrectness at two points. (1) The true opposite of προστι-
θεμένου, both according to A.’s usage and according to the nature
of things, is not διαιρουμένου but ἀφαιρουμένου ; (2) even if ἀφαιρου-
μένου be read, the text would have to be supposed to be an
ilogical confusion of two ways of saying the same thing, 7
προστιθεμένου ἢ ἀφαιρουμένου τοῦ εἶναι, and προστιθεμένου ἢ τοῦ
εἶναι 7j τοῦ μὴ εἶναι. A. can hardly be credited with so gross a
confusion, and though the Greek commentators agree in having,
substantially, the vulgate reading, they have great difficulty in
defending it. There are many other traces of interpolations which
were current even in the time of the Greek commentators (cf.
the apparatus criticus at ?17, 29, 3221-9, 3492-6). The text as
emended falls completely into line with such passages as De Int.
16716 καὶ yàp ὁ τραγέλαφος σημαίνει μέν τι, οὔπω δὲ ἀληθὲς ἢ ψεῦδος,
I. 1. 24516-24 291
ἐὰν μὴ τὸ εἶναι 7) μὴ εἶναι προστεθῇ, 21027 én” ἐκείνων τὸ εἶναι Kai
τὸ μὴ εἶναι προσθέσεις.
18-20. συλλογισμὸς ... εἶναι. The original meaning of συλλο-
γίζεσθαι is ‘to compute, to reckon up’, as in Hdt. 2. 148 τὰ ἐξ
᾿Ἑλλήνων τείχεά τε καὶ ἔργων ἀπόδεξιν συλλογίσαιτο. But in Plato
the meaning ‘infer’ is not uncommon, e.g. Grg. 479 c τὰ συμ-
Baivovra ἐκ τοῦ λόγου... σ., R. 516 b a. περὶ αὐτοῦ ὅτι κτλ. So too
in Plato we have συλλογισμός in the sense of ‘reasoning’, in Crat.
4128 σύνεσις. . . δόξειεν dv ὥσπερ σ. εἶναι, and in Tht. 186d ἐν
μὲν... τοῖς παθήμασιν οὐκ eve ἐπιστήμη, ἐν δὲ τῷ περὶ ἐκείνων σ. In
A. συλλογίζεσθαι and συλλογισμός, in the sense of ‘reasoning’ are
both rare in the Topics (συλλογίζεσθαι 101*4, 153%8, 157535-0,
160623, συλλογισμός i. and 12 passim, 13077, 139°30, 156?20, 21,
157518, >38, 1588-30), but common in the Sophistics Elenchi. It has
sometimes been thought that the parts of the Topics in which the
words occur were added later, after the doctrine of the syllogism
had been discovered; but this is not necessary, since the words
occur already in Plato, and the developed Aristotelian doctrine
is not implied in the Topics passages.
The definition here given of συλλογισμός is wide enough to cover
all inference. Thus A. does not give a new meaning to the word;
but the detailed doctrine which follows gives an account of some-
thing much narrower than inference in general, since it excludes
both immediate inference and constructive inference in which
relations other than that of subject and predicate are used, as
in‘A = B, B=C, Therefore A =C’.
21-2. τὸ δὲ διὰ ταῦτα... ἀναγκαῖον. This excludes, as Al.
points out (21. 21-23. 2), (1) μονολήμματοι συλλογισμοί, enthymemes
in the modern sense of that word, such as ‘A is B, Therefore it
is C'; (2) what the Stoics called ἀμέθοδοι λόγοι, such as ‘A is
greater than B, B is greater than C, Therefore A is greater than
C’, where (according to Al.) another premiss is implied—‘that
which is greater than that which is greater than a third thing is
greater than the third thing’; (3) arguments of which the pre-
misses need recasting in order to bring them into syllogistic form,
e.g. ‘asubstance is not destroyed by the destruction of that which is
not a substance, A substance is destroyed by the destruction of its
parts, Therefore the parts of a substance are substances’ (4722-8).
22-4. τέλειον... ἀναγκαῖον. Superficially this definition of a
perfect syllogism looks as if it were identical with the definition of
a syllogism given in P18-2o. But if it were identical, this would
imply that so-called ἀτελεῖς συλλογισμοί (i.e. inferences in the
second and third figures) are not συλλογισμοί, while both *12-13
292 COMMENTARY
and 22-6 imply that they are. The solution of the difficulty lies
in noticing that φανῆναι τὸ ἀναγκαῖον is used in *24 in contrast
with γενέσθαι τὸ ἀναγκαῖον in the definition of syllogism. An
imperfect syllogism needs the introduction of no further pro-
position (ἔξωθεν ὅρου) to guarantee the truth of the syllogism,
but it needs it to make the conclusion obvious. The position of
imperfect syllogisms is quite different from that of the non-
syllogistic inferences referred to in >21-2n. The latter need
premisses brought in from outside; the former need, in order that
their conclusions may be clearly seen to follow, the drawing out
(by conversion) of premisses implicit in the given premisses, or
an indirect use of the premisses by reductio ad impossibile.
26. οὐ μὴν εἴληπται διὰ προτάσεων, ‘but have not been secured
by way of premisses’.
26-8. τὸ δὲ... ἐστιν, ‘for A to be in B as in a whole is the
same as for B to be predicated of every A’. If ‘animal’ is pre-
dicated of every man, man is said to be in animal as in a whole
to which it belongs. That this is the meaning of ἐν ὅλῳ εἶναι is
clear from 2532-5.
29. τοῦ ὑποκειμένου. Al's commentary (24. 27-30) implies
that he did not read these words (which are absent also from his
quotations of the passage in 167. 17, 169. 25) ; and their presence
in the MSS. is due to Al.’s using the phrase τοῦ ὑποκειμένου in his
interpretation. The sense is conveyed sufficiently without these
words.
CHAPTER 2
Conversion of pure propositions
25:1. Every proposition (A) states either that a predicate
belongs, that it necessarily belongs, or that it admits of belonging,
to a subject, (B) is either affirmative or negative, and (C) either
universal, particular, or indefinite.
S. Of assertoric statements, (1) the universal negative is con-
vertible, (2) the universal affirmative is convertible into a par-
ticular, (3) so is the particular affirmative, (4) the particular
negative is not convertible.
14. (1) If no B is A4, no A is B. For if some A (say C) is B, it
will not be true that no B is A; for C isa B.
17. (2) If all Bis A, some A is B. Forifno A is B, no Bis 4;
but ex hypothesi all B is A.
20. (3) If some B is 4, some A is B. Forif no A is B, no B is A.
22. (4) If some B is not A, it does not follow that some A is
not B. Not every animal is a man, but every man is an animal.
I. 1. 24526 — 2. 25334 293
2573. καθ᾽ ἑκάστην πρόσρησιν, in respect of each of these
phrases added to the terms, ie. ὑπάρχει, ἐξ ἀνάγκης ὑπάρχει,
ἐνδέχεται ὑπάρχειν. πρόσθεσις is used similarly in De Int. 21927, 30.
6. ἀντιστρέφειν. Six usages of this word may be distinguished
in the Analytics. (1) It is used, as here, of the conversion or
convertibility of premisses. (2) It is used in the closely associated
sense of the conversion or convertibility of terms. (3) It is used
of the substitution of one term for another, without any suggestion
of convertibility. (4) It is used of the inference (pronounced to
be valid) from a proposition of the form 'B admits of (ἐνδέχεται)
being A’ to one of the form ‘B admits of not being A’, or vice
versa. (5) It is used of the substitution of the opposite of a
proposition for the proposition, without (of course) any suggestion
that this is a valid inference. (6) By combining the meaning ‘change
of direction’ (as in (1) and (2)) with the meaning ‘passage from
a proposition to its opposite’, we find the word used of an argu-
ment in which from one premiss of a syllogism and the opposite of
the conclusion the opposite of the other premiss is proved.
Typical examples of these usages are given in the Index.
14-17. llpàrov . . . ἐστιν. The proof that a universal negative
can be simply converted is by ἔκθεσις, i.e. by supposing an imagin-
ary instance, in this case a species of A of which B is predicable.
‘Ifno Bis A,no A is B. For if there is an A, say C, which is B,
it will not be true that no B is A (for C is both a B and an 4);
but ex hypothesi no B is an A.’
15-34. εἰ οὖν... ὑπάρχοι. In this and in many other passages
the manuscripts are divided between such forms as 7@ A and
τῶν A before or after τινί, οὐδενί, or μηδενὶ ὑπάρχει. The sense
affords no reason why A. should have written sometimes τῷ
and sometimes τῶν; we should expect one or other to appear
consistently. The following points may be noted: (1) in still
more passages the early manuscripts agree in reading τῷ. (2) Al.
has 7@ almost consistently (e.g. in 31. 2, 3, 7, 21, 23, 24, 26; 32.
12 (bis), 13, 19, 24 (bis), 28; 33. 20; 34. 9, 11, 18, 19 (bis), 26 (bis),
27, 28, 29, 31; 35. 1, 16, 25, 26, 27; 36. 4, 6; 37. 10 (bis), 13). (3) The
reading rà is supported by such parallels as μηδενὸς τοῦ B
(25940, 2659, 2736, 21, b6 (bis), 28233, 6o*1, or as μηδενὶ τῷ ἐσχάτῳ
(2625, 5). (4) 7@ is more in accord with A.'s way of thinking of the
terms of the syllogism; the subject he contemplates is A, the
class, not the individual A's. I have therefore read τῷ wherever
there is any respectable ancient authority for doing so.
294 COMMENTARY
CHAPTER 3
Conversion of modal propositions
2527. So too with apodeictic premisses ; the universal negative
is convertible into a universal, the affirmative (universal or parti-
cular) into a particular. For (1) if of necessity A belongs to no B,
of necessity B belongs to no A; for if it could belong to some 4,
A would belong to some B. If of necessity A belongs (2) to all or
(3) to some B, of necessity B belongs to some 4 ; for if this were
not necessary, A would not of necessity belong to any B. (4) The
particular negative cannot be converted, for the reason given
above.
37. What is necessary, what is not necessary, and what is
capable of being may all be said to be possible. In all these cases
affirmative statements are convertible just as the corresponding
assertoric statements are. For if A may belong to all or to some
B, B may belong to some 4; for if not, A could not belong to
any B.
b3. Aniong statements of negative possibility we must distin-
guish. When a non-conjunction of an attribute with a subject is
said to be possible (1) because it of necessity is the case or (2)
because it is not of necessity not the case (e.g. (1) 'it is possible
for a man not to be a horse' or (2) 'it is possible for white to belong
to no garment’), the statement is convertible, like the correspond-
ing assertoric proposition ; for if it is possible that no man should
be a horse, it is possible that no horse should be a man ; if it is
possible that no garment should be white, it is possible that
nothing white should be a garment; for if ‘garment’ were neces-
sarily predicable of something white, ‘white’ would be necessarily
predicable of some garment. The particulary negative is incon-
vertible, like an assertoric O proposition.
r4. But (3) when something is said to be possible because it
usually is the case and that is the nature of the subject, negative
statements are not similarly convertible. This will be shown later.
19. The statement ‘it is contingent for A to belong to no B’ or
‘for A not to belong to some B' is affirmative in form (‘is contin-
gent' answering to 'is', which always makes an affirmation, even
in a statement of the type ‘A is not- B^), and is convertible on the
same terms as other affirmatives.
25°29. ἑκατέρα, ie. both the universal and the particular
affirmative proposition.
29-34. εἰ μὲν γὰρ... ὑπάρχοι. Becker (p. 9o) treats this
I. 3. 25329 — "19 295
section as spurious on the ground that in 229-32 (1) ‘Necessarily
no B is A’ is said to entail (2) ‘Necessarily no A is B' because (3)
'Some A may be B' would entail (4) 'Some B may be A', while
in 240-53 (3) is said to entail (4) because (1) entails (2) ; and that
there is a similar circulus in probando in 232-4 when combined
with >ro-13. The charge of circulus must be admitted, but the
reasoning is so natural that the contention that A. could not have
used it is not convincing.
36. πρότερον ἔφαμεν, cf. *10-14.
37-19. "Emi δὲ τῶν ἐνδεχομένων . . . λέγωμεν. The difficulties
of this very difficult passage are largely due to the fact that A.,
in order to complete his discussion of conversion, discusses the
conversion of problematic propositions without stating clearly
a distinction between two senses of ἐνδέχεσθαι which he states
clearly enough in later passages. He has pointed out in ch. 2
that, of assertoric propositions, A propositions are convertible
per accidens, E and I propositions simply, and O propositions
not at all; and in 25?27-36 that the same is true of apodeictic
propositions. He now turns to consider the convertibility of
problematic propositions, i.e. whether a proposition of the form
ἐνδέχεται παντί (or tut) τῷ Bro A ὑπάρχειν (or μὴ ὑπάρχειν) entails
one of the form ἐνδέχεται παντί (or tet) τῷ A τὸ B ὑπάρχειν (or
μὴ ὑπάρχειν). This depends, he says, on the sense in which
ἐνδέχεται is used. At first sight it looks as if he distinguished three
senses, τὸ ἀναγκαῖον, τὸ μὴ ἀναγκαῖον, τὸ δυνατόν. But these are
plainly not three senses of ἐνδεχόμενον, which could not be said
ever to mean either ‘necessary’ or ‘not necessary’. He can only
mean that there are three kinds of case to which ἐνδεχόμενον can
be applied. When he says τὸ ἀναγκαῖον ἐνδέχεσθαι λέγομεν, he
clearly means that that which is necessary may a fortiori be said
to be possible. The reference of τὸ μὴ ἀναγκαῖον is less clear.
Al. and P. suppose it to refer to the existent, which can similarly
be said a fortiori to be possible. But that interpretation does not
square with the example given in 56—7, ἐνδέχεσθαι τὸ λευκὸν
μηδενὶ ἱματίῳ ὑπάρχειν. It is not a fact that no garment is white;
there is only a possibility that none should be so. What the
example illustrates is that which, without being necessary, is
possible in the sense of being not impossible. xai yap τὸ ἀναγκαῖον
Kal τὸ μὴ ἀναγκαῖον ἐνδέχεσθαι λέγομεν must be a brachylogical
way of saying 'Not only can we say of what is necessary that it
is possible, but we can (in the same sense, viz. that they are not
impossible) say this of things that are not necessary'.
These two applications of νυδέχεσθαι are what is illustrated in
296 COMMENTARY
bs—r3. We say, ‘For all men, not being horses is possible’, because
necessarily no man is a horse; and we say ‘For all garments, not
being white is possible’, because no garment is necessarily white.
In >4-5 the evidence is pretty equally divided between τῷ ἐξ
ἀνάγκης ὑπάρχειν 7 τῷ μὴ ἐξ ἀνάγκης ὑπάρχειν and τῷ ἐξ ἀνάγκης
μὴ ὑπάρχειν ἣ τῷ μὴ ἐξ ἀνάγκης ὑπάρχειν. The former reading
brings the text into line with 438; the latter brings it into line
with 57-8. But neither reading gives a good sense. While τὸ μὴ
ἀναγκαῖον in 338 may serve as a brachylogical way of referring
to one kind of case in which ἐνδέχεται may be used, τῷ μὴ ἐξ ἀνάγκης
ὑπάρχειν cannot serve as a reason for using it in that case.
Becker's insertion of μή (p. 87), in which a late hand in B has
anticipated him, alone gives the right sense. In 54-5 A. says that
some things are said to be possible because they are necessary,
others because they are not necessarily not the case; in 55-8 he
illustrates this by saying that it is said to be possible that no
man should be a horse because necessarily no man is so, and that
it is said to be possible that no garment should be white because
it is not necessary that any should. The variation of reading in
^4 and the omission in ὃς are amply accounted for by the fact that
these two applications of ἐνδέχεται are in 55-8 illustrated only by
examples of the possibility of not being something—these alone
being relevant to the point he is making about convertibility. Cf.
a similar corruption in 37435-6.
τὸ ἀναγκαῖον and τὸ μὴ ἀναγκαῖον (238) refer to two applica-
tions of one sense of ἐνδέχεται, that in which it means ‘is possible’,
ie. ‘is not impossible’; to what does τὸ δυνατόν refer? For this
we turn to A.’s main discussion of τὸ ἐνδεχόμενον. In 32318
he defines it as οὗ μὴ ὄντος ἀναγκαίου, τεθέντος δ᾽ ὑπάρχειν, οὐδὲν
ἔσται διὰ τοῦτ᾽ ἀδύνατον. Since that, and only that, which is im-
possible has impossible consequences, this amounts to defining τὸ
ἐνδεχόμενον as that which is neither impossible nor necessary. (He
adds that in another sense (as we have already seen) the necessary
is said to be ἐνδεχόμενον.) It is to this that τὸ δυνατόν must point,
and that is quite in accord with the doctrine of δύναμις pia
ἐναντίων, in which a δύναμις is thought of as a possibility of opposite
realizations, neither impossible and neither necessary. When A.
uses ἐνδεχόμενον in this sense I translate it by ‘contingent’ ; when
he uses it in the other, by 'possible'.
What A. maintains in the present passage is the following
propositions :
(1) ‘For all B, being A is possible’ entails ‘For some 4, being
B is possible’.
I. 3. 25337 — "19 297
(2) ‘For all B, being A is contingent’ entails ‘For some 4,
being B is contingent'.
(3) ‘For some B, being A is possible’ entails ‘For some A,
being B is possible'.
(4) ‘For some B, being A is contingent’ entails ‘For some A,
being B is contingent’.
(5) ‘For all B, not being A is possible’ entails ‘For all A, not
being B is possible’.
(6) ‘For all B, not being A is contingent’ entails ‘For some A,
not being B is contingent’ (οὐκ ἀντιστρέφει in 617 means
‘is not stmply convertible’).
(7) ‘For some B, not being A is possible’ is inconvertible.
(8) ‘For some B, not being A is contingent’ entails ‘For some
A, not being B is contingent’.
A. argues for propositions (1)-(4) in *4o-53. ‘If for all or some B
being A is possible or contingent, for some A being B is (respec-
tively) possible or contingent; for if it were so for no A, neither
would A be so for any B.’ The argument is sound when ἐνδέχεται
means 'is possible', but not when it means 'is contingent'. For
then what A. is saying is that if for all (or some) B being A is
neither impossible nor necessary, for some A being B is neither
impossible nor necessary, since if for all 4 being B were impossible
or necessary, for all B being A would be impossible or necessary.
Now if for all A being B is impossible, for all B being A is im-
possible ; but if for all A being B is mecessary, it only follows that
for some B being A is necessary. Thus the conclusion of the
reductio should run ‘Either for all B being A would be impossible
or for some B it would be necessary'. The error is, however, not
important, since this proposition would still contradict the original
assumption that for all B being 4 is neither impossible nor
necessary. b2-3 ef . . . πρότερον need not be excised (as it is by
Becker, p. 9o), since the mistake is à natural and venial one.
For propositions (s) and (7) A. argues correctly in 53-14. To
propositions (6) and (8) he turns in ^14-19. In 32>4~13 (cf. De Int.
19*18—22) A. distinguishes two cases of contingency—one in which
the subject has a natural tendency to have a certain attribute and
has it more often than not, and one in which its possession of the
attribute is a matter of pure chance. It is by an oversight that
in 2514-15 A. paraphrases τὸ δυνατόν of ^39 by a reference to the
first alone of these two cases. The essential difference he has in
mind turns not at all on the difference between the two cases, but
on the difference between the sense in which both alike may be
said ἐνδέχεσθαι (viz. that they are neither impossible nor necessary)
298 COMMENTARY
and the other sense of ἐνδέχεσθαι, in which it means simply ‘not
to be impossible’. It is on this alone that (as we shall see) A.’s
point about convertibility (his whole point in the present passage)
turns. The oversight may to some extent be excused by the fact
that A. thinks contingency of the second kind (where neither
realization is taken to be more probable than the other) no
proper object of science (3218-22).
Proposition (6) has sometimes been treated as a curious error
on A.’s part, and Maier, for instance (2 a. 36 n.), has an elaborate
argument in which he tries to account psychologically for the
supposed error. But really there is no error. For the reason for
the statement A. refers us (25518-19) to a later passage, viz.
36535-37*31. But in order to understand that passage we must
first turn to an intervening passage, 32?29-^r. A. there points
out, obviously rightly, that where ἐνδέχεται is used in the strict
sense, propositions stating that something ἐνδέχεται are capable
of a special kind of conversion, which I venture to call comple-
mentary conversion.
‘For all B, being A is contingent’ entails ‘For all B, not being
A is contingent’ and ‘For some B, not being A is contingent’.
‘For all B, not being A is contingent’ entails ‘For all B, being
A is contingent’ and ‘For some B, being A is contingent’.
‘For some B, being A is contingent’ entails ‘For some B, not
being A is contingent’.
‘For some B, not being A is contingent’ entails ‘For some B,
being A is contingent’.
With this in mind, let us turn to 36535-37231. A. there gives
three arguments to show that ‘For all B, not being A is contin-
gent’ does not entail ‘For all A, not being B is contingent’. His
first argument (36537-37?3) is enough to prove the point. The
argument is: (i) ‘For all B, being A is contingent’ entails (as we
have seen) (ii) ‘For all B, not being A is contingent’. (iii) ‘For
all A, not being B is contingent’ entails (iv) ‘For all A, being B
is contingent’. Therefore if (ii) entailed (iii), (i) would entail
(iv), which it plainly does not. Therefore (ii) does not entail (iii).
Two things may be added: (1) ‘For all B, not being A is con-
tingent’ does entail ‘For some A, not being B is contingent’;
(2) as A. says in 2517-18, ‘For some B, not being A is contingent’
does entail ‘For some A, not being B is contingent’. Both of these
entailments escape the objection which A. shows to be fatal to
any entailment of ‘For all A, not being B is contingent’ by ‘For
all B, not being A is contingent’.
b2-3. δέδεικται yap ... πρότερον, cf. *29-32.
I. 3. 2552-25 299
12-13. τοῦτο... πρότερον, cf. *32-4.
I3. ὁμοίως δὲ... ἀποφατικῆς, i.e. ‘For some B, not being A is
possible’ is inconvertible, as ‘Some B is not A’ and ‘Some B is
necessarily not A’ are.
I4. ὡς ἐπὶ τὸ πολύ. ABd’ have ὡς ἐπὶ πολύ, and this form
occurs in some or all of the MSS. in a few other passages (in E
in Phys. 196>11, 13, 20, in all MSS. in Probl. 90249). But the Greek
commentators read ὡς ἐπὶ τὸ πολύ pretty consistently, and the
shorter form is probably a clerical error.
X5. καθ᾽ 8v tpdTov . . . ἐνδεχόμενον, ‘which is the strict sense
we assign to “‘possible”’ ’.
19-24. viv δὲ. . . ἑπομένων. Though A. has distinguished
judgements of the forms ‘For B, being A is contingent’, ‘For B,
not being A is contingent’ as affirmative and negative (339, ^3),
he now points out that in form they are both affirmative. In both
cases something is said to be contingent, just as, both in 'B is A'
and in ‘B is not- A', something is said to be something else.
Maier (2 a. 324 n. 1) thinks that this section, which in its final
sentence refers forward to ch. 46, is probably, with that chapter,
a late addition, by A. himself. But cf. my introductory n. to
that chapter. Becker's contention (p. 91) that this section is a
late addition by some writer familiar with De Int. 12 seems to me
unconvincing; I find nothing here that A. might not well have
written.
24. δειχθήσεται δὲ... ἑπομένων. The point is discussed at
length in ch. 46, where A. points out the difference between “A is
not equal’ and ‘A is not-equal', viz. that τῷ μὲν ὑπόκειταί τι, τῷ
ὄντι μὴ ἴσῳ, Kal τοῦτ᾽ ἔστι τὸ ἄνισον, τῷ δ᾽ οὐδέν (51526—-7). Le.,
‘A is not-equal’ is not a negative proposition, merely contradicting
‘A is equal’; it is an affirmative proposition asserting that A
possesses the attribute which is the contrary of ‘equal’.
28. κατὰ δὲ Tas ἀντιστροφὰς... ἄλλαις. We have to ask
whether the present statement refers to (a) the first two applica-
tions of ἐνδέχεται or (b) to the third, and what ταῖς ἄλλαις means.
If the statement refers to (a), ταῖς ἄλλαις means negative assertoric
and apodeictic propositions, and A. is saying that, in spite of
their affirmative form (b19-25), negative problematic propositions
of type (a) are, like negative assertoric and apodeictic proposi-
tions, convertible if universal and inconvertible if particular (as
he has said in 3-14). If it refers to (b), rats ἄλλαις means affirma-
tive problematic propositions of type (b), and A. is saying that
the corresponding negative propositions, like these, are incon-
vertible (i.e. not simply convertible) if universal, and convertible
300 COMMENTARY
if particular. Maier (2 a. 27 and n.) adopts the first view, AL, P.,
and Waitz the second. The question is, I think, settled in favour
of the second view by the fact that the natural noun to be sup-
plied with ταῖς ἄλλαις is καταφάσεσιν (cf. 522).
CHAPTER 4
Assertoric syllogisms in the first figure
25°26. Let us now state the conditions under which syllogism
is effected. Syllogism should be discussed before demonstration,
because it is the genus to which demonstration belongs.
32. When three terms are so related that the third is included
in the middle term and the middle terrn included in or excluded
from the first, the extremes can be connected by a perfect syllo-
gism.
37- (A) Both premisses universal
AAA (Barbara) valid.
40. EAE (Celarent) valid.
26*2. AE proves nothing; this shown by contrasted instances.
9. EE proves nothing; this shown by contrasted instances.
13. We have now seen the necessary and sufficient conditions
for a syllogism in this figure with both premisses universal.
17. (B) One premiss particular
If one premiss is particular, there is a syllogism when and only
when the major is universal and the minor affirmative.
23. (a) Major premiss universal, minor particular affirmative.
AII (Darii) valid.
25. EIO (Ferio) valid.
30. (δ) Major premiss particular, minor universal. IA and OA
prove nothing; this shown by contrasted instances.
36. IE and OE prove nothing; this shown by contrasted in-
stances.
39. (c) Major premiss universal, minor particular negative.
AO proves nothing ; this shown by contrasted instances.
bro. EO proves nothing; this shown by contrasted instances.
14. That AO and EO prove nothing can also be seen from the
facts that the minor premiss Some C is not B is true even if No C
is B is true, and that AE and EE have already been seen to
prove nothing.
I. 4. 2526-36 301
21. (C) Both premisses particular
II, OO, IO, OI prove nothing; this shown by contrasted in-
stances.
26. Thus (1) to give a particular conclusion in this figure, the
terms must be related as described ; (2) all syllogisms in this figure
are perfect, since the conclusion follows directly from the pre-
misses ; (3) all problems can be dealt with in this figure, since it
can prove an A, an E, an I, or an O conclusion.
25°26. Διωρισμένων δὲ τούτων λέγωμεν. Here, and in 3217,
b4, 24, the evidence is divided between λέγωμεν and λέγομεν, but
the sense demands λέγωμεν. There are many passages in A. in
which the MSS. give only λέγομεν (in similar contexts), but
Bonitz rightly pronounces that λέγωμεν should always be read
(Index, 424558425210).
27-8. ὕστερον δὲ... ἀποδείξεως, in the Posterior Analytics.
28-31. πρότερον δὲ... ἀπόδειξις. The premisses of demon-
stration, in addition to justifying the conclusion, must be ἀληθῆ,
πρῶτα καὶ ἄμεσα, γνωριμώτερα xal πρότερα καὶ αἴτια τοῦ συμ-
περάσματος (An. Post. 71919-7297).
32-4. ὥστε τὸν ἔσχατον... μὴ εἶναι, i.e. so that the minor
term is contained in the middle term as in a whole (i.e. as species
in genus), and the middle term is (sc. universally) included in or
excluded from the major as in or from a whole.
36. ὃ καὶ τῇ θέσει γίνεται μέσον points to the position of the
middle term in a diagram. B. Einarson in A.J.P. lvii (1936),
166-9 gives reasons for thinking that, on the model of the dia-
grams used by the Greeks to illustrate the theory of proportion,
A. illustrated the three figures by the following diagrams:
First figure Second figure Third figure
major middle major
A ————— A (or M) ——————— . A (or I1)
middle major minor
B ———— B (or N) —————— B (or P)
minor minor middle
D ——— I'(o 5) ——— I (or Σ) ———
where the length of the lines answers to the generality of the
terms. The principle on which these lines of varying length were
assigned to the three terms is this: In the primary kind of pro-
position, the universal affirmative, the predicate must be at least
as general as the subject and is usually more general; and
negative and particular propositions are by analogy treated as
302 COMMENTARY
if this were equally true of them. Thus any term which in any
of the three propositions appears as predicate is treated as being
more general than the term of which it is predicated. The para-
digms of the three figures being (first figure) B is A, C is B,
Therefore C is A; (second figure) B is A, C is A, Therefore C is B;
(third figure) C is A, C is B, Therefore B is A, the comparative
length of the lines to be assigned to the terms becomes obvious.
Alternatively it might be thought that the diagrams took the
form:
First figure Second figure Third figure
No a = major
A ἔπεισα one ác
middle middle mide V middle
r
minor minor ome A minor
B Ὁ
This would serve better to Perd the use of σχῆμα, as meaning
the distinctive shape of each of the three modes of proof. But
it is negated by the fact that A. describes the middle term as
coming first in the second figure and last in the third figure
(26539, 28215).
39-40. πρότερον... λέγομεν, 24928-30.
2672-9. εἰ δὲ... λίθος. It is noticeable that in this and follow-
ing chapters, where A. states that a particular combination of
premisses yields no conclusion he gives no reason for this, e.g. by
pointing out that an undistributed middle or an illicit process
is involved ; but he often points to an empirical fact which shows
that the conclusion follows. E.g. here, instead of giving the
reason why All B is A, No C is B yields no conclusion, he simply
points to one set of values for A, B, C (animal, man, horse) for
which, all B being A and no C being B, all C is in fact A, and to
another set of values (animal, man, stone) for which, all B being
A and no C being B, no C is in fact A. Since in the one case all
C is A, a negative conclusion cannot be valid; and since in the
other case no C is A, an affirmative conclusion cannot be valid.
Therefore there is no valid conclusion (with C as subject and A
as predicate). This type of proof I call proof by contrasted
instances.
In giving such proofs by ὅροι A. always cites them in the follow-
ing order : first figure, major, middle, minor ; second figure, middle,
major, minor; third figure, major, minor, middle.
2. εἰ 86. .. ἀκολουθεῖ. Al. plainly read ἀκολουθεῖ (55. 10),
I. 4. 2553926838 303
and the much commoner ὑπάρχει is much more likely to have been
substituted for ἀκολουθεῖ than vice versa.
II-12. ὅροι roO ὑπάρχειν... μονάς. Le., no line is scientific
knowledge, no medical knowledge is a line, and in fact all medical
knowledge is scientific knowledge. On the other hand, no line
is a science, no unit is a line; but in fact no unit is a science.
Therefore premisses of this form cannot prove either a negative
or an affirmative.
17-21. Ei δ᾽... ἀδύνατον. 418-20 refers to combinations of
a universal major premiss with a particular affirmative minor,
420 ὅταν δὲ πρὸς τὸ ἔλαττον to combinations of a particular major
with a universal minor, 220 7j kai ἄλλως πως ἔχωσιν of ὅροι to com-
binations of a universal major with a particular negative minor.
Comparison with 2726-8 (second figure) and 2855 (third figure)
shows that 26217 εἰ δ᾽ ὁ μὲν καθόλου τῶν ὅρων ὁ δ᾽ ἐν μέρει πρὸς τὸν
ἕτερον means ‘if the predicate of one premiss is predicated univer-
sally of its subject, and that of the other non-universally of is
subject’. Maier’s τὸ δ᾽ for ὁ δ᾽ (2 a. 76 n. 3) finds no support in
the evidence and is far from being an improvement.
24. τὸ ἐν ἀρχῇ λεχθέν, cf. 2428-30.
27. ὥρισται... λέγομεν, 24630.
29. τὸ ΒΓ, i.e. the premiss ‘B belongs to C’.
32. τοῦ ἀδιορίστου ἢ κατὰ μέρος ὄντος. The MSS., except f,
have οὔτε ἀδορίστου ἢ κατὰ μέρος ὄντος (sc. τοῦ ἑτέρου, i.e. the major
premiss). But (1) the ellipse of τοῦ ἑτέρου is impossible, and (2)
ἀδιορίστου arid κατὰ μέρος are no true alternatives to ἀποφατικοῦ
and καταφατικοῦ. Waitz is no doubt right in reading τοῦ, which
derives support from Al. ; for, ignoring ἀδιορίστου ἢ as introducing
an unimportant distinction, he says (61. 20-1) τοῦ (so the MSS.;
Wallies wrongly emends to τὸ) δὲ κατὰ μέρος ὄντος εἶπεν ἀντὶ
τοῦ "τῆς μείζονος᾽- αὕτη γὰρ γίνεται κατὰ μέρος.
34-6. Spor... ἀμαθία. 1.6., some states are good, and some
not good, all prudence is a state; and in fact all prudence is good.
On the other hand, some states are good, and some not good,
all ignorance is a state; and in fact no ignorance is good. Thus
premisses of the form IA or OA do not warrant either a negative
or an affirmative conclusion.
38. ὅροι... κόραξ. I.e., some horses are white, and some not
white, no swans are horses; and in fact all swans are white. On
the other hand, some horses are white, and some not white, no
ravens are horses; and in fact no ravens are white. Thus pre-
misses of the form IE or OE do not warrant either a negative
or an affirmative conclusion,
304 COMMENTARY
b3. ἀδιορίστου τε Kai ἐν μέρει ληφθέντος. These words are a
pointless repetition of the previous line, and should be omitted.
There is no trace of them in Al.’s or in P.’s exposition.
6-10. ὑποκείσθωσαν ... συλλογισμός. The fact that, all men
being animals, and some white things not being men, some white
things are animals and some are not, shows that premisses of
the form AO do not warrant a universal conclusion; but it does
not show that a particular conclusion cannot be drawn. Therefore
here A. falls back on a new type of proof. Within the class of
white things that are not men we can find a part A, e.g. swans,
none of whose members are (and a fortior? some of whose members
are not) men, and all are animals; and another part none of
whose members are (and therefore a fortior: some of whose
members are not) men, and mone are animals. If the original
premisses (All men are animals, Some white things are not men)
warranted the conclusion Some white things are not animals,
then equally All men are animals, Some swans are not men,
would warrant the conclusion Some swans are not animals; but
allare. And if the original premisses warranted the conclusion
Some white things are animals, then equally All men are animals,
Some snow is not a man, would warrant the conclusion Some
snow is an animal; but no snow is. Therefore the original pre-
misses prove nothing.
10-14. πάλιν... οὐδενός. The proof that premisses of the
form EO prove nothing is exactly like the proof in 53-1o that
premisses of the form AO prove nothing. The fact that, no men
being inanimate, and some white things not being men, some
white things are and others are not inanimate, shows that a
universal conclusion does not follow from EO. And the further
fact that, no men being inanimate, and some swans not being
men, no swans are inanimate, shows that EO does not yield a
particular affirmative conclusion ; and the fact that, no men being
inanimate, and some snow not being a man, all snow is inanimate,
shows that EO does not yield a particular negative conclusion.
14-20. ἔτι... τούτων. A. gives here a second proof that AO
yields no conclusion. Some C is not B, both when no C is B and
when some is and some is not. But we have already proved
(22-9) that All B is A, NoC is B, proves nothing. It follows that
All B is A, SomeC is not B, proves nothing. This is the argument
ἐκ τοῦ ἀδιορίστου (from the ambiguity of a particular proposition)
which is used in 27?20-3, 27-8, 28528-31, 2996, 35h11.
23. ἢ τὸ μὲν... διωρισμένον, ‘or one indefinite and the other
a definite particular statement'.
I. 4. 2653-28 305
24-5. ὅροι δὲ... λίθος. Some white things are animals, and
some not, some horses are white, and some not; and all horses
are animals. On the other hand, Some white things are animals,
and some not, some stones are white, and some not; but in fact
no stones are animals. Thus premisses of the form II, OI, 10,
or OO cannot prove either a negative or an affirmative.
26-8. Φανερὸν ... γίνεται. This sums up the argument in
877-625. To justify a particular conclusion, the premisses must
be of the form AI (*23-5) or EI (#25-30). A. ignores the fact that
AA, EA, which warrant universal conclusions, a fortiori warrant
the corresponding particulars.
CHAPTER 5
Assertoric syllogisms 1n the second figure
26°34. When the same term belongs to the whole of one class
and to no member of another, or to all of each, or to none of either,
I call this the second figure; the common predicate the middle
term, that which is next to the middle the major, that which is
farther from the middle the minor. The middle is placed outside
the extremes, and first in position. There is no perfect syllogism
in this figure, but a syllogism is possible whether or. not the
premisses are universal.
2723. (A) Both premisses universal
There is a syllogism when and only when one premiss is
affirmative, one negative. (a) Premisses differing in quality.
EAE (Cesare) valid; this shown by conversion to first figure.
9. AEE (Camestres) valid; this shown by conversion.
14. The validity of EAE and AEE can also be shown by
reductio ad impossibile. These moods are valid but not perfect,
since new premisses have to be imported.
18. (b) Premisses alike in quality. AA proves nothing; this
shown by contrasted instances.
20. EE proves nothing ; this shown by contrasted instances.
26. (B) One premiss particular
(a) Premisses differing in quality. (a) Major universal. EIO
(Festino) valid; this shown by conversion.
36. AOO (Baroco) valid; this shown by reductio ad impossibile.
b4. (B8) Minor universal. OA proves nothing; this shown by
contrasted instances.
6. IE proves nothing ; this shown by contrasted instances.
4985 X
306 COMMENTARY
ro. (b) Premisses alike in quality. (c) Major universal. EO
(No N is M, Some 5 is not M) proves nothing. If both some & is
not M and some 4s, we cannot show by contrasted instances that
EO proves nothing, since all & will never be N. We must there-
fore fal! back upon the indefiniteness of the minor premiss; since
O is true even when E is true, and EE proved nothing, EO proves
nothing.
23. AI proves nothing ; this must be shown to follow from the
indefiniteness of the minor premiss.
28. (8) Minor universal. OE proves nothing; this shown by
contrasted instances.
32. IA proves nothing; this shown by contrasted instances.
34. Thus premisses alike in quality and differing in quantity
prove nothing.
36. (B) Both premisses particular
II, OO, IO, OI prove nothing; this shown by contrasted in-
stances.
28*1. It is now clear (1) what are the conditions of a valid
syllogism in this figure; (2) that all syllogisms in this figure are
imperfect (needing additional assumptions that either are im-
plicit in the premisses or—in reductio ad impossibile—are stated
as hypotheses ; (3) that no affirmative conclusion can be drawn in
this figure.
26534-6. Ὅταν δὲ... δεύτερον. This is not meant to be a
definition of the second figure, since it mentions only the case
in which both premisses are universal. But it indicates the general
characteristic of this figure, that in it the premisses have the
same predicate.
37-8. μεῖζον δὲ... κείμενον. It is not at first sight clear why
A. should say that in the second figure the major term is placed
next to the middle term, while in the third figure the minor is
so placed (28413-14). Al. criticizes at length (72. 26-75. 9) an
obviously wrong interpretation given by Herminus, but his own
further observations (75. 10-34) throw no real light on the ques-
tion. P. (87. 2-19) has a more plausible explanation, viz. that in
the second figure (PM, SM, SP) the major term is the more akin
to the middle, because while the middle term figures twice as
predicate, the major term figures so once and the minor term not
at all. On the other hand, in the third figure (MP, MS, SP), the
minor term is the more akin to the middle because, while the
middle term occurs twice as subject, the minor occurs once as
subject and the major term never.
I. 5. 26534— 2741 307
This explanation is open to two objections. (1) It is far from
obvious, and A. could hardly have expected an ordinary hearer
or reader to see the point in the complete absence of any explana-
tion by himself. (2) τὸ πρὸς τῷ μέσῳ κείμενον naturally suggests
not affinity of nature but adjacent position in the formulation
of the argument. The true explanation is to be found in the
diagram used to illustrate the argument—the first of the two
diagrams in 25636n. It may be added that in A.’s ordinary
formulation of a second-figure argument (e.g. κατηγορείσθω τὸ
M τοῦ μὲν Ν μηδενός, τοῦ δὲ E παντός, 275-6) the major term N
is named next after the middle term M, while in the ordinary
formulation of the third figure (e.g. ὅταν καὶ τὸ IT καὶ τὸ P παντὶ
τῷ L' ὑπάρχῃ, 28*18) the minor term P is named next before the
middle term 2.
39. τίθεται... θέσει. In 28214-15 A. says that in the third
figure τίθεται τὸ μέσον ἔξω μὲν τῶν ἄκρων, ἔσχατον δὲ τῇ θέσει.
When he says of the middle term in the second figure that it is
placed outside the extremes, we might suppose that it was
because it is the predicate of both premisses (the subject being
naturally thought of as included in the predicate, because it is
so in an affirmative proposition). But that would not account
for his saying that in the third figure, where the middle term is
subject of both premisses, it is outside the extremes. His meaning
is simply that in his diagram the middle term comes above both
extremes in the second figure, and below both in the third, and
that in his ordinary formulation the middle term does not come
between the extremes in either figure; it is named before them
both in the second figure, after them both in the third. ‘M belongs
to no N, and to all &’ (second figure). ‘Both IJ and P belong to
all Σ᾽ (third figure).
27°91. τέλειος... σχήματι. A. holds that the conclusion, in
the second and third figures, cannot be seen directly to follow
from the premisses, as it can in the first figure. Accordingly he
proves the validity of the valid moods in these figures by showing
that it follows from the validity of the valid moods in the first
figure. Sometimes the proof is by conversion, i.e. by inferring
from one of the premisses the truth of its converse, and thus
getting a first-figure syllogism which proves either the same
conclusion or one from which the original conclusion can be got
by conversion. Thus in *6-9 he shows the validity of Cesare as
follows: If No N is M and All is M, No Z is N; for from No N
is M we can infer that No M is N, and then we get the first-figure
syllogism No M is N, All E is M, Therefore No & is N.
308 COMMENTARY
Sometimes the proof is by reductio ad impossibile, i.e. by showing
that if the conclusion were denied, by combining its opposite
with one of the premisses we should get a conclusion that con-
tradicts the other premiss. Thus in 414-15 he indicates that
Cesare can be shown as follows to be valid (and Camestres
similarly): If No Nis M and All Sis M, it follows that No & is N.
For suppose that some & is N. Then by the first figure we can
show that if no Nis M and some & is N, it would follow that some
& is not M. But ex hypothesi all & is M.
2-3. kai καθόλου... ὄντων, ie. both when the predicates of
both premisses are predicated universally of their subjects and
when they are not both so predicated. ὅρων is frequently used
thus brachylogically to refer to premisses.
8. τοῦτο... πρότερον, 25540-2622.
10. τὸ = τῷ N. Proper punctuation makes it unnecessary to
adopt Waitz's reading, τῷ & τὸ N.
14. ὥστ᾽ ἔσται... συλλογισμός, i.e. so that Camestres re-
duces to the same argument as Cesare did in 35-9, i.e. to Celarent.
14-15. ἔστι δὲ... ἄγοντας, cf. ^1 n.
19-20. Spor... μέσον οὐσία. I.e., all animals are substances, all
men are substances, and all men are animals. On the other hand,
all animals are substances, all numbers are substances, but no
numbers are animals. Thus in this figure AA proves nothing.
As Al. observes (81. 24-8), A. must not be supposed to hold
seriously that numbers are substances; he often takes his in-
stances rather carelessly, and here he simply uses for the sake of
example a Pythagorean tenet.
21-3. ὅροι τοῦ ὑπάρχειν. . . λίθος. Le., no animals are lines,
no men are lines, and in fact all men are animals. On the other
hand, no animals are lines, no stones are lines; but in fact no
stones are animals. Therefore in this figure EE proves nothing.
24. ws ἐν ἀρχῇ εἴπομεν, ?3-5.
36. γίνεται yàp . . . σχήματος, i.e. in Ferio (26225-30).
*x-2. καὶ εἰ... μὴ παντί, This is not a new case, but an alterna-
tive formulation to et τῷ μὲν Ν παντὶ τὸ M, τῷ δὲ 5 τινὶ μὴ ὑπάρχει
(531).
5-6. Spor... κόραξ. Le., some substances are not animals,
al ravens are animals; but in fact all ravens are substances.
On the other hand, some white things are not animals, all ravens
are animals; and in fact no ravens are white. Therefore in this
figure OA proves nothing.
6-8. ὅροι τοῦ ómápxew . . . ἐπιστήμη. Le. some substances
are animals, no units are animals; but in fact all units are sub-
I. 5. 2722 —»38 309
stances. On the other hand, some substances are animals, no
sciences are animals; and in fact no sciences are substances.
Therefore in this figure IE proves nothing.
For.the treatment of units as substances cf. *19-20 n.
16-23. Spot... ἔσται. That EO in the second figure proves
nothing cannot be shown in the way A. has adopted in other
cases, viz. by contrasted instances (cf. 262-9 n). He points
(616) to an instance in which, no N being M, and some & not being
M, no Z is N; no snow is black, some animals are not black, and
no animal is snow. But there cannot be a case in which all E is
N, so long as the minor premiss is taken to mean that some & is
not M and some is; for if no Nis M and all & is N, it would follow
that no & is M, whereas the original minor premiss is taken to
mean that some & is and some is not M. He therefore falls back
on pointing out that Some 4 is not M is true even when no &
is M, and on reminding us that No N is M, No & is M proves
nothing (as was shown in ?20-3). The argument ἐκ τοῦ ἀδιορίστου
(from the ambiguity of the particular proposition) has been
already used in 26514-20.
26-8. Spor... δεικτέον. L.e., all swans are white, some stones
are white; but in fact no stones are swans. Therefore AI in
the second figure does not warrant an affirmative conclusion.
That it does not warrant a negative conclusion is shown (as in
the previous case, 520-3) by pointing out that Some J is M is true
even when all & is M, and that All N is M, All & is M proves
nothing.
31-2. ὅροι τοῦ ὑπάρχειν... λευκόν-λίθος-κόραξ. I.e., some
animals are not white, no ravens are white; and in fact all ravens
are animals. On the other hand, some stones are not white, no
ravens are white; but no ravens are stones. Thus OE in the
second figure proves nothing.
32—4. εἰ δὲ... κύκνος. Le., some animals are white, all snow
is white; but in fact no snow is an animal. On the other hand,
some animals are white, all swans are white; and in fact all
swans are animals. Thus IA in the second figure proves nothing.
36-8. ἀλλ᾽ οὐδ᾽... ἀδιορίστως, ‘nor does anything follow if a
middle term belongs to part of each of two extremes (II), or
does not belong to part of each of them (OO), or belongs to part
of one and does not belong to part of the other (IO, OJ), or does
not belong to either as a whole (OO), or belongs without deter-
mination of quantity’. ἢ μηδετέρῳ παντί is not a new case, but an
alternative formulation to τινὲ ἑκατέρῳ μὴ ὑπάρχει; cf. >1-2 n.;
so Al. 92. 33-94. 4. The awkwardness would be removed by
310 COMMENTARY
omitting ἢ μὴ ὑπάρχει in 537 with B’, but this seems more likely
to be a mistake due to homoioteleuton.
Waitz reads in 537 (with one late MS.) ἢ μηδ᾽ ἑτέρῳ παντί, which
he interprets as meaning ἢ τῷ ἑτέρῳ μὴ παντί, i.e. as expressing
alternatively what A. has already expressed by rà δὲ μή (i.e. τῷ δέ
τινι μή), the reference being to the combination IO or OI. But
ἢ μηδ᾽ ἑτέρῳ παντί could not mean this.
38. ἢ ἀδιορίστως, i.e. two premisses of indeterminate quantity
are in respect of invalidity like two particular premisses.
38-9. ὅροι δὲ... ἄψυχον. Le., some animals are white and
some not, some men are white and some not, and in fact all men
are animals. On the other hand, some animals are white and
some not, some lifeless things are white and some not; but in
fact no lifeless thing is an animal. Thus in this figure II, OI, IO,
or OO proves nothing.
2842. ὡς ἐλέχθη, in 2773-5, 26-32.
6. ἃ ἢ ἐνυπάρχει ... ἢ τίθενται ὡς ὑποθέσεις. The plural τίθενται
is used carelessly, by attraction to the number of ὑποθέσεις.
CHAPTER 6
Assertoric syllogisms in the third figure
28210. If two predicates belong respectively to all and to none
of a given term, or both to all of it, or to none of it, I call this the
third figure, the common subject the middle term, the predicates
extreme terms, the term farther from the middle term the major,
that nearer it the minor. The middle term is outside the extremes,
and last in position. There is no perfect syllogism in this figure,
but there can be a syllogism, whether or not both premisses are
universal.
17. (A) Both premisses universal
AAI (Darapti) valid; this shown by conversion, reductio ad
impossibile, and ecthests.
26. EAO (Felapton) valid; this shown by conversion and by
reductio ad impossibile.
30. AE proves nothing; this shown by contrasted instances.
33. EE proves nothing ; this shown by contrasted instances.
36. Thus two affirmative premisses prove an I proposition ;
two negative premisses, nothing ; a negative major and an affirma-
tive minor, an O proposition; an affirmative major and a
negative minor, nothing.
I. 5. 27538—6. 28433 311
bs. (B) One premiss particular
(a) Two affirmative premisses give a conclusion. IAI (Disamis)
valid ; this shown by conversion.
1x. AII (Datisi) valid; this shown by conversion, reductio ad
impossibile, and ecthesis.
15. (δ) Premisses differing in quality. (o) Affirmative premiss
universal. OAO (Bocardo) valid; this shown by reductio ad
impossibile and by ecthesis.
22. AO (All S is P, Some S is not R) proves nothing. If some S
is not R and some ts, we cannot find a case in which no R is P; but
we can show the invalidity of any conclusion by taking note of
the indefiniteness of the minor premiss.
31. (B) Negative premiss universal. EIO (Ferison) valid ; this
shown by conversion.
36. IE proves nothing ; this shown by contrasted instances.
38. (c) Both premisses negative. OE proves nothing; this
shown by contrasted instances.
2952. EO proves nothing; that this is so must be proved from
the indefiniteness of the minor premiss.
6. (C) Both premisses particular
II, OO, IO, OI prove nothing; this shown by contrasted
instances.
xi. It is clear then (1) what are the conditions of valid syllo-
gism in this figure; (2) that all syllogisms in this figure are im-
perfect; (3) that this figure gives no universal conclusion.
28:13-15. μεῖζον... θέσει. For the meaning cf. 26537-8 n.,
39 n.
23. τῷ ἐκθέσθαι, i.e. by exposing to mental view a particular
instance of the class denoted by the middle term. A. uses ἔκθεσις
(1) as a technical term in this sense, (2) of the procedure of
setting out the words in an argument that are to serve as the
terms of a syllogism. Instances of both usages are given in our
Index. B. Einarson in A.J.P. lvii (1936), 161-2, gives reasons for
thinking that A.’s usage of the word is adopted from ‘the ἔκθεσις
of geometry, where the elements in the enunciation are repre-
sented by actual points, lines, and other corresponding elements
in a figure'.
28. ὁ yàp αὐτὸς τρόπος, i.e. as that in 319-22.
29. τῆς ΡΣ προτάσεως, i.e. the premiss 'R belongs to S’.
30. καθάπερ ἐπὶ τῶν πρότερον, cf. 2714-15, 38-51, 28222-3.
31-3. Spor... ἄνθρωπος. Le., all men are animals, no men
312 COMMENTARY
are horses, but all horses are animals. On the other hand, all
men are animals, no men are lifeless, and no lifeless things are
animals. Therefore in this figure AE can prove nothing.
34-6. Spor τοῦ ὑπάρχειν... ἄψυχον. Le., no lifeless things
are animals, no lifeless things are horses; and in fact all horses
are animals. On the other hand, no lifeless things are men, no
lifeless things are horses; but in fact no horses are men. Thus in
the third figure EE proves nothing.
br4-r5. ἔστι δ᾽ ἀποδεῖξαι... πρότερον, i.e. by reductio ad im-
possibile as in the case of Darapti (*22-3) and Felapton (329-39),
or by ecthesis as in the case of Darapti (222-6).
15. πρότερον should be read, instead of προτέρων; cf. *30, 528,
31540, 35517, 3682, etc.
19-20. εἰ yap... ὑπάρξει. The sense requires a comma after
καὶ τὸ P παντὶ τῷ Σ, since this is part of the protasis.
20-1. δείκνυται... ὑπάρχει. This is the type of proof called
ἔκθεσις (423-6, 14).
22-31. ὅταν δ᾽... συλλογισμός. That AO in the third figure
proves nothing cannot be shown by the method of contrasted
instances. We can show that it does not prove a negative, by
the example ‘all animals are living beings, some animals are not
men; but all men are living beings’. But we cannot find an
example to show that the premisses do not prove an affirmative,
if Some S is not R is taken to imply Some S is R; for if all S is P
and some S is R, some R must be P, but we were trying to find
a case in which no R is P. We therefore fall back on the fact
that Some S is not R is true even when no S is R, and that All
S is P, No S is Καὶ has been shown in 330-3 to prove nothing.
28. ἐν rois πρότερον, 26514—20, 2720-3, 26-8.
36-8. ὅροι rod ὑπάρχειν. .. τὸ ἄγριον. Le., some wild things
are animals, no wild things are men; but in fact all men are
animals. On the other hand, some wild things are animals, no
wild things are sciences; and in fact no sciences are animals.
Thus IE in the third figure proves nothing.
39-29°6. ὅροι... δεικτέον. That OE proves nothing is shown
by contrasted instances: some wild things are not animals, no
wild things are sciences; but no sciences are animals; on the
other hand, some wild things are not animals, no wild things are
men, and all men are animals.
That EO does not prove an affirmative conclusion is shown by
the fact that no white things are ravens, some white things are
not snow, but no snow is a raven. We cannot give an instance
to show that a negative conclusion is impossible (i.e. a case in
I. 6. 28#34—29710 313
which, no S being P, and some S not being R, All R is in fact P),
if Some S is not R is taken to imply that some S is R; for if all
Ris P, and some S is R, some S must be P; but the case we were
trying to illustrate was that in which no S is P. We therefore
fall back on the fact that Some S is not R is true even when no
S is R, and that if no S is P, and no S is R, nothing follows
(28233—6). Cf. 26514—20 n.
297-8. ἢ ὁ μὲν... ὑπάρχῃ. These words could easily be
spared, since the case they state differs only verbally from what
follows, ὁ μὲν τινὲ ὁ δὲ μὴ παντί. But elsewhere also (27336-*z,
636-7) A. gives similar verbal variants, and the omission of the
words in question by B, C, and JZ is probably due to homoio-
teleuton.
9-10. ὅροι δὲ... ζῶον-ἄψυχον-λευκόν. I.e., some white things
are animals and some not, some white things are men and some
not; and in fact all men are animals. On the other hand, some
white things are animals and some not, some white things are
lifeless and some not; but in fact no lifeless things are animals.
Thus II, OI, IO, OO in the third figure prove nothing.
CHAPTER 7
Common properties of the three figures
29719. In all the figures, when there is no valid syllogism, (1)
if the premisses are alike in quality nothing follows; (2) if they are
unlike in quality, then if the negative premiss is universal, a
conclusion with the major term as subject and the minor as
predicate follows. E.g. if all or some B is A, and noC is B, by
converting the premisses we get the conclusion Some A is not C.
27. If an indefinite proposition be substituted for the parti-
cular proposition the same conclusion follows.
30. All imperfect syllogisms are completed by means of the
first figure, (1) ostensively or (2) by reductio ad impossibile. In
ostensive proof the argument is put into the first figure by con-
version of propositions. In reductio the syllogism got by making
the false supposition is in the first figure. E.g. if all C is A and is
B, some B must be A; for if no B is A and all C is B, no C is
A; but ex hypothesi all is.
Pr. Allsyllogisms may be reduced to universal syllogisms in the
first figure. (1) Those in the second figure are completed by
syllogisms in the first figure—the universal ones by conversion of
the negative premiss, the particular ones by reductio ad impossibile.
314 COMMENTARY
6. (2) Particular syllogisms in the first figure are valid by their
own nature, but can also be validated by veductio using the
second figure ; e.g. if all B is A, and someC is B, some C is A; for
if no C is A, and all B is A, no C will be B.
11. So too with a negative syllogism. If no B is A, and some
C is B, some C will not be A; for if all C is A, and no B is A, no
C will be B.
xs. Now if all syllogisms in the second figure are reducible to
the universal syllogisms in the first figure, and all particular
syllogisms in the first are reducible to the second, particular
syllogisms in the first will be reducible to universal syllogisms in it.
19. (3) Syllogisms in the third figure, when the premisses are
universal, are directly reducible to universal syllogisms in the first
figure; when the premisses are particular, they are reducible to
particular syllogisms in the first figure, and thus indirectly to
universal syllogisms in that figure.
26. We have now described the syllogisms that prove an
affirmative or negative conclusion in each figure, and how those
in different figures are related.
29719-27. Δῆλον δέ... συλλογισμός. These generalizations
are correct, but A. has omitted to notice that OA in the second
figure and AO in the third give a conclusion with P as subject.
A.’s recognition of the fact that AE and IE in the first figure
yield the conclusion Some P is not S amounts to recognizing the
validity of Fesapo and Fresison in the fourth figure; but he does
not recognize the fourth as a separate figure. He similarly in
539-14 recognizes the validity of the other moods of the fourth
figure—Bramantip, Dimaris, Camenes. For an interesting study
of the development of the theory of the fourth figure from A.’s
hints cf. E. Thouverez in Arch. f. d. Gesch. d. Philos. xv (1902),
49-110; cf. also Maier, 2 a. 94-100.
27-9. δῆλον... σχήμασιν. In three of the moods which A.
has stated to yield a conclusion with the major term as subject
and the minor as predicate (IE in all three figures) the affirmative
premiss is particular. He here points out that an indefinite
premiss, i.e. one in which neither ‘all’ nor ‘some’ is attached to
the subject, will produce the same result as a particular premiss.
31-2. ἢ yàp δεικτικῶς... πάντες. An argument is said to be
δεικτικός, ostensive, when the conclusion can be seen to follow
either directly from the premisses (in the first figure) or from
propositions that follow directly from the premisses (as when
an argument in the second or third figure is reduced to the first
I. 7. 29319— 22 315
figure by conversion of a premiss). A reductio ad impossibile, on
the other hand, uses a proposition which does not follow from
the original premisses, viz. the opposite of the conclusion to be
proved.
A. says nothing of the proof by ἔκθεσις which he has often used,
because, being an appeal to our intuitive perception of certain
facts (cf., for instance, 2822-6), not to reasoning, it is formally
less cogent. In any case it was used only as supplementing proof
by conversion, or by reductio ad impossibile, or by both.
bg. of μὲν καθόλου... ἀντιστραφέντος. The validity of Cesare
and Camestres has been so established in 27*5-9, 9-14.
5-6. τῶν δ᾽ ἐν μέρει... ἀπαγωγῆς. The validity of Baroco
has been so established in 27236-55. The validity of Festino was
established differently (27*32—6), viz. by reduction to Ferio; and
that establishment of it would not illustrate A.’s point here,
which is that all syllogisms may be reduced to universal syllogisms
in the first figure. The proof of the validity of Festino which he
has in mind must be the following: 'No P is M, Some S is M,
Therefore some S is not P. For if all S is P, we can have the
syllogism in Celarent (first figure) No P is M, All S is P, Therefore
no S is M, which contradicts the original minor premiss.'
18. oi κατὰ μέρος, SC. ἐν τῷ πρώτῳ.
19-21. οἱ δ᾽ ἐν τῷ τρίτῳ... συλλογισμῶν. The main proof of
the validity of Darapti (2817-22) was by reduction to Darii,
which would not illustrate A.’s present point, that all syllogisms
can be validated by universal syllogisms in the first figure. But
in 28422-3 he said that Darapti can also be validated by reductio
ad impossibile, and that is what he has here in mind. All M is P,
All M is S, Therefore some S is P. For if no S is P, we have the
syllogism No S is P, All M is S, Therefore No M is P, which
contradicts the original major premiss.
Similarly Felapton was in 2826-9 validated by reduction to
Ferio, but can be validated by reducto ad impossibile (ib. 29-30)
using a syllogism in Barbara.
21-2. ὅταν δ᾽ ἐν μέρει... σχήματι. Disamis and Datisi were
validated by reduction to Darii (2857-11, 11-14), Ferison (ib.
33-5) by reduction to Ferio. But Bocardo (ib. 16-20) was validated
by reductio ad impossibile, using a syllogism in Barbara—which
would not illustrate A.'s point, that the non-universal syllogisms
in the third figure are validated by non-untversal syllogisms in the
first figure. To illustrate this point he would have needed to
have in mind a different proof of Bocardo, viz. the following:
"Transpose the premisses Some M is not P, All M is S, and convert
316 COMMENTARY
the major by negation. Then we have All M is S, Some not-P
is M, Therefore Some not-P is S. Therefore Some S is not-P.
Therefore Some S is not P.’ But conversion by negation is not
a method he has hitherto allowed himself, so that Al. is right in
saying (116. 30-5) that A. has made a mistake. His general point,
however, is not affected—that ultimately all the moods in all
the figures are validated by the universal moods of the first
figure; for Bocardo is validated by reductio ad impossibile using
a syllogism in Barbara. :
26-8. Oi μὲν οὖν... ἑτέρων. A. has shown in chs. 4-6 the
position of syllogisms in each figure, with respect to validity or
invalidity, and in ch. 7 the position with regard to reduction of
syllogisms in one figure to syllogisms in another.
CHAPTER 8
Syllogisms with two apodetctic premisses
29°29. It is different for A to belong to B, to belong to it of
necessity, and to be capable of belonging to it. These three facts
will be proved by different syllogisms, proceeding respectively
from necessary facts, actual facts, and possibilities.
36. The premisses of apodeictic syllogisms are the same as
those of assertoric syllogisms except that ‘of necessity’ will be
added in the formulation of them. A negative premiss is conver-
tible on the same conditions, and ‘being in a whole’ and ‘being
true of every instance' will be similarly defined.
3073. In other cases the apodeictic conclusion will be proved
by means of conversion, as the assertoric conclusion was; but in
the second and third figures, when the universal premiss is
affirmative and the particular premiss negative, the proof is not
the same; we must set out a part of the subject of the particular
premiss, to which the predicate of that premiss does not belong,
and apply the syllogism to this; if an E conclusion is necessarily
true of this, an O conclusion will be true of that subject. Each
of the two syllogisms is validated in its own figure.
29531. τὰ δ᾽... ὅλως, ‘while others do not belong of necessity,
or belong at all’.
30?2. τό τε yap στερητικὸν ὡσαύτως ἀντιστρέφει, Le. is con-
vertible when universal, and not when particular (cf. 2535-7,
12-13). Affirmative propositions also are convertible under the
same conditions in apodeictic as in assertoric syllogisms; but A.
Mentions only negative propositions, because he is going to point
I. 7. 29526 —8. 30°14 317
out (36535-37231) that these when in the strict sense problematic
are not convertible under the same conditions as when they are
assertoric or apodeictic.
2-3. kai τὸ ἐν ὅλῳ... ἀποδώσομεν, cf. 24526—30.
3-9. ἐν μὲν οὖν... ἀπόδειξις. Le., in all the moods of the
second and third figures except A"O*0" in the second and OnA^On
in the third a necessary conclusion from necessary premisses is
validated in the same way as an assertoric conclusion from
assertoric premisses, i.e. by reduction to the first figure. But this
method cannot be applied to AnO^O^ and O^A^O^. Take A^»O^O».
‘All B is necessarily A, Some C is necessarily not A, Therefore
some C is necessarily not B.' The assertoric syllogism in Baroco
was validated by reductio ad impossibile (27436->3), by supposing
the contradictory of the conclusion to be true. The contradictory
of Some C is necessarily not B is All C may be B. And this, when
combined with either of the original premisses, produces not a
simple syllogism with both premisses apodeictic, but a mixed
syllogism with one apodeictic and one problematic premiss. But
Aristotle cannot rely on such a syllogism, since he has not yet
examined the conditions of validity in mixed syllogisms.
9-14. ἀλλ᾽ ἀνάγκη... σχήματι. A. therefore falls back on
another method of validation of A^O^»O^ and O^A^O». Take
A^O^"O», ‘All B is necessarily A, Some C is necessarily not A,
Therefore some C is necessarily not B.' Take some species of C
(say D) which is necessarily not A. Then all B is necessarily A, All
D is necessarily not A, Therefore all D is necessarily not B (by
Camestres). Therefore some C is necessarily not B.
Again take OnA*O». ‘Some C is necessarily not A, All C is
necessarily B, Therefore some B is necessarily not A.’ Take
a species of C (say D) which is necessarily not A. Then All D is
necessarily not A, All D is necessarily B, Therefore some B is
necessarily not A (by Felapton). ἐκθεμένους ᾧ τινὶ ἑκάτερον μὴ
ὑπάρχει means ‘setting out that part of the subject of the parti-
cular negative premiss, of which the respective predicate in each
of the two cases (A"O"O^ and O^A^O») is not true’.
Waitz has a different interpretation, with which we need not
concern ourselves, since it is plainly mistaken (cf. Maier, 2a.
106 n.) Al. gives the true interpretation (121. 15-122. 16). He
adds that this is a different kind of ἔκθεσις from that used with
regard to assertoric syllogisms. There, he says, τὸ ἐκτιθέμενον
was τι τῶν αἰσθητῶν xai μὴ δεομένων δείξεως (122. 19), whereas
here there is not an appeal to perception but τὸ ἐκτιθέμενον enters
into a new syllogism which validates the original one. He is
318 COMMENTARY
mistaken in describing the former kind of ecthesis as appealing
to a perceptible individual thing; the appeal was always to a
species of the genus in question. But he is right in pointing out
that the former use of ecthesis (e.g. in 28¢12-16) was non-syllogistic,
while the new use of it is syllogistic.
II-12. εἰ δὲ... τινός. This applies strictly only to the proof
which validates A^O^O^; there we prove that B is necessarily
untrue of all D (κατὰ τοῦ ἐκτεθέντος) and infer that it is necessarily
untrue of some C (κατ᾽ ἐκείνου τινός). In the proof which validates
O^A^On, τὸ ἐκτεθέν (D) is middle term and nothing is proved of it.
The explanation is offered by AL, who says (122. 15-16) ὥστ᾽ εἰ
ἐπὶ μορίου τοῦ I” ἡ δεῖξις ὑγιής, kai ἐπὶ τινὸς τοῦ I ὑγιὴς δεῖξις
ἔσται; i.e. in the case of Bocardo the words we are commenting
on are used loosely to mean ‘if the proof in which the subject
of the two premisses is D is correct, that in which the subject is
C is also correct’.
12-13. τὸ yàp ἐκτεθὲν . . . ἐστιν, ‘for the term set out is identi-
cal with a part of the subject of the particular negative premiss'.
I3-14. γίνεται δὲ... σχήματι, 1.6. the validation of AnOvOa
in the second figure and of O^A1O" in the third is done by syllo-
gisms in the second and third figure respectively.
CHAPTER 9
Syllogisms with one apodeictic and one assertoric premiss, in the
first figure
30715. It sometimes happens that when one premiss is neces-
sary the conclusion is so, viz. if that be the major premiss.
(A) Both premisses universal
(a) Major premiss necessary. A"AA®, E2AE® valid.
23. (b) Minor premiss necessary. AA^A^* invalid; this shown
by reductio ad impossibile and by an example.
32. EA"E® invalid; this shown in the same way.
33- (B) One premiss particular
(a) If the universal premiss is necessary the conclusion is so;
(b) if the particular premiss is necessary the conclusion is not so.
37- (a) A^II» valid.
br. EnIO? valid.
2. (b) AI»I" invalid, since the conclusion 15 cannot be validated
by reductio.
5. EI^O^ invalid; this shown by an instance.
I. 8. 30211— 9. 30428 319
Ch. 1o discusses combinations of an assertoric with an apodeictic
premiss in the second figure, ch. 11 similar combinations in the
third figure. Though in ch. 9 there is no explicit limitation to the
first figure, it in fact discusses similar combinations in that figure.
Since the substitution of an apodeictic premiss for one of the
premisses of an assertoric syllogism will plainly not enable us
to get a conclusion when none was to be got before, the only
point to be discussed in these chapters is, which of the valid
combinations will, when this substitution is made, yield an
apodeictic conclusion. Thus in ch. 9 A. discusses only the moods
corresponding to Barbara, Celarent, Darii, and Ferio; in ch. 1o
only those corresponding to Cesare, Camestres, Festino, and
Baroco; in ch. 11 only those corresponding to Darapti, Felapton,
Datisi, Disamis, Ferison, and Bocardo.
In 30215-23 A. maintains that when, and only when, the major
premiss is apodeictic and the minor assertoric, an apodeictic con-
clusion may follow. His view is based on treating the predicate of
a proposition of the form ‘B is necessarily A’ as being ‘necessarily
A’; for if this is so, ‘All B is necessarily A, AIL C is B’ justifies the
conclusion All C is necessarily A ; while, on the other hand, ‘All B
is A, AC is necessarily B' contains more than is needed to prove
that all C is A, but not enough to prove that it is necessarily A.
Thus his view rests on a false analysis of the apodeictic proposition.
3025-8. ci γὰρ... ὑπάρχειν. The point to be proved is that
from All B is A, All C is necessarily B, it does not follow that all
C is necessarily A. If all C were necessarily A, says A., one could
deduce both by the first figure—from ΑἹ] C is necessarily A, Some
B is necessarily C (got by conversion of All C is necessarily B)—
and by the third—from All C is necessarily A, All C is necessarily
B—that some B is necessarily A; but this is ψεῦδος (since all
we know is that all B is A).
Al. rightly points out (128. 31-129. 7) that this argument,
while resembling a reductio ad impossibile, is different from it.
A. does not assume the falsity of an original conclusion in order
to prove its validity, as he does in such a reductio. In order to
prove that a certain conclusion does not follow, he supposes that
it does, and shows that if it did, it would lead to knowledge which
certainly cannot be got from the original premisses. A. calls the
conclusion of this reductio-syllogism not impossible but ψεῦδος
(227), by which he means that ‘Some B is necessarily A’, while
compatible with ‘All B is A’, cannot be inferred from it, nor
from it--'All C is necessarily B'; i.e. it may be false though the
original premisses are true.
320 COMMENTARY
Maier (2 a. 110 n. 1) criticizes Al. on the ground that his account
implies that the premiss All B is A is compatible with two con-
tradictory statements—Some B is necessarily A (A.’s ψεῦδος)
and No B is necessarily A (which A. expressly states to be com-
patible with All B is A, in *27-8). But Al. is right; All Bis A is
compatible with either statement, though all three are not com-
patible together.
40. τὸ yàp Γ ὑπὸ τὸ B ἐστί. More strictly, part of Γ falls under
B (*38-9).
b2-5. εἰ δὲ... συλλογισμοῖς. A. is dealing here with the com-
bination All B is A, Some C is necessarily B. Al.'s first interpreta-
tion of this difficult passage (133. 19-29) is: This combination gives
an assertoric (not an apodeictic) conclusion (οὐκ ἔσται τὸ συμ-
πέρασμα dvayykatov), because nothing impossible results from this,
i.e. because by combining the conclusion Some C is A with either
of the premisses we cannot get a conclusion contradicting the
other premiss. This is obviously true, but the interpretation is
open to two objections: (1) that it is a very insufficient reason
(and one to which there is no parallel in A.) for justifying a con-
clusion; and (2) that it does not agree with the words καθάπερ
οὐδ᾽ ἐν τοῖς καθόλου συλλογισμοῖς. In *23-8 A. showed that the
conclusion from AA^ cannot be A", because that would yield
a false (or rather, unwarranted) conclusion when combined with
one of the original premisses; and that bears no resemblance
to the present argument, as interpreted above.
AL, feeling these difficulties, puts forward a second interpreta-
tion (133. 29-134. 20) (his third and fourth suggestions, 134. 21-31,
135. 6-15, while not without interest, are less satisfactory): The
conclusion from AI^ cannot be apodeictic, because such a con-
clusion cannot be established by a reductio ad impossibile. An
attempt at such a reduction would say 'If it is not true that some
C is necessarily A, it is possible that no C should be A’. But from
this, combined with the original minor premiss Some C is neces-
sarily B, it only follows that it is possible that some B should not
be A (cf. 4052-3), which does not contradict the original major
premiss. On the other hand (Al. supposes A. to mean us to
understand), if we deduce from our original premisses only that
some C is A, we can prove this by a reductio. For if no C is A,
and some C is necessarily B, we get Some B is not A (32*1-4),
which contradicts the original premiss All B is A.
This is a type of argument for which there s a parallel, viz. in
36*19-25, where A. argues that a certain combination yields only
a problematic conclusion, because an assertoric conclusion cannot
I. 9. 30*40— 56 321
be established by a reductio. But (as Maier contends, 2 a. 112 n.)
the attempted reductio which A. had in mind is more likely to
have been that which combines It is contingent that no C should
be A with the original major premiss All B is A. From this
combination nothing, and therefore nothing impossible, follows.
This is more likely to have been A.'s meaning, since the invalidity
of AE* as premisses is put right in the forefront of his treat-
ment of combinations of an assertoric and a problematic premiss
in the second figure (37519-23), and may well have been in his
mind here.
Even this argument, however, is quite different from that used
in dealing (in 3025-8) with the corresponding universal syllogism.
οὐδὲν yap ἀδύνατον συμπίπτει must therefore be put within brackets,
instead of being preceded by a colon and followed by a comma.
It is a fair inference that A. held that where an apodeictic
consequence does follow it can be established by a reductio.
E.g., he would have validated the syllogism All B is necessarily
A, AU C is B, Therefore all C is necessarily A, by the reductio
If some C were not necessarily A, then since all C is B, some B
would not be necessarily A ; which contradicts the original major
premiss.
5-6. ὁμοίως δὲ... λευκόν. Le. EI^ does not establish O»,
as we can see from the fact that, while it might be the case that
no animals are in movement, and that some white things are
necessarily animals, it could not be true that some white things
are necessarily not in movement, but only that they are not in
movement.
CHAPTER 10
Syllogisms with one apodeictic and one assertoric premiss, in the
second figure
3057. (A) Both premisses universal
(a) If the negative premiss is necessary the conclusion is so; (b)
if the affirmative premiss is necessary (AE, EA») the conclusion
is not so.
(a) E"AE^ valid; this shown by conversion.
I4. AE®E® valid; this shown by conversion.
18. (b) A[7EE® invalid; this shown (a) by conversion.
24. (B) by reductio.
31- (y) by an example.
4985 Y
322 COMMENTARY
21. (B) One premiss particular
(a) When the negative premiss is universal and necessary the
conclusion is necessary; (b) when the affirmative premiss is
universal the conclusion is not necessary.
5. (a) E^IO" valid; this shown by conversion.
xo. (b) A"OO® invalid; this shown by an example.
x5. AO*0? invalid; this shown by an example.
3057-9. "Emi 86 . . . ἀναγκαῖον. This is true without exception
only when the premisses are universal (for AO" does not yield
an apodeictic conclusion (31415-17)), and in this paragraph A.
has in mind only the combinations of two universal premisses.
18-19. Ei δὲ... ἀναγκαῖον. This includes the cases ATE, EA®.
In ?2o-4o A. discusses only the first case. He says nothing about
EA^, because it is easily converted into EA® in the first figure,
which has already been shown to give only an assertoric conclu-
sion (432-3).
22-4. δέδεικται... ἀναγκαῖον, *32-3.
26-7. μηδενὶ... ἀνάγκης, ‘necessarily belongs to none’, not
‘does not necessarily belong to any’.
32-3. τὸ συμπέρασμα .. . ἀναγκαῖον, the conclusion is not a
proposition necessary in itself, but only a necessary conclusion
from the premisses.
34. καὶ ai προτάσεις ὁμοίως εἰλήφθωσαν, sc. to those in b2o—r,
31?r-17. Ὁμοίως δ᾽... ἀπόδειξις. In 92-3, 5-10 A. points out
that Festino with the major premiss apodeictic gives an apodeictic
conclusion. In 33-5, 10-15, 15-17 he points out that Baroco (1)
with major premiss necessary, and (2) with minor premiss neces-
sary, gives an assertoric conclusion. He omits Festino with
minor premiss necessary—No P is M, Some S is necessarily M.
This is equivalent to No M is P, Some S is necessarily M, and he
has already pointed out that this yields only an assertoric con-
clusion (3ob5—6).
In the whole range of syllogisms dealt with in chs. 4—22 this
is the only valid syllogism, apart from some of those which are
validated by the ‘complementary conversion’ of problematic
propositions, that A. fails to mention.
14-15. of yàp αὐτοὶ... συλλογισμῶν, cf. 30533-8. If all men
are necessarily animals, and some white things are not animals,
then some white things are not men, but it does not follow that
they are necessarily not men.
17. διὰ yàp τῶν αὐτῶν ὅρων ἡ ἀπόδειξις, cf. 30533-8. If all
I. ro. 3057 — 11. 3164 323
men are in fact animals, and some white things are necessarily not
animals, it does not follow from the data that they are necessarily
not men.
CHAPTER 11
Syllogisms with one apodeictic and one assertoric premiss, in the
third figure
31°18. (A) Both premisses universal
(a) When both premisses are affirmative the conclusion is
necessary. (b) If the premisses differ in quality, (a) when the
negative premiss is necessary the conclusion is so; (£) when the
affirmative premiss is necessary the conclusion is not so.
24. (a) A^AI^ valid; this shown by conversion.
41. AAPI^ valid; this shown by conversion.
33- (8) (a) E»AO" valid; this shown by conversion.
37. (B) EA*O" invalid; cf. the rule stated for the first figure,
that if the negative premiss is not necessary the conclusion is
not so.
bg. Its invalidity also shown by an example.
12. (B) One premiss particular
(a) When both premisses are affirmative, (a) if the universal
premiss is necessary so is the conclusion. [4.515 valid; this shown
by conversion.
19. AnII* valid for the same reason.
20. (P) If the particular premiss is necessary, the conclusion is
not so. AIn"I" invalid, as in the first figure.
27. Its invalidity also shown by an example.
31. I^AI" invalid; this shown by the same example.
43. (b) Premisses differing in quality. E^IO^ valid.
37. OAO®, EI*?O^, O^AO» invalid.
40. Invalidity of OA"O* shown by an example.
32?1. Invalidity of EI*O* shown by an example.
4. Invalidity of O*AO» shown by an example.
31?31-3. ὁμοίως δὲ... ἐξ ἀνάγκης. If all C is A and C is neces-
sarily B, then all C is necessarily B and some A is C. Therefore
some A is necessarily B. Therefore some B is necessarily A.
41—^1. τὸ δὲ Γ τινὶ τῶν B, sc. necessarily.
2-4. δέδεικται γὰρ... ἀναγκαῖον. A. did not say this in so
many words in the discussion of mixed syllogisms in the first
figure (ch. 9). But he said (3015-17) that if the major premiss is
not apodeictic, the conclusion is not apodeictic. And in the first
324 COMMENTARY
figure only the major premiss can be negative. Thus the former
statement includes the present one.
810. ἢ εἰ μή... τούτων. Since the suggestion that every
animal is capable of being good might be rejected as fanciful, A.
substitutes another example. If no horse is in fact awake (or
‘is in fact asleep’), and every horse is necessarily an animal, it
does not follow that some animal is necessarily not awake (or
‘not asleep’).
15-20. ἀπόδειξις δ᾽... ἐστίν. In 516-19 JA"I® is validated as
AAnI^ was in *31-3. The premisses are Some C is A, All C is
necessarily B. Converting the major premiss and transposing the
premisses, we get All C is necessarily B, Some A is C, Therefore
some A is necessarily B. Therefore some B is necessarily A.
In brg~20 A®II" is validated as A"AI" was in ?24-3o. The pre-
misses are All C is necessarily A, Some C is B. Converting the
minor premiss, we get All C is necessarily A, Some B is C, There-
fore some B is necessarily A.
25-6. ὅτε δ᾽... ἀναγκαῖον, 30*35-7, 2-5.
31-3. ὁμοίως δὲ... ἀναγκαῖον. If we use the same terms in
the same order we get A. saying ‘It might be true that some
animals are necessarily awake, and that all animals are in fact
two-footed, and yet untrue that some two-footed things are
necessarily awake'. But, as Al. and P. observe, he is more likely
to have meant that it might be true that some animals are neces-
sarily two-footed, and that all animals are in fact awake, and yet
untrue that some waking things are necessarily two-footed.
38. ἢ τὸ στερητικὸν κατὰ μέρος, sc. ἀναγκαῖον τεθῇ, Cf. 3224-5.
39-40. τὰ μὲν yàp . . . ἐροῦμεν, i.e. (1) that neither Some C is
not A, All C is necessarily B, nor No C is A, Some C is necessarily
B, yields an apodeictic conclusion follows for the same reason
for which No C is A, ΑΙ! C is necessarily B, does not yield one
(1337-510). (2) That Some C is necessarily not A, All C is B, does
not yield an apodeictic conclusion follows for the same reason for
which Some C is necessarily A, All C is B, does not yield one
(631-3).
40-1. ὅροι δ᾽... μέσον ἄνθρωπος. Le., it might be the case
that some men are not awake, and that all men are necessarily
animals, and yet not true that some animals are necessarily not
awake.
3294-5. ὅταν δὲ... μέσον ζῷον. Le. it might be true that
some animals are necessarily not two-footed, and that all
animals are in movement, and yet not true that some things that
are in movement are necessarily not two-footed.
I. 11. 3158— 12. 3287 325
In giving instances of third-figure syllogisms, À. always names
the middle term last. Therefore we should read not δίπουν
μέσον, which is the best supported reading, but μέσον ζῷον or
ζῷον μέσον, and of these the former (which is the reading of C)
is most in accordance with A.’s usual way of speaking (cf. 27320,
282335, 538, 31541). The other readings must have originated from
δίπουν having been written above the line as a proposed emenda-
tion of ζῷον.
CHAPTER 12
The modality of the premisses leading to assertoric or apodeictic
conclusions
32*6. Thus (1) an assertoric conclusion requires two assertoric
premisses; (2) an apodeictic conclusion can follow from an
apodeictic and an assertoric premiss ; (3) in both cases there must
be one premiss of the same modality as the conclusion.
32*6—7. Φανερὸν οὖν... ὑπάρχειν. ὑπάρχειν is here (as often
elsewhere) used not to distinguish an affirmative from a negative
proposition, but an assertoric from an apodeictic. A. here says
that an assertoric proposition requires two assertoric premisses.
But in chs. 9-11 he has shown that many combinations of an
assertoric with an apodeictic premiss yield an assertoric con-
clusion. The two statements can be reconciled by noticing that
when A. says an assertoric conclusion requires two assertoric
premisses, he means that this is the minimum support for an
assertoric conclusion. Now an apodeictic premiss says more than
an assertoric, and a problematic premiss says less; therefore an
assertoric and an apodeictic premiss can prove an assertoric
conclusion, but an assertoric and a problematic premiss cannot.
Cf. the indication in 2953o-2 that A. thinks of the possible as
including the actual, and the actual as including the necessary.
It should be noted, however, that A. has not proved what he
here describes as φανερόν. He has proved (1) that an assertoric
conclusion can be drawn from two assertoric premisses, and from
an assertoric and an apodeictic premiss, and (2) that an apodeictic
conclusion in certain cases follows from an assertoric and an
apodeictic premiss; but he has not proved that an assertoric
conclusion requires that each premiss be at least assertoric (i.e.
be assertoric or apodeictic) ; and in chs. 16, 19, 22 he argues that
certain combinations of an apodeictic with a problematic con-
clusion yield an assertoric conclusion.
326 COMMENTARY
CHAPTER 13
Preliminary discussion of the contingent
32:16. We now proceed to discuss the premisses necessary for
a syllogism about the possible. By ‘possible’ I mean that which
is not necessary but the supposition of which involves nothing
impossible (the necessary being possible only in a secondary
sense).
[21. That this is the nature of the possible is clear from the
opposing negations and affirmations; ‘it is not possible for it to
exist’, ‘it is incapable of existing’, ‘it necessarily does not exist’
are either identical or convertible statements; and so therefore
are their opposites; for in each case the opposite statements are
perfect alternatives.
28. The possible, then, will be not necessary, and the not
necessary will be possible.]
29. It follows that problematic propositions are convertible—
not the affirmative with the negative, but propositions affirmative
in form are convertible in respect of the opposition between the
two things that are said to be possible; i.e. ‘it is capable of belong-
ing’ into ‘it is capable of not belonging’, ‘it is capable of belonging
to every instance’ into ‘it is capable of belonging to no instance’
and into ‘it is capable of not belonging to every instance’, ‘it is
capable of belonging to some instance’ into ‘it is capable of not
belonging to some instance’; and so on.
36. For since the contingent is not necessary, and that which is
not necessary is capable of not existing, if it is contingent for A to
belong to B it is also contingent for it not to belong.
bx. Such propositions are affirmative; for being contingent
corresponds to being.
4- ‘Contingent’ is used in two senses: (1) In one it means ‘usual
but not necessary’, or ‘natural’; in this sense it is contingent that
a man should be going grey, or should be either growing or
decaying (there is no continuous necessity here, since there is not
always a man, but when there is a man he is either of necessity
or usually doing these things).
10. (2) In another sense it is used of the indefinite, which is
capable of being thus and of being not thus (e.g. that an animal
should be walking, or that while it is walking there should be an
earthquake), or in general of that which is by chance.
13. In either of these cases of contingency ‘B may be 4A’ is
convertible with ‘B may not be A’: in the first case because
I. 13. 32*16-29 327
necessity is lacking, in the second because there is not even a
tendency for either alternative to be realized more than the other.
18. There is no science or demonstration of indefinite combina-
tions, because the middle term is only casually connected with
the extremes ; there is science and demonstration of natural com-
binations, and most arguments and inquiries are about such.
Of the former there can be inference, but we do not often look
for it.
23. These matters will be more fully explained later; we now
turn to discuss the conditions of inference from problematic pre-
misses. ‘A is contingent for B' may mean (1) ‘A is contingent for
that of which B is asserted' or 'A is true of that for which B is
contingent’. If B is contingent for C and A for B, we have two
problematic premisses; if A is contingent for that of which B is
irue, a problematic and an assertoric premiss. We begin with
syllogisms with two similar premisses.
32*16-*22. περὶ δὲ τοῦ évBexopévou . . . ζητεῖσθαι. With this
passage should be compared 25337-^19 and the n. thereon.
18-21. λέγω δ᾽... λέγομεν. In 318-20 A. gives his precise view
of ro ἐνδεχόμενον. It is that which is not necessary, but would
involve no impossible consequence; and since that, and only
that, which is itself impossible involves impossible consequences,
this amounts to defining τὸ ἐνδεχόμενον as that which is neither
necessary nor impossible. ‘Necessary’ and ‘impossible’ are not
contradictories but contraries; τὸ ἐνδεχόμενον is the contingent,
which lies between them. It is only in a loose sense that the
necessary can be said ἐνδέχεσθαι (220~-1)—in the sense that it is
not impossible.
21-9. ὅτι δὲ... ἐνδεχόμενον. Though this passage occurs in
all the MSS. and in Al. and P., it seems impossible to retain it in
the text. In #18-20 A. has virtually defined τὸ ἐνδεχόμενον as
that which is neither impossible nor necessary, in #21-8 it is
identified with the not impossible, and in 328-9 with the not
necessary. Becker (pp. 11-13) seems to be right in treating the
passage as an interpolation by a writer familiar with the doctrine
of De Int. 22*14-37. That passage contains several corruptions,
but with the necessary emendations it is found to identify τὸ
ἐνδεχόμενον with the not impossible, i.e. to state the looser sense
of the term in which, as A. observes here in ?2o-r, even the neces-
sary is ἐνδεχόμενον. But, since the complementary convertibility
of problematic propositions which is stated in 32329-^: implies
that the ἐνδεχόμενον is not necessary, the interpolator introduces
328 COMMENTARY
the sentence in *28-9 to lead up to it, but overshoots the mark by
completely identifying the ἐνδεχόμενον with the not necessary,
instead of with that which is neither necessary nor impossible.
29-35. συμβαίνει δὲ... ἄλλων. Since that which is contingent
is not necessary, it follows that (1) ‘For all B, being A is con-
tingent' entails ‘For all B, not being A is contingent’ and ‘For
some B, not being A is contingent’, (2) ‘For some B, being A is
contingent’ entails ‘For some B, not being A is contingent’.
(3) ‘For all B, not being A is contingent’ entails ‘For all B, being
A is contingent’ and ‘For some B, being A is contingent’, (4)
‘For some B, not being A is contingent’ entails ‘For some B,
being A is contingent’.
by-3. εἰσὶ δ᾽... πρότερον. Le., just as 'B is not-A’ is an
affirmative proposition, ‘Bis capable-of-not-being A’ is affirmative.
A. has already remarked in 25521 that in this respect τὸ ἐνδέχεται
τῷ ἔστιν ὁμοίως τάττεται.
4-22. Διωρισμένων δὲ... ζητεῖσθαι. In 25514-15 A. carelessly
identified τὸ ἐνδεχόμενον in the strict sense with τὸ ὡς ἐπὶ τὸ πολὺ
καὶ τῷ πεφυκέναι. He here points out that τὸ ἐνδεχόμενον in the
strict sense, that which is neither impossible nor necessary, occurs
in two forms, one in which one alternative is habitually realized,
the other only occasionally, and another in which there is no
prevailing tendency either way. The distinction has, as he points
out in 18-22, great importance for science, since that which is
habitual may become an object of scientific study while the
purely indeterminate cannot. But it should be noted that the
distinction plays no part in his general doctrine of the logic of
contingency, as it is developed in chs. 13-22. Apart from other
considerations the doctrine of complementary conversion, which
is fundamental to his logic of the problematic syllogism, has no
application to a statement that something is true ὡς ἐπὶ τὸ πολύ,
since ‘B is usually A’ is not convertible with 'B is usually not
A’. Becker (pp. 76-83) views the whole passage with suspicion,
though he admits that it may have an Aristotelian kernel. It
seems to me to be genuinely Aristotelian, but to be a note having
no organic connexion with the rest of chs. 13-22.
4. πάλιν λέγωμεν can hardly mean ‘let us repeat’; for, though
A. speaks in 25b14 of ὅσα τῷ ὡς ἐπὶ τὸ πολὺ kai τῷ πεφυκέναι
λέγεται ἐνδέχεσθαι, he says nothing there of τὸ ἀόριστον. πάλιν
λέγωμεν means ‘let us go on to say’—a usage recognized in Bonitz,
Index, 559>13--14. For the reading λέγωμεν cf. 25526 n.
13-15. ἀντιστρέφει μὲν οὖν... ἐνδεχομένων. The xat of the
Greek MSS. is puzzling. Al.’s best suggestion is that A. means
I. 13. 32829537 329
that ‘B may be A’ is convertible with ‘B may not be A’ as well
as with ‘A may be B'; but probably I' and Pacius are right in
omitting the word.
18-23. ἐπιστήμη δὲ... ἑπομένοις. What A. means is this: If
all we know of the connexion between A and B, and between
B and C, is that B is capable of being A and that C is capable of
being B, then though we can infer that C is capable of being 4,
the resulting probability of C's being A is so small as not to be
worth establishing. On the other hand, if we know that B tends
to be A, and that C tends to be B, the conclusion 'C tends to be
A’ will be important enough to be worth establishing. And since
in nature, according to A.’s view, most of the connexions we can
establish are statements of tendency or probability rather than
of strict necessity, most λόγοι and σκέψεις actually have premisses
and conclusions of this order.
A. postpones the discussion of the usual and the ἀόριστον to
an indefinite future (623). There is no passage of the Analytics
that really fulfils the promise; but 4332-6 and An. Post. 75533-6,
8719-27, 9628-19 touch on the subject.
25-37. ἐπεὶ δὲ... ἄλλοις. The passage is a difficult one, and
neither the statement with which it opens (525-7) nor the structure
of the first sentence can be approved; but correct punctuation
makes the passage at least coherent, and in view of the undisputed
tradition by which it is supported we should hardly be justified
in accepting Becker's excisions (pp. 36-7). A. starts with the
statement that (1) ‘For B, being A is contingent’ is ambiguous,
meaning either (z) ‘For that to which B belongs, being A is
contingent’ or (3) ‘For that for which B is contingent, being A
is contingent’. He then (627-30) supports this by the premisses
(a) that (4) καθ᾽ οὗ τὸ B, τὸ A ἐνδέχεται may mean either (2) or
(3) (because it is not clear whether ὑπάρχει or ἐνδέχεται is to be
understood after τὸ B), and (b) that (1) means the same as (4);
and (531-2) repeats his original statement as following from
these premisses.
In the remainder of the passage A. applies to the syllogism the
distinction thus drawn between two senses of καθ᾽ οὗ τὸ B, τὸ
A ἐνδέχεται. If in the major premiss A is said to be contingent
for B, which is in the minor premiss said to be contingent for C,
we have two problematic premisses. If in the major premiss 4
is said to be contingent for B, which is in the minor premiss said
to be true of C, we have a problematic and an assertoric premiss.
A. proposes to begin with syllogisms with two similar premisses,
καθάπερ xai ἐν τοῖς ἄλλοις, i.e. as syllogisms with two assertoric
330 COMMENTARY
premisses (chs. 4-6) and those with two apodeictic premisses
(ch. 8) were treated before those with an apodeictic and an
assertoric premiss (chs. 9-11).
CHAPTER 14
Syllogisms in the first figure with two problematic premisses
32538. (A) Both premisses universal
AcAcAs valid.
3371. EcAcEs valid.
5. AcEcA¢ valid, by transition from E¢ to Ae.
12. EcEcAs valid, by the same transition.
17. Thus if the minor premiss or both premisses are negative,
there is at best an imperfect syllogism. -
21. (Β) One or both premisses particular
(a) If the major premiss is universal there is a syllogism.
A-*I-*I* valid.
25. E*I«Ov valid.
27. (B) If the universal premiss is affirmative, the particular
premiss negative, we get a conclusion by transition from Os to I*.
AcOcle valid.
34. (5) If the major premissis particular and the minor universal
(IcAc, OcEs, I*Es, OcA»), or if (c) both premisses are particular
(IcIe, O«Oe, I*Oc, OcI9), there is no conclusion. For the middle
term may extend beyond the major term, and the minor term
may fall within the surplus extent; and if so, neither A‘, Es, Is,
nor O* can be inferred.
b3. This may also be shown by contrasted instances. A pure or
a necessary conclusion cannot be drawn, because the negative
instance forbids an affirmative conclusion, and the affirmative
instance a negative conclusion. A problematic conclusion cannot
be drawn, because the major term sometimes necessarily belongs
and sometimes necessarily does not belong to the minor.
18. It is clear that when each of two problematic premisses is
universal, in the first figure, a conclusion always arises—perfect
when the premisses are affirmative, imperfect when they are
negative. ‘Possible’ must be understood as excluding what is
necessary—a point sometimes overlooked.
32540-3371. τὸ yàp ἐνδέχεσθαι... ἐλέγομεν, i.e. we gave (in
2525—32), as one of the meanings of ‘A may belong to all B',
32725-3 B y E
I. 14. 32540— 3334 331
“A may belong to anything to which B may belong’. From this
it follows that if A may belong to all B and B to all C, A may
belong to all C.
33°3-5. τὸ yàp καθ᾽ οὗ... ἐνδεχομένων, ‘for the statement
that A is capable of not being true of that of which B is capable
of being true, implied that none of the things that possibly fall
under B is excluded from the statement’. μὴ ἐνδέχεσθαι in 34 is
used loosely for ἐνδέχεσθαι μὴ ὑπάρχειν.
5-7. ὅταν δὲ... συλλογισμός, because premisses of the form
AE in the first figure prove nothing.
7-8. ἀντιστραφείσης δὲ... ἐνδέχεσθαι, 1.6. when from ‘B is
capable of belonging to no C’ we infer ‘B is capable of belonging
to all C' : cf. 32429->r.
8. γίνεται ὁ αὐτὸς ὅσπερ πρότερον, 1.6. as in 32538-40.
IO. τοῦτο δ᾽ εἴρηται πρότερον, in 352229-P1.
21-3. 'Eav δ᾽..... τέλειος. If τέλειος be read, the statement will
not be correct ; for in ?27-34 A. goes on to point out that when the
particular premiss is negative and the universal premiss affirma-
tive, the latter being the major premiss, there is no τέλειος
συλλογισμός. There is no trace of τέλειος in Al. (169. 20) or in
P.’s comment (158. 13), and it is not a word they would have been
likely to omit to notice if they had had it in their text. Becker
(p. 75) seems to be right in wishing to omit it.
24-5. τοῦτο δὲ... ἐνδέχεσθαι. Waitz reads παντί after ἐνδέ-
χεσθαι (following B’s second thoughts), on the ground that it is
the remark in 32525-32 rather than the definition of τὸ ἐνδέχεσθαι
in 32418-20 that is referred to. But the latter may equally well
be referred to, and the reading παντί no doubt owes its origin to
the fact that one of Al's two interpretations (169. 23-9) is that
ἐνδέχεσθαι is to be understood as if it were ἐνδέχεσθαι παντί. Al,
however, thinks the definition of τὸ ἐνδέχεσθαι in 32418-20 may
equally well be referred to (169. 30-2).
29. τῇ δὲ θέσει ὁμοίως ἔχωσιν, i.e. ‘but the universal premiss
is still the major premiss'.
29-30. οἷον... ὑπάρχειν. A. does not explicitly mention the
case in which the premisses are EcOs, which can be dealt with on
the same lines as the case mentioned, A«O«.
32. ἀντιστραφείσης δὲ τῆς ἐν μέρει refers not to conversion in
the ordinary sense but to conversion from 'B may not belong to
C' to ‘B may belong to C' ; cf. 32229-br.
33. τὸ αὐτὸ... πρότερον, 1.6. as in 324.
34. καθάπερ... ἀρχῆς, i.e. as ACE* gave the same conclusion
as A*A* (85-12).
332 COMMENTARY
34-8. ’Eav δ᾽... συλλογισμός. The first three ἐάν τε clauses
express alternatives falling under one main hypothesis; the
fourth expresses a new main alternative. Therefore there should
be a comma after ὁμοιοσχήμονες (237).
The combinations referred to are IcAc, OcEs, “Ἐς, OcAs, IIe,
OcOs, IcOc, Ocl¢, Since a proposition of the form ‘For all B,
not being A is contingent’ is convertible with ‘For all B, being
A is contingent’, and one of the form ‘For some B, not being A
is contingent’ with ‘For some B, being A is contingent’ (dvri-
στρέφουσιν ai κατὰ τὸ ἐνδέχεσθαι προτάσεις, >2, cf. 32329-b1), all
these combinations are reducible to the combinations ‘For some
B, being A is contingent, For all C (or For some C), being B is
contingent’. Now since B may extend beyond A (238-9), we may
suppose that C is the part of B which extends beyond 4 (i.e. for
which being A is not contingent). Then no conclusion follows ;
there is an undistributed middle.
b3-8. ἔτι δὲ. . . ἱμάτιον. The examples given are κοινοὶ
πάντων, i.e. they are to illustrate all the combinations of premisses
mentioned in *34-8 n. The reasoning therefore is as follows: The
premisses It is possible for some white things to be animals (or
not to be animals), It is possible for all (or no, or some) men
to be white (or for some men not to be white) might both be
true. But in fact it is not possible for any man not to be an animal.
Therefore a negative conclusion is impossible. On the other hand,
the same major premiss and the minor premiss It is possible for
all (or no, or some) garments to be white (or for some garments
not to be white) might both be true. But in fact it is not possible
for any garment fo be an animal. Therefore an affirmative con-
clusion is impossible. Therefore no conclusion is possible.
II-I3. ὁ μὲν yap... καταφατικῷ. Le. the possibility of an
affirmative conclusion is precluded by the fact that sometimes,
when the premisses are as supposed (i.e. the major premiss parti-
cular, in the first figure), the major term cannot be true of the
minor; and the possibility of a egative conclusion is precluded
by the fact that sometimes the major term cannot fail to be true
of the minor.
14-16. kai παντὶ τῷ ἐσχάτῳ τὸ πρῶτον ἀνάγκη (sc. ὑπάρχειν),
i.e. in some cases (e.g. every man must be an animal), καὶ οὐδενὶ
ἐνδέχεται ὑπάρχειν, i.e. in some cases (e.g. no garment can be an
animal).
16-17. τὸ yàp ἀναγκαῖον... ἐνδεχόμενον, cf. 32719.
21. πλὴν κατηγορικῶν μὲν τέλειος. That AcAs yields a direct
conclusion has been shown in 32538-3531.
I. 14. 33534 —523 333
στερητικῶν δὲ ἀτελής. That E«-E* yields a conclusion indirectly
has been shown in 412-17.
23. κατὰ τὸν εἰρημένον διορισμόν, cf. 32418-20.
ἐνίοτε δὲ λανθάνει τὸ τοιοῦτον, i.e., the distinction between the
genuine ἐνδεχόμενον (that which is neither impossible nor necessary)
and that which is ἐνδεχόμενον only in the sense that it is not
impossible.
CHAPTER 15
Syllogisms in the first figure with one problematic and one assertoric
premiss
33°25. (A) Both premisses universal
(a) When the major premiss is problematic (and (a) the minor
affirmative», the syllogism is perfect, and establishes contingency ;
(b) when the minor is problematic, the syllogism is imperfect, and
those that are negative establish a proposition of the form ‘A
does not belong to any C (or to all C) of necessity".
33- (a) (a) A*AA* valid; perfect syllogism.
36. E-AE-* valid; perfect syllogism.
4442. (b) When the minor premiss is problematic, a conclusion
can be proved indirectly by reductio ad impossibile. We first lay
it down that if when A is, B must be, when A is possible B must
be possible. For suppose that, though when A is, B must be, A
were possible and B impossible. If, then, that which was pos-
sible, when it was possible for it to be, might come into being,
while that which was impossible, when it was impossible for it to
be, could not come into being, but at the same time A were
possible and B impossible, A might come into being, and be,
without B.
12. We must take 'possible' and 'impossible' not only in
reference to being, but also in reference to being true and to
existing.
x6. Further, ‘if A is, B is’ must not be understood as if A were
one single thing. Two conditions must be given, as in the pre-
misses of a syllogism. For if Γ 15 true of 4, and A of Z, F must be
true of Z, and also if each of the premisses is capable of being
true, so is the conclusion. If, then, we make A stand for the
premisses, and B for the conclusion, not only is B necessary if 4
is, but B is possible if A is.
25. It follows that if a false but not impossible assumption be
made, the conclusion will be false but not impossible. For since
334 COMMENTARY
it has been shown that when, if A is, B is, then if A is possible,
B is possible, and since A is assumed to be possible, B will be
possible; for if not, the same thing will be both possible and
impossible.
34. «(5) (a) Minor premiss a problematic affirmative.» In view
of all this, let A belong to all B, and B be contingent for all C.
Then A must be possible for all C (&A*AP valid). For let it not be
possible, and let B be supposed to belong to all C (which, though
it may be false, is not impossible). If then A is not possible for
all C, and B belongs to all C, A is not possible for all B (by a
third-figure syllogism). But A was assumed to be possible for all
B. A therefore must be possible for all C; for by assuming the
opposite, and a premiss which was false but not impossible, we
have got an impossible conclusion.
b(2. We can also effect the reductio ad impossibile by a first-
figure syllogism.)
7. We must understand 'belonging to all of a subject' without
exclusive reference to the present; for it is of premisses without
such reference that we construct syllogisms. If we limit the
premiss to the present we get no syllogism ; for (1) it might happen
that at a particular time everything that is in movement should
be a man ; and being in movement is contingent for every horse;
but it is impossible for any horse to be a man;
14. (2) it might happen that at a particular time everything
that was in movement was an animal; and being in movement is
contingent for every man; but being an animal is not contingent,
but necessary, for every man.
19. EAcEP valid; this shown by reductio ad 1mpossibile using
the third figure. What is proved is not a strictly problematic
proposition but ‘A does not necessarily belong to any C’.
41. We may also show by an example that the conclusion is not
strictly problematic ;
37. and by another example that it is not always apodeictic.
Therefore it is of the form ‘A does not necessarily belong to any C'.
3553. (b) (B) Minor premiss a problematic negative. AEcAP
valid, by transition from E* to A*.
rr. EE*Ep valid, by transition from E* to A°.
20. (Return to (a)> (a) (B) Major premiss problematic, minor
negative. AcE, EcE prove nothing; this shown by contrasted
instances.
25. Thus when the minor premiss is problematic a conclusion
is always possible; sometimes directly, sometimes by transition
from E* in the minor premiss to A°.
I. 15. 33525-33 335
30. (B) One premiss particular
(a) When the major premiss is universal, then (a) when the
minor is assertoric and affirmative there is a perfect syllogism
(proof as in the case of two universal premisses) (AcIIe, E-IO«
valid).
35- (8) When the minor premiss is problematic there is an
imperfect syllogism—proved in some cases (AlcIp, EIcO?) by
reductio ad impossibile, while in some cases transition from the
problematic premiss to the complementary proposition is also
required,
bz. viz. when the minor is negative (AOcI», EOcOp).
8. (y) When the minor premiss is assertoric and negative
(AcO, EsO) nothing follows; this shown by contrasted instances.
1x. (b) When the major premiss is particular (IcA, IcE, OcA,
OcE, IAs, TEs, OAs, OE»), nothing follows; this shown by con-
trasted instances.
14. (C) Both premisses particular
When both premisses are particular nothing follows ; this shown
by contrasted instances.
20. Thus when the major premiss is universal there is always a
syllogism ; when the minor so, never.
33°25-33. Ἐὰν δ᾽... ὑπάρχειν. A. lays down here four im-
portant generalizations: (1) that all the valid syllogisms (in the
first figure) which have a problematic major and an assertoric
minor are perfect, i.e. self-evidencing, not requiring a reductio ad
impossibie; (2) that they establish a possibility in the strict
sense (according to the definition of possibility in 32318-20; (3)
that those which have an assertoric major and a problematic
minor are imperfect; and (4) that of these, those that establish
a negative establish only that a certain disconnexion is possible
in the loose sense. This distinction between a strict and a wider
use of the term ‘possible’ is explained at length in 34519-35?2;
'possible' in the strict sense means 'neither impossible nor
necessary', in the wider sense it means 'not impossible'.
All four generalizations are borne out in A.’s treatment of the
various cases in the course of the chapter. But syllogisms with
an assertoric major and a problematic minor which prove an
affirmative (no less than those which prove a negative)—viz.
those with premisses AA‘ (34334-52), AE? (3523-11), AI* (ib.
35-?1), or AO* (35>2-8)—are validated by a reductio ad impossibile,
and A.’s arguments in 34527-37 and in 3715-29 show that any
336 COMMENTARY
syllogism so validated can only prove a possibility in the wider
sense of possibility. Becker (pp. 47-9) therefore proposes to read
in 3329-31 ἀτελεῖς re πάντες of συλλογισμοὶ Kal οὐ τοῦ... ἐνδεχο-
μένου, ἀλλὰ τοῦ μὴ ἐξ ἀνάγκης ὑπάρχειν. But 530-3 ἀλλὰ...
ὑπάρχειν shows that A. has in mind Aere only conclusions stating a
negative possibility ; he seems to have overlooked the point that
those which state a positive possibility similarly state a possibility
only in the wider sense.
A. does not state his reason either for saying that when the
major premiss is assertoric and the minor problematic, the
syllogism is imperfect, or for saying that the possibility established
is only possibility in the wider sense. But it is not difficult to
divine his reasons. For the first dictum his reason must, I think,
be that while ‘All B is capable of being A, AliC is B' are premisses
that are already in the correct form of the first figure, ‘All B is
A, All C is capable of being B’ are premisses that in their present
form have no middle term. For the second dictum his reason
must be the following: For him ἐνδέχεται in its strict sense is a
statement of genuine contingency ; 'It is possible that all C should
be B' says that for all C it is neither impossible sor necessary
that it should be B. Now when all B is A, A may be (and usually
will be) a wider attribute than B, and if so, when C's being B
is contingent, its being A may be not contingent but necessary.
The most, then, that could follow from the premisses is that it
is not impossible that all C should be 4. :
A.'s indirect proof that this follows is, as we shall see, not
convincing. He would have done better, it might seem, to say
simply that ‘All B is A, For all C being B is contingent (neither
impossible nor necessary)' entail It is not impossible that all C
should be A. But that would have been open to the objection
that it is not in syllogistic form, having no single middle term.
And it is open to a less formal objection. All-the existing B's
may be A, and it may be not impossible that all the C's should be
B, and yet it may be impossible that all the C's should have the
attribute A which all the existing B's have. This difficulty A.
tries to remove by his statement in 34>7-18 that to make the
conclusion ‘It is not impossible that all C should be A’ valid, the
premiss All B is A must be true not only of all the B's at a parti-
cular time. But this proviso is not strict enough. Even if all the
B's through all time have had, have, and will have the attribute
A, the premisses will not warrant the conclusion It is not im-
possible that all C should be A, unless A is an attribute which is
necessary to everything that is B, either as a precondition or
I. 15. 3421-24 337
as a necessary consequence of its being B. In other words, to
justify the conclusion we need as major premiss not All B is A,
but All B is necessarily A.
34°1-33. Ὅτι μὲν οὖν... ἀδύνατον. This section is an ex-
cursus preparatory to the discussion of the combination AA‘ in
434-?2. In that combination the premisses are All B is A, For
all C, B is contingent. In the reductio ad imposstbile by which A.
establishes the conclusion It is possible that all C should be A,
he takes as minor premiss of the reductio-syllogism not the
original minor premiss, but All C 7s B, and justifies this on the
ground that this premiss is at worst false, not impossible, so that
if the resultant syllogism leads to an impossible conclusion, that
must be put down to the other premiss, i.e. to the premiss which
is the opposite of the original conclusion. He sees that this
procedure needs justification, and to provide this is the object
of the present section.
7. οὕτως ἐχόντων, i.e. so that, if A is, B must be.
12-15. δεῖ δὲ... ἕξει. A. has in 45-7 laid down the general
thesis that if, when A is, B must be, then when A is possible,
B must be possible. In *7—12 he has illustrated this by the type
of case in which ‘possible’ means ‘capable of coming into being’,
i.e. in which it refers to a potentiality for change. He now points
out that the thesis is equally true with regard to possibility as
it is asserted when we say ‘it is possible that A should be truly
predicated of, and should belong to, B' (ἐν τῷ ἀληθεύεσθαι καὶ
ὧν τῷ Undpyew)—where there is no question of change. It is
possibility in the latter sense that is involved in the application A.
makes of the general thesis to the case of the syllogism (*19—24).
The reference of kai ὁσαχῶς ἄλλως λέγεται τὸ δυνατόν (414) is not
clear. Al. thinks it refers to τὸ ὡς ἐπὶ τὸ πλεῖστον, τὸ ἀόριστον, and
τὸ én’ ἔλαττον (cf. 3264-22), or to the possibility which can be
asserted of that which is necessary (2538), or to other kinds of
possibility recognized by the Megarian philosophers Diodorus and
Philo. None of these is very probable. Maier's view (2 a. 155-6)
that the reference is to possibility ‘on the ground of the syllogism’
(as exhibited in 319-24) can hardly be right, since this is surely
identical with that ἐν τῷ ἀληθεύεσθαι καὶ ἐν τῷ ὑπάρχειν. More
likely the phrase is a mere generality and A. had no particular
other sense of possibility in mind.
18-19. olov órav ... συλλογισμόν, 'Le., when the premisses
are so related as was prescribed in the doctrine of the simple
syllogism' (chs. 4-6).
22-4. ὥσπερ οὖν... δυνατόν, ie. we can now apply the
4985 Z
338 COMMENTARY
general rule stated in ^5-7 to the special case in which A stands
for the premisses of a syllogism and B for its conclusion.
ὥσπερ οὖν εἴ τις θείη. . . συμβαίνοι ἄν is a brachylogy for
οὕτως οὖν ἔχει ὥσπερ ei τις θείη... συμβαίνοι γὰρ av. The usage is
recognized in Bonitz, Index, 872b29-39.
25-52. Τούτου δὲ... ἀδύνατον. A. has shown in 41-24 that
if a certain conclusion would be true if certain premisses were
true, it is capable of being true if the premisses are capable of
being true. He now (225-33) applies that principle in this way:
The introduction into an argument of a premiss which, though
unwarranted by the data, is not impossible, cannot produce an
impossible conclusion. The fact that an impossible conclusion
follows must be due to another premiss which zs impossible.
And this principle is itself in *34-2 applied to the establishment,
by reductio ad tmpossibile, of the validity of the inference ‘If all
B is A, and all C may be B, all C may be A’. The reductio should
run ‘For if not, some C is necessarily not A. But if we add to this
the premiss All C is B (which even if false is not impossible, since
we know that all C may be B), we get the conclusion Some B
is not A; which is impossible, since it contradicts the datum All
Bis A. And the impossibility of the conclusion must be due not
to the premiss which though unwarranted is not impossible; the
other premiss (Some C is necessarily not A) must be impossible
and our original conclusion, All C may be A, true.’
The usually accepted reading in #38 εἰ οὖν τὸ μὲν A μὴ ἐνδέχεται
τῷ I’ makes A. commit the elementary blunder of treating No C
can be A as the contradictory of All C can be A ; of this we cannot
suppose A. guilty, so that n must be right in reading παντί before
τῷ I'. Two difficulties remain. (1) In 438-40 A. says that Some C
cannot be A, All C is B yields the conclusion Some B cannot be
A, while in 31537-9 he says that such premisses yield only the
conclusion Some B is not A. (2) In 34*40-1 he says ‘it was assumed
that all B may be A’, while what was in fact assumed in #34 was
that all B is A. To remove the first difficulty Becker supposes
(p. 56) that ro A οὐ παντὶ τῷ B ἐνδέχεται (^39) means not Some B
cannot be A, but It follows that some B is not A ; and to remove
the second difficulty he excises ἐνδέχεσθαι in *41. But (a) though
ἀνάγκη is sometimes used to indicate not an apodeictic proposition
but merely that a certain conclusion follows, and though τὸ A
οὐ παντὶ τῷ B ἐνδέχεται ὑπάρχειν might perhaps mean ‘it follows
that not all B is A’, I do not think τὸ A οὐ παντὶ τῷ B ἐνδέχεται
can mean this; and (8) all the external evidence in 441 is in favour
of ἐνδέχεσθαι. It is much more likely that A., forgetting the rule
Ι. 15. 3452550 339
laid down in 3137-9, draws the conclusion Some B cannot be
A, and that to complete the reductio he transforms (as he is
justified in doing) the ‘All B is A’ of #34 into the ‘It is not im-
possible that all B should be A’ of #41 (a proposition which
‘All B is A’ entails).
Both Becker (p. 53) and Tredennick charge A. with committing
the fallacy of saying ‘since (1) Some C cannot be A and (2) All
C is B cannot both be true compatibly with (3) the datum All
B is A, and (2) is compatible with (3), (1) must be incompatible
with (3) and therefore false’; whereas in fact (1) also when taken
alone is compatible with (3), as well as (2), and it is only the
combination of (1) and (2) that is incompatible with (3); so that
the reductio fails. The charge is not justified. A.’s argument is
really this: ‘Suppose that All B is A and AllC can be B are true.
(2) is plainly compatible with both of them together and we may
suppose a case in which it is true. Now (1) and (2) plainly entail
Some B cannot be A, which is false, since it contradicts one of
the data. But (2) is in the supposed case true, therefore (1) must
be false and All C can be A must be true.’ The status of (1) and
that of (2) are in fact quite different ; (2) is compatible with both
the data taken together, (1) with each separately but not with
both together.
25-7. Τούτου δὲ... ἀδύνατον. A. knows well (ii. 2-4) that if
a premiss is false it does not follow that the conclusion will be
false, so that ψεῦδος in ?27 cannot mean ‘false’. Both in #25 and in
227 ψεῦδος καὶ οὐκ ἀδύνατον means ‘unwarranted by the data but not
incompatible with them’ ; for the usage cf. 37422 and Poet. 1460422.
29-30. ἐπεὶ γὰρ. . . δυνατόν, cf. ?c—15.
37. τοῦτο δὲ ψεῦδος, 1.6. unwarranted by the data; cf. 425-7 n.
b2-6. [ἐγχωρεῖ δὲ... éyxopeiv.] This argument claims to bea
reductio ad impossibile, but is in fact nothing of the sort. A
reductio justifies the drawing of a certain conclusion from certain
premisses by supposing the contradictory of the conclusion and
showing that this, with one of the premisses, would prove the
contradictory of the other premiss. But here the original con-
clusion (For all C, A is possible) is proved by a manipulation of
the original premisses, and from its truth the falsity of its con-
tradictory is inferred. Becker seems to me justified in saying
(p. 57) that A. could not have made this mistake, and that it
must be the work of a rather stupid glossator. Al. and P. have
the passage, but we have found other instances of glosses which
had before the time of Al. found their way into the text; cf.
24>17-18 n.
340 COMMENTARY
7-18. Act 86 .. . Bvoplfovras. A. points out here that if the
combination of a problematic with a universal assertoric premiss
is to produce a problematic conclusion, the assertoric premiss
must state something permanently true of a class, not merely
true of the members it happens to contain at a particular time.
He proves his point by giving instances in which a problematic
conclusion (All S may be P) drawn from a combination which
offends against this rule is untrue because in fact (2) no S can be
P or (b) all S must be P. (a) It might be true that everything
that is moving (at a particular time) is a man, and that it is
possible for every horse to be moving ; but no horse can be a man.
(b) It might be true that everything that is moving (at a particular
time) is an animal, and that it is possible that every man should
be moving; but the fact (not, as A. loosely says, the συμπέρασμα)
is necessary, that every man should be an animal.
There is a flaw in the reasoning in (b). The reductio in 736-52
only justified the inferring, from the premisses AA‘, of the con-
clusion AP, not of the conclusion A‘; for A. shows in ?27-37 and
3715-29 that any reductio can establish only a problematic
proposition in which 'possible' — 'not impossible', not one in
which it — 'neither impossible nor necessary', while he here
assumes that what it establishes, when the truth of the assertoric
premiss is not limited to the present moment (ro), is a problematic
proposition of the stricter sort. Becker (p. 58) infers that 14-17
ἔτι ἔστω... ζῷον 15 a later addition. But it is not till further on
in the chapter (P27-37) that A. makes the point that a reductio
can only validate a problematic proposition of the looser kind,
and he could easily have written the present section without
noticing the point. Becker's suspicion (ib.) of διὰ... συλλογισμός
(8-11) seems equally unjustified.
19-31. Πάλιν ἔστω... φάσεως. A. here explains the point
made without explanation at 33529-31, that arguments in the first
figure with an assertoric major and a problematic minor, when
they prove a negative possibility, do not prove a problematic
proposition as defined in 3218-20 (λέγω δ᾽ ἐνδέχεσθαι καὶ τὸ
ἐνδεχόμενον, od μὴ ὄντος ἀναγκαίου, τεθέντος δ᾽ ὑπάρχειν, οὐδὲν
ἔσται διὰ τοῦτ᾽ ἀδύνατον).
The premisses No B is A, For all C, being B is contingent, are
originally stated to justify the conclusion For all C, not being A
ἐνδέχεται (619-22). This A. proves by a reductio ad impossibile
(522-7): ‘For suppose instead that some C is necessarily A, and
that all C is B (which is unwarranted by the data (cf. *25-7 n.)
but not impossible, since it is one of our data that it is possible
Ι. 15. 347—352 341
for all C to be B). It follows that some B is A (I^AI in the third
figure, 3131-3). But it is one of our data that no B is A. And
since All C is B is at most false, not impossible, it must be our
other premiss (Some C is necessarily A) that has led to the
impossible result. It is therefore itself impossible, and the original
conclusion ‘It is possible that no C should be A’ is true.
‘This argument’, says A. (527-31), ‘does not prove that for all
C, not being A is ἐνδεχόμενον according to the strict definition of
ἐνδεχόμενον (i.e. that which we find in 32218-20), viz. that for all
C, not being A is neither impossible nor necessary, but only that
for no C is being A necessary (i.e. that for all C, not being A is
not impossible) ; for that is the contradictory of the assumption
made in the reductio syllogism (for that was that for some C,
being A is necessary, and what is established by the reductio is
the contradictory of this). In other words, the reductio has
proceeded as if being impossible were the only alternative to being
ἐνδεχόμενον (whereas there is another alternative—that of being
necessary), and has established only that for all C, not being A
is ἐνδεχόμενον in the loose sense in which what is necessary may
be said to be ἐνδεχόμενον, cf. 32220-1. But in the strict sense what
is ἐνδεχόμενον is neither impossible nor necessary, and the reductio
has not established that for all C, not being A is ἐνδεχόμενον in
this sense. Becker's excision of >19-352 (p. 59) is unjustified.
23. καθάπερ πρότερον, i.e. as in 236-7.
26. ψεύδους yàp τεθέντος, cf. *25—7 n.
31-35?2. ἔτι δὲ... ὅρους. (x) Nothing that is thinking is a
raven, For every man, to be thinking is contingent. But it is not
contingent, but necessary, that no man should be a raven. On
the other hand, (2) Being in movement belongs to no science, For
every man it is contingent that science should belong to him.
But it is not necessary, but only contingent, that being in move-
ment should belong to no man.
The second example is (as A. himself sees—Anaréov βέλτιον τοὺς
ὄρους, 35?2) vitiated by the ambiguity of ὑπάρχειν (for which see
ch. 34). But take a better example such as Al. suggests (196.
8-11). (za) Nothing that is at rest is walking, For every animal
to be at rest is contingent. But it is not necessary, but only
contingent, that no animal should be walking. Thus, since
premisses of the same form are in case (1) compatible with its
being necessary that no C should be A, and in case (2a) with its
being contingent that no C should be 4, they cannot prove either,
but only that it is not necessary that any C should be A. This
establishes, as A. says, the same point which was made in 527-31.
342 COMMENTARY
3545-6. ἀντιστραφείσης δὲ... πρότερον. This is the process
already stated in 32329-^1 to be justified, that of inferring from
‘For C, not being B is contingent’ that for C, being B is contingent.
AE:* is in fact reduced to AA*. καθάπερ ἐν τοῖς πρότερον refers
to the validation of Ac-E-A* in 3335-12.
10-11. ὥσπερ πρότερον... θέσει refers to the treatment of
AASAP in 34234—*2.
II-20. tov αὐτὸν Bé τρόπον... συλλογισμός. EE* is here
similarly reduced to EAs, for which see 34?19-35?2.
I2. ἀμφοτέρων τῶν διαστημάτων. A. not infrequently uses
διάστημα of a syllogistic premiss; the usage is probably connected
with a diagrammatic representation of the syllogism.
20-4. ἐὰν δὲ... πίττα. A. here reverts to the case in which
the major premiss is problematic, the minor assertoric, and dis-
cusses the combinations omitted in 3333-40, viz. those in which
the minor premiss is negative (both premisses being, as throughout
33625-35230, supposed to be universal), viz. ACE and EcE. He
offers no general proof of the invalidity of these moods, but shows
their invalidity by instances. The invalidity of AcE is shown by
the fact that (a) while it is contingent for all animals to be white,
and no snow is an animal, in fact all snow is necessarily white,
but (5) while it is contingent for all animals to be white, and no
pitch is an animal, in fact all pitch is necessarily not white. Thus
premisses of this form cannot entail either It is possible that no
C should be A or It is possible for all C to be A.
The invalidity of EcE is shown by the fact that (a) while it is
contingent for all animals not to be white, and no snow is an
animal, in fact all snow is necessarily white, but (δ) while it is
contingent for all animals not to be white, and no pitch is an
animal, in fact all pitch is necessarily not white. Thus premisses
of this form cannot entail either It is possible that no C should be
A or It is possible for all C to be A.
20-1. ἐὰν δὲ... ὑπάρχειν, ‘if the minor premiss is that B
belongs to no C, not that B is capable of belonging to no C’.
28-30. πλὴν ὁτὲ μὲν. . . εἰρήκαμεν. AACAP (34234-b2) and
EA-*EP (34519-3522) have been proved by reductio ad impossibile,
AEcAP (3523-11) and EEcEp (ib. 11-20) by converting ‘For all
C, not being B is contingent’ into ‘For all C, being B is contingent’
(ἀντιστραφείσης τῆς προτάσεως). ἐξ αὐτῶν therefore is not meant
to exclude the use of reductio, but only to exclude the comple-
mentary conversion of problematic propositions; it does not
amount to saying that the proofs are τέλειοι.
34-5. καθάπερ kai kaBóAou . . . πρότερον, cf. 33533-6, 36-40.
1, 15.3555 ΠῚ 343
40-2. πλὴν of μὲν. . . πρότερον. What A. means is that
AI'IP and II*O» are proved by veductio, as were AACAP(34734~%6)
and EA-*EP (34519-31), and that AOcIP and EOcOpP are proved by
complementary conversion (reducing AO* to Als, and EOs to
EI*) followed by reduciio. The vulgate reading omits καί in Pr,
but C has «ai, which is also conjectured by P.
AleIp may be validated by a reductio to E^IO^ in the third
figure, EIc¢Op by one to A"II" in that figure.
br. καθάπερ ἐν τοῖς πρότερον, sc. as in ?3-20.
2-8. ἔσται δὲ... συλλογισμός. The combinations AOs, EO*,
which are here dealt with, are the two, out of the four enumerated
in *35-4o, which need complementary conversion, so that καί
in b2 is puzzling. Waitz thinks that A. meant to say xai (both)
ὅταν... τὸ ὑπάρχειν, ἡ δ᾽ ἐν μέρει... λαμβάνῃ, καὶ ὅταν ἡ καθόλου
πρὸς τὸ μεῖζον ἄκρον τὸ μὴ ὑπάρχειν, ἡ δ᾽ ἐν μέρει ἡ αὐτή, but (for-
getting the original xat) telescoped this into the form we have.
This is possible, but it seems preferable to omit καί.
4. ἢ μὴ ὑπάρχειν seems to be the work of the same interpolator
who has inserted the same words in >23 and elsewhere. ὑπάρχειν
is used of all assertoric, as opposed to problematic, propositions.
8-9. ὅταν δὲ... συλλογισμός. This formula, ‘when the parti-
cular premiss is a negative assertoric’, would strictly cover the
combinations AcO, E*O, OAs, OEs. But in >11-14 A. proceeds
to speak generally of the cases in which the major premiss is
particular and the minor universal, among which OA* and OE*
are of course included. We must therefore suppose him to be here
speaking only of AcO and EO; i.e. we must suppose the condition
ὅταν καθόλου jj τὸ πρὸς τὸ μεῖζον ἄκρον (235-6, cf. ^3) still to govern
the present passage.
9-11. ὅροι... ἀπόδειξιν. διὰ yap τοῦ ἀδιορίστου ληπτέον τὴν
ἀπόδειξιν is to be understood by reference to 26>1q-21, where A.
applies the method of refutation διὰ τοῦ ἀορίστου to the combina-
tions AO and EO in the first figure. The combinations to be
examined here are For all B, being A is contingent, Some C is
not B, and For all B, not being A is contingent, Some C is not
B. A. is to prove that these yield no conclusion, διὰ τῶν ὅρων, i.e.
by pointing to a case in which premisses of this form are com-
patible with its being in fact impossible that any C should not
be A, and a case in which they are compatible with its being
in fact impossible that any C should be A. Take, for example, the
proof that A«O yields no conclusion. (a) For all animals, being
white is contingent, and some snow is not an animal. But it is
impossible that any snow should not be white. (5) For all animals,
344 COMMENTARY
being white is contingent, and some pitch is not an animal.
And it is impossible that any pitch should be white. Therefore
A*O does not justify the statement either of a negative or of an
affirmative possibility. But it occurs to À. that the three pro-
positions in (5) cannot all be true if Some C is not B is taken to
imply (as it usually does in ordinary speech) that some C ἐς B.
He therefore points out that the form Some C is not B is ἀδιόρι-
στον, assertible when no C is B as well as when some C is B and
some is not.
15-16. εἴτ᾽ ἐνδέχεσθαι... ἐναλλάξ. A. goes beyond the sub-
ject of the chapter to point out that not only when one premiss
is assertoric and the other problematic (ἐναλλάξ), but also when
both are problematic or both are assertoric, two particular
premisses prove nothing.
17-19. ἀπόδειξις δ᾽. . . ἱμάτιον. The same examples will
serve to show the invalidity of all the combinations referred to in
bri-14 and 14-17. Take, for example, IcA. It might be the case
that for some white things, being animals is contingent, and that
all men are in fact white; and all men are necessarily animals. On
the other hand, it might be the case that for some white things,
being animals is contingent, and that all garments are in fact
white; but necessarily no garments are animals. Therefore pre-
misses of the form IA cannot prove either a negative or a positive
possibility.
ἀπόδειξις δ᾽... πρότερον refers to 33*34-58, which dealt with
the corresponding combinations with both premisses problematic,
and used the same examples.
20-2. φανερὸν οὖν... οὐδενός. A. here sums up the results
arrived at in 2?3o-^r4 with regard to combinations of one universal
and one particular premiss. The statement is not quite accurate,
for he has in *8-11 pointed out that the combinations AcO, EcO
prove nothing.
CHAPTER 16
Syllogisms 1n the first figure with one problematic and one apodcictic
premiss
35°23. When one premiss is necessary, one problematic, the
same combinations will yield a syllogism, and it will be perfect
when the minor premiss is necessary (A°A®, E*An, AcI®, E«In);
when the premisses are affirmative (AcA", AcI", A"As, A7I*), the
conclusion will be problematic; but if they differ in quality, then
when the affirmative premiss is necessary (EcA", EI", AnEs,
1. 15. 35 15-22 345
A*O¢) the conclusion will be problematic, but when the negative
premiss is necessary (E"Ac, EI‘) both a problematic and an
assertoric conclusion can be drawn; the possibility stated in the
conclusion must be interpreted in the same way as in the previous
chapter. A conclusion of the form ‘C is necessarily not A’ can
never be drawn.
37- (A) Both premisses universal
(a) If both premisses are affirmative the conclusion is not
apodeictic. A"Acgives the conclusion AP by an imperfect syllogism.
36*2. AcA® gives the conclusion A* by a perfect syllogism.
7. (b) Major premiss negative, minor affirmative. E»A* gives
the conclusion E by reductio ad impossibile.
15. A fortiori it gives the conclusion EP.
17. EcA® gives, by a perfect syllogism, the conclusion E^, not
E; for E* is the form of the major premiss, and no proof of E by
reductio ad impossibile is possible.
25. (c) Major premiss affirmative, minor negative. A"E* gives
the conclusion AP by transition from Es to A-.
27. A*E^ gives no conclusion; this shown by contrasted
instances.
28. (d) Both premisses negative. E«E^ gives no conclusion;
this shown by contrasted instances.
32. (B) One premiss particular
(a) <Major premiss universal) (a) Premisses differing in
quality. (i) (Universal) negative premiss necessary. EPI? gives
the conclusion O, by reductio ad impossibile.
39. (ii) Particular affirmative premiss necessary. EI^ gives
only a problematic conclusion (O*).
40. (B) Both premisses affirmative. When the universal pre-
miss is necessary (Δ. 51“), there is only a problematic conclusion (IP).
b3. (b) Minor premiss universal. (a) When the universal pre-
miss is problematic (I"E*, O"Ee, I"Ac, O7A-»), nothing follows;
this shown by contrasted instances.
7. (B) When the universal premiss is necessary (IcE®, OcE»,
IcA»5, O*A»), nothing follows; this shown by contrasted instances.
12. (C) Both premisses particular
When both premisses are particular nothing follows ; this shown
by contrasted instances.
1g. Thus it makes no difference to the validity of a syllogism
whether the non-problematic premiss is assertoric or apodeictic,
346 COMMENTARY
except that if the negative premiss is assertoric the conclusion is
problematic, while if the negative premiss is apodeictic both a
problematic and an assertoric conclusion follow.
In this chapter A. lays it down (3523-36) that if, in the com-
binations of an assertoric with a problematic premiss discussed
in ch. 15, an apodeictic premiss be substituted for an assertoric,
the validity of the argument will not be affected, but, if anything,
only the nature of the conclusion. The combinations recognized
in ch. 15 as valid are ACA, ἘΞΑ, AAs, EAs, AEs, EEs, A-I, ἘΠῚ,
Als, EI*, AOs, EOr. Of the combinations got by substituting an
apodeictic for an assertoric premiss, AcI" is omitted in the subse-
quent discussion, but what A. says of A*A^ (3672-7) would
mutatis mutandis apply to it. A»O« and E^O* are omitted, but
are respectively reducible to A^I and E®I¢ (for which v. 3624o—*2,
334—9) by conversion from For some C, not being B is contingent
to For some C, being B is contingent (32?29-*1).
35°32-4. τὸ δ᾽ ἐνδέχεσθαι... . πρότερον, i.e. where a syllogism
is said (as in 630-2) to prove both a problematic and an assertoric
conclusion, the former is not problematic in the strict sense
defined in 32?18-2o0 (where All C admits of not being A means
It is neither impossible nor necessary that no C should be A), but
only in the wider sense stated in 33>30-1, 3427-8 (where it means
It is not impossible that no C should be A). That is because the
conclusion is simply inferred a fortiori from the main conclusion
that no C is A (36215717). Cf. 34*19-31 n.
3671-2. τὸν αὐτὸν yàp τρόπον . . . πρότερον, i.e. the conclu-
sion AP from A^A* will be proved by a reductio ad impossibile, as
the conclusion from AA‘ was in 34?34-?2. The reductio of A»A«-A»
will be in O^AO in the third figure.
7-17. Ei δὲ... ὑπάρχειν. A. shows here that from the pre-
misses E"Ac in the first figure (1) E follows by a reductio ad
impossibile using E^IO^ in the first figure (3051-2), and (2) EP
follows a fortiori.
8-9. καὶ τὸ μὲν A... τῷ B. ABd have ἐξ ἀνάγκης after τῷ B,
but Al. had not these words in his text, and their introduction
is almost certainly due to his using them in his interpretation
(208. 11-12). He introduces them by way of pointing out that
τὸ A μηδενὶ ἐνδεχέσθω τῷ B here means ‘let it not be possible for
any B to be A’, not ‘let it be possible that no B should be A’;
but that is made sufficiently clear by the words ἔστω πρῶτον ἡ
στερητικὴ ἀναγκαία in 38. The combination pydevi ἐνδέχεσθαι
ἐξ ἀνάγκης would, I think, be unparalleled in A.
I. 16. 353236831 347
IO. ἀναγκὴ δὴ... ὑπάρχειν. This is not meant to be a neces-
sary proposition, but to express the necessary sequence of the
assertoric proposition No C is A from the premisses.
IO-I5. κείσθω γὰρ... ἀρχῆς. The words of which Becker
(p. 44) expresses suspicion are (as he points out) correct, though
unnecessary, and may be retained.
18. καὶ τὸ μὲν A... ὑπάρχειν. The difference must be noted
between τὸ A ἐνδεχέσθω μηδενὶ τῷ B ὑπάρχειν, 'lct it be pos-
sible for A to belong to no B’, and ?34 εἰ τὸ μὲν A μηδενὶ τῷ B
ἐνδέχεται ὑπάρχειν, ‘if it is impossible for A to belong to any B'.
20-4. ἀλλ᾽ οὐ... ἀδύνατον. A. gives two reasons why the
conclusion from ‘For all B, not being A is contingent, It is neces-
sary that all C be B' is ‘For all C, not being A is contingent’, not
‘NoCis A’. The first is that the major premiss is only problematic.
The second is that the conclusion No C is A could not be proved
by reductio ad impossibile, since (so the argument must continue)
if we assume its opposite Some C is A, and take with this the
original major premiss, we get the combination 'For all B, not
being A is contingent, Some C is A’, from which we cannot infer
the contradictory of the original minor premiss, viz. It is possible
that some C should not be B. This follows from the general
principle stated in 37519-22, that in the second figure an affirma-
tive assertoric and a negative problematic premiss prove nothing.
Thus in 323 τινί must be right. The MSS. of Al. record τινὲ μή
as a variant (210. 32), but Al.'s commentary (ib. 32-4) shows that
the variant he recognized was τινί. μηδενί, the reading he accepts
(210. 21—30), is indefensible.
26. διὰ τῆς ἀντιστροφῆς, i.e. by the conversion of For all C,
not being B is contingent into For all C, being B is contingent ;
cf, 32229-br.
27. καθάπερ ἐν τοῖς πρότερον, i.e. as with the corresponding
mood (AE-*A») treated of in the last chapter (3523-11).
28-31. οὐδ᾽ Grav... πίττα. It is implied that when both pre-
misses are negative and the minor is problematic (E^E*), a con-
clusion can be drawn, viz. by the complementary conversion of
E^E* into E^A*, which combination we have seen to be valid
(97217).
29-31. ὅροι δ᾽... πίττα. For all animals, being white, and
not being white, are contingent, it is necessary that no snow
should be an animal, and in fact it is necessary that all snow
should be white. On the other hand, for all animals, being white,
and not being white, are contingent, it is necessary that no pitch
should be an animal, but in fact it is necessary that so pitch
348 COMMENTARY
should be white. Thus AcE" and E-E^ in the first figure prove
nothing.
42- 12. Τὸν αὐτὸν δὲ τρόπον... χιών. A. now proceeds to
consider cases in which the premisses differ in quantity. 53-12
expressly considers those in which the minor premiss is universal,
so that *33-b2 must be concerned only with those in which the
major premiss is universal. Further, the statement in *33-4 must
be limited to the case in which it is the universal premiss that is a
negative apodeictic proposition.
When A. says (b7-12) that when the universal premiss is
apodeictic and the particular premiss problematic, nothing
follows, he seems to be condemning inter alia EnIe, E^Oc, A7I*,
A^O*, which are valid; but he will be acquitted of this mistake
if we take the condition ‘if the minor premiss is universal’ to be
carried over from 53-4.
32. Tov αὐτὸν δὲ τρόπον . .. συλλογισμῶν. This follows from
the fact that if in a valid first-figure syllogism we substitute a
particular minor premiss for a universal one, we get a particular
conclusion in place of the original universal conclusion.
34-9. olov ci... ἐνδέχεσθαι. E^IcO is proved by a reductio in
E^AE^ in the first figure. A. omits to add that OP follows a
fortiori (cf. 35530-2). ἀνάγκη means ‘it follows’, as in *10 (where
see n.).
34. εἰ τὸ pevA... ὑπάρχειν. Cf. 518 n.
I-2. οὐκ ἔσται... συλλογισμός, ie. the conclusion will be
problematic.
2. ἀπόδειξις δ᾽... πρότερον. This must mean that E«I"Oc is
a perfect syllogism as was ΕΑ Ἐς (217-25), and that A®IcIP is
proved by a reductio as was AnAcAP (35538-3622). The reductio
of A*IcIp will be effected in A"E"E® in the second figure.
5-7. ὅροι δὲ .. . ἱμάτιον. Le. it is necessary that some white
things should and that others should not be animals; for all men,
being white, and not being white, are contingent; and in fact
all men are necessarily animals. On the other hand, it is necessary
that some white things should and that others should not be
animals; for all garments, being white, and not being white, are
contingent; but it is necessary that no garment be an animal.
Thus in the first figure InAc, I^Ec, OAs, O^E- prove nothing.
8-12. στερητικοῦ μὲν... χιών. Le. it is contingent that some
white things should be, and that they should not be, animals; it
is necessary that no raven be white ; and every raven is necessarily
an animal. On the other hand, it is contingent that some white
things should be, and that they should not be, animals; it is
I. 16. 36332— 524 349
necessary that no pitch be white; but necessarily no pitch is
an animal. Thus IcE", O«E^ in the first figure prove nothing.
Again, it is contingent that some white things should be, and
that they should not be, animals; every swan is necessarily
white; and every swan is necessarily an animal. On the other
hand, it is contingent that some white things should be, and that
they should not be, animals; all snow is necessarily white; but
necessarily mo snow is an animal. Thus IcA», OcA® in the first
figure prove nothing.
12-18. οὐδ᾽ ὅταν... Spor.
A
(Major) Some white things are necessarily animals, some neces-
sarily not.
(Minor) Some men are necessarily white, some necessarily not.
(Minor) Some lifeless things are necessarily white, some
necessarily not.
B
(Major) For some white things, being animals is contingent ; for
some white things, not being animals is contingent.
(Minor) For some men, being white is contingent ; for some men,
not being white is contingent.
(Minor) For some lifeless things, being white is contingent ; for
some lifeless things, not being white is contingent.
Combining a major from A with a minor from B or vice versa,
we can get true propositions illustrating all the possible combina-
tions of an apodeictic with a problematic proposition, both parti-
cular, in the first figure. That such premisses do not warrant a
negative conclusion is shown by the fact that all men are neces-
sarily animals; that they do not warrant an affirmative con-
clusion, by the fact that all lifeless things are necessarily mot
animals.
19-24. Φανερὸν odv ... ὑπάρχειν. Le. the valid combinations
of a problematic with an apodeictic premiss are the same, in
respect of quality and quantity, as the valid combinations of a
problematic with an assertoric (for which v. ch. 15). The only
difference is that where a negative premiss is assertoric (i.e. in
the combinations EAs, EEs, EIv, EO*) the conclusion is problema-
tic, and where a negative premiss is apodeictic (i.e. in the com-
binations E»As, E^Ec, E»Iv, E»O*) both a problematic and an
assertoric conclusion follow. A. says 'the negative premiss', not
'a negative premiss', though in some of the combinations both
350 COMMENTARY
premisses are negative. This is because in these cases the other
premiss, being problematic, is in truth no more negative than it is
affirmative, since For allC, not being B is contingent is convertible
with For all C, being B is contingent (3229-1).
24-5. δῆλον δὲ... σχημάτων. This sentence is quite indefen-
sible. A. has said in 3325-7; that in the first figure valid com-
binations of a problematic major and an assertoric minor yield
a perfect (i.e. self-evidencing) syllogism, and has pointed this
out in dealing with the several cases (AcA, E«A, A-I, E-I). In
3523-6 he has said the same about the valid combinations of a
problematic major with an apodeictic minor, and has pointed
this out in dealing with the cases AcA*, EcA^, Eel" (4515 is not
expressly mentioned). He could not possibly have summed up
his results by saying that all the valid syllogisms are imperfect.
Some unintelligent scribe has lifted the sentence bodily from
39?1-3, his motive no doubt being to have at the end of the treat-
ment of the modal syllogism in the first figure a remark corre-
sponding to what A. says at the end of his treatment of modal
syllogism in the other two figures (3921-3, 40515-16).
CHAPTER 17
Syllogisms in the second figure with two problematic premisses
3626. In the second figure, two problematic premisses prove
nothing. An assertoric and a problematic premiss prove nothing
when the affirmative premiss is assertoric; they do prove some-
thing when the negative, universal premiss is assertoric. So too
when there are an apodeictic and a problematic premiss. In these
cases, too, the conclusion states only possibility in the loose sense,
not contingency.
35. We must first show that a negative problematic proposition
is not convertible. If for all B not being A is contingent, it does
not follow that for all A not being B is contingent. For (1) sup-
pose this to be the case, then by complementary conversion it
follows that for all A being B is contingent. But this is false ; for
if for all B being A is contingent, it does not follow that for all A
being B is contingent.
37*4- (2) It may be contingent for all B not to be A, and yet
necessary that some A be not B. It is contingent for every man
not to be white, but it is not contingent that no white thing should
be a man; for many white things cannot be men, and what is
necessary is not contingent.
I. 16. 3624-5 351
9. (3) Nor can the converse be proved by reductio ad tmpossibile.
Suppose we said ‘let it be false that it is contingent for all A not
to be B; then it is not possible for no A to be B. Then some A
must necessarily be B, and therefore some B necessarily A. But
this is impossible.’
14. The reasoning is false. If it is not contingent for no A to
be B, it does not follow that some A is necessarily B. For we can
say ‘it is not contingent that no 4 should be B’, (a) if some A is
necessarily B, or (b) if some A is necessarily not B; for that which
necessarily does not belong to some A cannot be said to be
capable of not belonging to all A; just as that which necessarily
belongs to some A cannot be said to be capable of belonging to
all A.
20. Thus it is false to assume that since C is not contingent
for all D, there is necessarily some D to which it does not
belong; it may belong to all D and it may be because it
belongs necessarily to some, that we say it is not contingent for all.
Thus to being contingent for all, we must oppose not ‘necessarily
belonging to some' but 'necessarily not belonging to some'. So
too with being capable of belonging to none.
29. Thus the attempted reductio does not lead to anything
impossible. So it is clear that the negative problematic proposi-
tion is not convertible.
32. Now assume that A is capable of belonging to no B, and to
all C (EcA*). We cannot form a syllogism (1) by conversion (as we
have seen) ; nor (2) by reductio ad impossibile. For nothing false
follows from the assumption that B is not capable of not belonging
to all C ; for A might be capable both of belonging to all C and of
belonging to no C.
38. (3) If there were a conclusion, it must be problematic, since
neither premiss is assertoric. Now (a) if it is supposed to be
affirmative, we can show by examples that sometimes B is not
capable of belonging to C. (b) If it is supposed to be negative, we
can show that sometimes it is not contingent, but necessary, that
no C should be B.
63. For (a) let A be white, B man, C horse. A is capable of
belonging to all C and to no B, but B is not capable of belonging
to C ; for no horse is a man. (b) Nor is it capable of not belonging ;
for it is necessary that no horse be a man, and the necessary is not
contingent. Therefore there is no syllogism.
1o. Similarly if the minor premiss is negative (ἘΠ), or if the
premisses are alike in quality (AcA‘, E«E*), or if they differ in
quantity (AcI¢, AcOr, Eels, IeAc, IcEs, OcAs, ΟΞ ΕΠ), or if both are
352 COMMENTARY
particular or indefinite (I*Ie, IcOc, OcIe, OcO^) ; the same contrasted
instances will serve to show this.
16. Thus two problematic premisses prove nothing.
36>26-33. Ἔν δὲ τῷ δευτέρῳ... προτάσεων. These statements
are borne out by the detailed treatment in chs. 17-19, except
for the fact that I*E, OcE, IcE", OcE" prove nothing. These
are obviously condemned by their breach of the rule that in the
second figure the major premiss must be universal (to avoid
illicit major).
33-4. Set 86 . . . πρότερον, ie. the problematic conclusion
must be interpreted not as stating a possibility in the strict sense,
something that is neither impossible nor necessary (32218-20), but
a possibility in the sense of something not impossible (33^29-33,
34627-31). This follows from the fact that problernatic conclu-
sions in the second figure are validated by reductio ad impossibile ;
for the reductio treats being impossible as if it were the only
alternative to being ἐνδεχόμενον, while in fact there is another
alternative, viz. being necessary.
37-373. κείσθω yap... στερητικόν. (1) For all B, being A is
contingent entails (2) For all B, not being A is contingent; (3)
For all A, not being B is contingent entails (4) For all A, being B
is contingent. Therefore if (2) entailed (3), (1) would entail (4),
which it plainly does not.
39-40. kai αἱ évavriat ... ἀντικείμεναι. The precise meaning
of this is that Ἐπ is inferrible from A‘ and vice versa, and Oc
from I* and vice versa, and O¢ from As‘, and I¢ from Es. A* is
not inferrible from O*, nor Ἐπ from Iv. Cf. 32429-35 n. À* and
E* are ἐναντίαι; AS and Oe, and again Ἐπ and Ie, ἀντικείμεναι.
Ic and O¢ are probably reckoned among the ἐναντίαι, as I and O
are in s59>1o—though in 6323-30 they are included among the
ἀντικείμεναι (though only κατὰ τὴν λέξιν ἀντικείμεναι).
3798-9. τὸ δ᾽ ἀναγκαῖον .... ἐνδεχόμενον, cf. 32418-20.
9-31. ᾿Αλλὰ pry ... στερητικόν. The attempted proof, by
reductio ad impossibile, that if for all B, not being A is contingent,
then for all A, not being B is contingent (36536--7) ends at
ἀδύνατον (37414), and A.’s refutation begins with od ydp. The
punctuation has been altered accordingly (Bekker and Waitz
have a full stop after τῶν B and a colon after ἀδύνατον, in #14).
The attempt to prove by reductio ad impossibile that τὸ A
ἐνδέχεται μηδενὶ τῷ B ὑπάρχειν entails τὸ B ἐνδέχεται μηδενὶ τῷ A
ὑπάρχειν goes as follows: Suppose the latter proposition false
(310). Then (X) τὸ B οὐκ ἐνδέχεται μηδενὶ τῷ A ὑπάρχειν. Then
I. 17. 36526-37337 353
(Y) it is necessary for B to belong to some A. Then (Z) it is
necessary for A to belong to some B. But ex hypothesi it is
possible for A to belong to no B. Therefore it must be possible
for B to belong to no A.
A.'s criticism in ?14-31 is as follows: The step from (X) to (Y)
is unsound. ‘It is necessary for B to belong to some A’ is not
the only alternative to τὸ B ἐνδέχεται μηδενὶ τῷ A ὑπάρχειν. There
is also the alternative ‘It is necessary for B not to belong to some
A’. Necessity, not only the necessity that some A be B, but
equally the necessity that some A be not B, is incompatible with
τὸ B ἐνδέχεται μηδενὶ τῷ Β ὑπάρχειν. That is the strict meaning
of évSéyerac—not ‘not impossible’ but ‘neither impossible nor
necessary’ (32418-21). The proper inference, then, in place of
(Y), is ‘Either it is necessary for B to belong to some A or it is
necessary for B not to belong to some A’. And from the second
alternative no impossible conclusion follows, so that the proof per
vmpossibile fails.
22. παντὶ yàp ὑπάρχει. The correct sense is given by n's
addition εἰ τύχοι, ‘there may be cases in which C belongs to all D'.
We should not read εἰ τύχοι, however, because it is missing both
in Al. (225. 31) and in P. (213. 27-8).
28. 60 τὸ ἐξ ἀνάγκης... ἀνάγκης. Waitz's reading οὐ μόνον
(so the MSS. Bdn) τὸ ἐξ ἀνάγκης... ἀλλὰ καὶ τὸ ἐξ ἀνάγκης κτλ
(BCdn) is supported by P. 214. 15-17, but not by Al. (226. 16-19,
27-30). The fuller reading seems to be an attempt to make things
easier. Not either alternative nor both, but the disjunction of the
two, is the proper inference from (X) (see *9—31 n.) ; but in answer
to the opponent's assumption of (Y) we must make the counter-
assumption It is necessary for B not to belong to some A; and
by pointing out this alternative we can defeat his argument.
34- εἴρηται yap... πρότασις, in 36535-37431. ἡ τοιαύτη mpó-
raats, ie. such a premiss as For all B, not being A is contingent.
35-7. ἀλλ᾽ οὐδὲ... ὑπάρχειν. What A. says, according to the
traditional reading, is this: Nor again can the inference ‘For all
B, not being A is contingent, For all C, being A is contingent,
Therefore for all C, not being B is contingent’ be established by
a reductio ad impossibile. For if we assume that for all C, being
B is contingent, and reason as follows: ‘For all B, not being A
is contingent, For all C, being B is contingent, Therefore for all
C, not being A is contingent’, we get no false result, since our
conclusion is compatible with the original minor premiss.
There is a clear fallacy in this argument. It takes ‘For all C,
being B is contingent’ as the contradictory of ‘For all C, not being
4985 Aa
354 COMMENTARY
B 1s contingent', in the same breath in which it points out that
‘For all C, not being A is contingent’ is compatible with ‘For all
C, being A is contingent’. A. cannot really be supposed to have
reasoned like this; Maier's emendation (2 a. 179 n.) is justified.
The argument then runs: Suppose that we attempt to justify
the original conclusion 'For all C, not being B is contingent', by
assuming its opposite, ‘For some C, not being B is not contingent’,
and interpret this as meaning ‘For some C, being B is necessary’
and combine with it the original premiss ‘For all B, not being A
is contingent’. The only conclusion we could get is ‘For some
C, not being A is contingent’. But so far is this from contradicting
the original minor premiss ‘For all C, being A is contingent’, that
the latter is compatible even with ‘For aJ C, not being A is
contingent'.
Al. and P. have the traditional reading, and try in vain to
make sense of it. As Maier remarks, the corruption may be due
to a copyist, misled by ?37, having thought that A. meant to
deduce as the conclusion of the reductio syllogism ‘For all C,
not being A is contingent’, and struck out the two μή᾽5 in order
to get a premiss that would lead to this conclusion. Cf. a similar
corruption in 255s.
bg-1o. τὸ δ᾽ àvaykatov . . . ἐνδεχόμενον, cf. 32736.
II. καὶ ἂν... στερητικόν, Le. if the premisses are For all B,
being A is contingent, For all C, not being A is contingent.
12-13. διὰ yàp τῶν αὐτῶν ὅρων... ἀπόδειξις, 1.6. we may use
the terms used in 63-10. For all men, being white, and not being
white, are contingent ; for all horses, being white, and not being
white, are contingent ; but it is necessary that no horse should be
a man.
15-16. ἀεὶ yàp . . . ἀπόδειξις, 1.6. for all men, and for some
men, being white, and not being white, are contingent; for all
horses, and for some horses, being white, and not being white, are
contingent ; but it is 2ecessary that no horse should be a man.
CHAPTER 18
Syllogisms in the second figure with one problematic and one assertoric
premiss
37>19. (A) Both premisses universal
(a) An assertoric affirmative and a problematic negative (Δ Ἐς,
ἘΞΑ) prove nothing; this shown by contrasted instances.
23. (b) Assertoric negative, problematic affirmative, EA«E»P
valid, by conversion.
I. 17. 3759— 18. 37°23 355
29. A*EEP valid, by conversion.
29. (c) Two negative premisses give a problematic conclusion
(EEcEP and E«EE»), by transition from E* to A°.
35. (d) Two affirmative premisses (AA‘, ASA) prove nothing;
this shown by contrasted instances.
39. (Β) One premiss particular
(a) Premisses differing in quality. (a) When the affirmative
premiss is assertoric (AOvc, OcA, IE*, E«I), nothing follows; this
shown by contrasted intances.
4832. (8) When the negative premiss is assertoric (and is
universal, and is the major premiss) (EI*), OP follows by conversion.
4. (ὁ) (α) When both premisses are negative and the assertoric
premiss is universal (and is the major premiss> (ΕΟ), ΟΡ follows
by transition from O* to 19,
8. When (a) (y) the negative premiss, or (b) (B) one of two
negative premisses, is a particular assertoric (AcO, OA‘, E*O,
OE»), nothing follows.
10. (C) Both premisses particular
When both premisses are particular nothing follows ; this shown
by contrasted instances.
37°19-38. Εἰ δ᾽... ἄνθρωπος. The combinations in which
one or both premisses are particular being dealt with in the next
paragraph, the present paragraph must be taken to refer to
combinations of two universal premisses (though there is an
incidental reference to the others in 22). It will be seen from the
summary above that all of these are dealt with. The generaliza-
tion that an affirmative assertoric and a negative problematic
premiss prove nothing (19-22) is true, whatever the quantity of
the premisses; but the statement that an affirmative problematic
and a negative assertoric give a conclusion (b23-4) is true without
exception only when both premisses are universal.
22-3. ἀπόδειξις δ᾽... ὅρων. If for simplicity we confine our-
selves to the case in which both premisses are universal (for the
same argument applies to that in which one is particular), the
combinations to be proved invalid are All B is A, For all C, not
being A is contingent, and For all B, not being A is contingent,
All C is A. Let us take the first of these. The invalidity of the
combination can be shown by the use of the same terms that
were used in 53-1o. It might be true that all men are white, and
that for all horses not being white is contingent ; but it is not true
356 COMMENTARY
either that for all horses being men is contingent, or that for all
horses not being men is contingent ; they are secessarily not men.
Thus from premisses of this form neither an affirmative nor a
negative contingency follows.
23-8. ὅταν δ᾽... σχήματος. ‘No B is A, For all C, being A is
contingent, Therefore it is not impossible that no C should be B'
is validated by conversion to ‘No A is B, For all C, being 4 is
contingent, Therefore it is not impossible that no C should be B'
(34919731).
29. ὁμοίως δὲ... στερητικόν. ‘For all B, being A is con-
tingent, No C is A’ is converted into ‘No A is C, For all B, being
A is contingent’, from which it follows (34b19-31) that it is not
impossible that no B should be C ; from which it follows that it is
not impossible that no C should be B. Maier argues (2 a. 18o-1)
that A.'s admission of this mood is a mistake, on the ground that
(on A.'s principle, stated in 36535-37531) ἐνδέχεται τὸ Γ μηδενὶ τῷ
B ὑπάρχειν does not entail ἐνδέχεται τὸ B μηδενὶ τῷ Γ ὑπάρχειν. But
that principle applies (as the argument in 36535-37431 shows)
only when ἐνδεχόμενον is used in its strict sense of ‘neither im-
possible nor necessary’, not when it is used in its loose sense of
‘not impossible’ (cf. 2537-19 n.).
29-35. ἐὰν δ᾽... σχῆμα, Le. EE* or EcE proves nothing
directly (as two negative premisses never do, in any figure), but
by the complementary conversion proper to problematic pro-
positions (32#29-1) we can reduce EE* (to take that example)
to ‘No A is B, For all C, being B is contingent’, and then by
simple conversion of the major premiss get a first-figure argument
which is valid. --πάλιν in 535 = ‘as in 524-8".
31. ἐνδέχεσθαι, sc. μὴ ὑπάρχειν. B actually has these words,
but it is more likely that they were added in B by way of inter-
pretation than that they were accidentally omitted in the other
MSS.
36-8. ὅροι . . . ἄνθρωπος. Le. ‘For every animal, being
healthy is contingent, Every man is healthy' is compatible with
its being necessary that every man should be an animal. On the
other hand, 'For every horse, being healthy is contingent, Every
man is healthy’ is compatible with its being necessary that no
man should be a horse.
Again 'Every animal is healthy, For every man, being healthy
is contingent' is compatible with every man's being necessarily
an animal On the other hand, ‘Every horse is healthy, For
every man, being healthy is contingent’ is compatible with its
being necessary that no man should be a horse.
I. 18. 3752338812 357
Thus AcA and AA: in the second figure prove nothing.
3821-2. τοῦτο δ᾽... «πρότερον. This refers to the examples in
3736-8. Take for instance Ec]. For all animals, not being healthy
is contingent, some men are healthy, and every man is necessarily
an animal. On the other hand, for all horses not being healthy is
contingent, some men are healthy, but every man is necessarily
not a horse.
Again, take AOc. ‘Every animal is healthy’ and ‘For some men,
not being healthy is contingent’ are compatible with its being
necessary that every man should be an animal. On the other
hand, ‘Every horse is healthy’ and ‘For some men, not being
healthy is contingent’ are compatible with its being necessary
that 4o man should be a horse.
3-7. ὅταν δὲ... συλλογισμός. These two statements are too
widely expressed. The first would include AcO, EIs, IcE, OA‘;
but in view of what A. says in #8-10 he is evidently thinking only
of the cases in which the negative premiss is a universal assertoric
proposition (which excludes AcO, OAs). Further, IcE, which
prima facie comes under this rule, and OcE, which prima facie
comes under the next, are in fact invalid because in the second
figure the major premiss must be universal, to avoid illicit major.
In both rules A. must be assuming the universal assertoric premiss
to be the major premiss.
3-4. ὅταν δὲ... πρότερον. ‘No B is A, For some C, being A
is contingent, Therefore for some C, not being B is possible' is
validated by conversion to ‘No A is B, For some C, being A is
contingent, Therefore for some C, not being B is possible'
(35335-"1). καθάπερ ἐν τοῖς πρότερον, i.e. as EA-EP in the second
figure was validated by conversion to EA-EP in the first (3724-8).
6-7. ἀντιστραφέντος δὲ. . . πρότερον, ie. as prescribed in
3732-3.
II-I2. ἀπόδειξις δ᾽... ὅρων. The reference is probably to the
proof by means of ὅροι in 37536-8. Take e.g. 115, Some animals
are healthy, for some men being healthy is contingent, and all
men are necessarily animals. On the other hand, some horses
are healthy, for some men being healthy is contingent, but
necessarily no men are horses. Therefore premisses of this form
cannot prove either a negative or an affirmative.
358 COMMENTARY
CHAPTER 19
Syllogisms in the second figure with one problematic and one
apodeictic premiss
38413. (A) Both premisses universal
(a) Premisses differing in quality. (a) Negative premiss apodeic-
tic: problematic and assertoric conclusion. (8) Affirmative pre-
miss apodeictic: no conclusion. (a) E^A*EP valid, by conversion.
E^A*E valid, by reductio ad impossibile.
25. ACE"Ep and AcE®E similarly valid.
26. (B) EcA" proves nothing; for (1) it may happen that C is
necessarily not B, as when A is white, B man, C swan. There is
therefore no problematic conclusion.
36. But neither is there (2) an apodeictic conclusion; for (i).
such a conclusion requires either two apodeictic premisses, or at
least that the negative premiss be apodeictic. (ii) It is possible,
with these premisses, that C should be B. For C may fall under B,
and yet A may be contingent for all B, and necessary for C, as
when C is awake, B animal, A movement. Nor do the premisses
yield (3) a negative assertoric conclusion; nor (4) any of the
opposed affirmatives.
bg. An^E-: similarly invalid.
6. (b) Both premisses negative. E"E-E and E^E-EP valid, by
conversion of E^ and transition from Es to As.
12. E*E^E and E-E^EP similarly valid.
13. (c) Two affirmative premisses (A"A‘, AcA") cannot prove a
negative assertoric or apodeictic proposition, because neither
premiss is negative; nor a negative problematic proposition,
because it may happen that it is ecessary that no C be B (this
shown by an instance); nor any affirmative, because it may
happen that it is necessary that no C be B.
24. (B) One remiss particular
(a) Premisses of different quality. (a) Negative premiss univer-
sal and apodeictic (being the major premiss>. E^I«O and E^I«O»
valid, by conversion.
27. (B) Affirmative premiss universal and apodeictic (A"Os,
OcA"): nothing follows, any more than when both premisses are
universal (A^E*, EcAx).
29. (b) Two affirmative premisses (A^Iv, IcA", A-In, InA9):
nothing follows, any more than when both premisses are universal
(πᾶς; A*A?).
I. 19. 38*13-35 359
31. (c) Both premisses negative, apodeictic premiss universal
(being the major premiss>. E^O«O and E^O*OP valid, by transi-
tion from O* to I*.
35. (C) Both premisses particular
Two particular premisses prove nothing; this shown by con-
trasted instances.
38. Thus (1) if the negative universal premiss is apodeictic,
both a problematic and an assertoric conclusion follow. (2) If
the affirmative universal premiss is apodeictic, nothing follows.
(3) The valid combinations of a problematic with an apodeictic
premiss correspond exactly to the valid combinations of a pro-
blematic with an assertoric premiss. (4) All the valid inferences are
imperfect, and are completed by means of the aforesaid figures.
38713-16. 'Eàv 8... ἔσται. τῆς μὲν στερητικῆς ... ὑπάρχει is
true without exception only when both premisses are universal,
and it is such combinations alone that A. has in mind in the first
three paragraphs. τῆς δὲ καταφατικῆς οὐκ ἔσται is true, whatever
the quantity of the premisses.
16-25. κείσθω yap... ἐνδέχεσθαι. From Necessarily no B is
A, For all C, being A is contingent, we can infer (x) that it is
possible that no C should be B; for by converting the major
premiss and dropping the ‘necessarily’ we get the premisses
No A is B, For all C, being A is contingent, from which it follows
that for all C, not being B is possible (34519-3522) : (2) that no C is
B; for if we ‘assume the opposite, we get the reductio ad impossibile
‘Necessarily no B is A, Some C is B, Therefore necessarily some C
isnot A (3ob1-2); but ex hypothest for all C, being A is con-
tingent; therefore no C is B’. Becker's suspicions about the final
sentence (p. 46) are unjustified.
25-6. τὸν αὐτὸν δὲ τρόπον . .. στερητικόν. From For all B,
being A is contingent, Necessarily no C is A, we can infer (1) that
for all C, not being B is possible; for by conversion the premisses
become Necessarily no A is C, For all B, being A is contingent,
from which it follows that for all B, not being C is possible
(3647-17), and therefore that for all C, not being B is possible:
(2) that no C is B; for if we assume the opposite, we get the
reductio ‘For all B, being A is contingent, Some C is B, Therefore
for some C, being A is contingent (35*3o-5); but ex hyfothesi
necessarily no C is A; therefore no C is B’.
29. συμβαίνει, not ‘it follows’, but ‘it sometimes happens’.
35. τὸ yàp ἐξ ἀνάγκης . . . ἐνδεχόμενον, cf. 32436.
360 COMMENTARY
36-7. τὸ yàp ἀναγκαῖον... συνέβαινεν. A. has proved in
3018-40 that in the second figure an apodeictic conclusion does
not follow if the affirmative premiss is apodeictic and the negative
assertoric. A fortiori such a conclusion will not follow if the
affirmative premiss is apodeictic and the negative problematic.
38-3. ἔτι Se... ὑπάρχειν. A. offers here a second proof that
the premisses (1) For all B, not being A is contingent, (2) All C
is necessarily A, do not yield the conclusion Necessarily no C is
B. (1) is logically equivalent to (14) For all B, being A is con-
tingent (for the general principle cf. 32#29->1), and in 439-40 A.
substitutes (1a) for (1). But (τα) For all B, being A is contingent,
(2) All C is necessarily A, and (3) All C is B, may all be true, as
in the instance 'For all animals, being in movement is contingent,
every waking thing is necessarily in movement, and every waking
thing is an animal'.
b3-4. οὐδὲ δὴ... καταφάσεων. A. has shown that EcA® does
not prove Ἐς (228-36) nor E^ (236-52) nor E (b2-3). He now adds
that (for similar reasons) it does not prove any of the opposites
of these (i.e. either the contradictories I*, I^, I, or the contraries
Ac, An, À ).—A]. plainly read καταφάσεων (238. 1), and the reading
φάσεων may be due to Al.’s (unnecessary) suggestion that xara-
φάσεων should be taken to mean φάσεων.
6-12. στερητικῶν μὲν... σχῆμα, Le. by complementary con-
version of the minor premiss (32329-^1) and simple conversion of
the major we pass from All B is necessarily not A, For all C, not
being A is contingent, to All A is necessarily not B, For all C,
being A is contingent, from which it follows that no C is B, and
that for all C, not being B is possible (3647-17).
12-13. κἄν «i... ὡσαύτως. A. is considering cases in which
both premisses are negative, so tbat at first sight it looks absurd
to say 'if it is the minor premiss that is negative'. But in the form
just considered (58-12) the minor premiss was no incurable
negative. Being problematic, it could be transformed into the
corresponding affirmative. A. now passes to the case in which
the minor premiss is incurably negative, i.e. is a negative apo-
deictic proposition: (1) ‘For all B, not being A is contingent,
(2) ΑΙ C is necessarily not A.’ Since we cannot have the minor
premiss negative in the first figure, reduction to that figure must
proceed by a roundabout method: (2a) ‘All A is necessarily not C,
(14) For all B, being A is contingent (by complementary conver-
sion, 32229-^r), Therefore no B is C (3647-17). Therefore noC is B.’
18-20. ἐξ ἀνάγκης . . . ἄνθρωπος, i.e. there are cases in which,
when it is necessary that all B be A and contingent that all C
I. 19. 38236 —h41 361
should be A, or contingent that all B should be A and necessary
that all C be A, it is necessary (and therefore not contingent) that
no C be B. E.g. all swans are necessarily white, for all men being
white is contingent, but all men are necessarily not swans.
21. οὐδέ ye... καταφάσεων. Here, as in ^4, Al.'s reading (239.
36-9) is preferable.
21—2. ἐπεὶ δέδεικται... ὑπάρχον, i.e. in certain cases, such as
that just mentioned in 519-20.
24-35. Ὁμοίως δ᾽... πρότερον. The first rule stated here
would prima facie include IcE®, and the last rule (P31-5) OcE®, but
these combinations are, in fact invalid because in the second figure
the major premiss must be universal, to avoid illicit major.
A. must be assuming the universal apodeictic premiss to be the
major premiss.
27. ἀπόδειξις δὲ... ἀντιστροφῆς. From Necessarily no B is
A, For some C, being A is contingent, (1) by converting the major
premiss we get the first-figure syllogism (36434-9) Necessarily no
A is B, For some C, being A is contingent, Therefore some C is
not B, and (2) from this conclusion we get For some C, not being
B is possible.
28-9. τὸν αὐτὸν yap τρόπον... ὅρων, ie. as in 430-65. Take
for instance OcA". For some men, not being white is contingent,
all swans are necessarily white, and necessarily no swans are
men. On the other hand, for some animals, not being in move-
ment is contingent, everything that is awake is necessarily in
movement, but necessarily everything that is awake is an animal.
30—1. kal yàp . . . πρότερον, i.e. as in 513-23.
31-2. ὅταν δὲ... σημαίνουσα, ‘when both premisses are nega-
tive and that which asserts the non-belonging of an attribute to
a subject (not merely that its not belonging is contingent) is
universal and apodeictic (not assertoric)’.
35. καθάπερ ἐν τοῖς πρότερον, i.e. we may infer a statement of
possibility and one of fact, as with the combination dealt with in
b25-7 (E^I9).
37. ἀπόδειξις δ᾽... ὅρων. The reference is to the terms used
in 230-^s to show that EcA" and A^E* prove nothing. Take, for
instance, IcIn. For some men being white is contingent; some
swans are necessarily white; but it is necessary that no swans
should be men. On the other hand, for some animals being in
movement is contingent; some waking things are necessarily in
movement ; and it is necessary that all waking things should be
animals.
38-41. Φανερὸν οὖν... οὐδέποτε. A. does not mean that all
362 COMMENTARY
combinations of a universal negative apodeictic premiss with any
problematic premiss yield a conclusion, but (1) that all valid
combinations containing such a premiss yield both a negative
problematic and a negative assertoric conclusion (for this v.
316-26, 66-13, 25-7), and (2) that no combination including a
universal affirmative apodeictic premiss yields a conclusion at all.
41-39?1. καὶ ὅτι... συλλογισμός, i.e. the valid combinations
of a problematic with an apodeictic premiss correspond exactly
to those of a problematic with an assertoric premiss. The former
are E^Ac, AcE^, EnEc, EcE^, E»Ie, E7Oc; the latter are EA‘, AcE,
EE*, EcE, Els, EOs (v. ch. 18).
3973. διὰ τῶν προειρημένων σχημάτων. Al. (242. 22-7) thinks
this means either ‘by means of the first figure’ or ‘by means of the
aforesaid moods’. Both interpretations are impossible; Maier
therefore thinks (2 a. 176 n. 2) that the words are a corruption of
διὰ τῶν ἐν τῷ προειρημένῳ σχήματι, i.e. in the first figure. But
EAcEP (3724-8), ASEEP (ib. 29), and E^A-EP (3816-25) have
been reduced to EAcEP in the first figure, which was itself in
34>19-31 reduced to I^AI in the third figure; and EIsOP (3843-4)
has been reduced to EI*O» in the first figure, which was itself
in 35335-^: reduced to APII^ in the third figure. Thus διὰ τῶν
προειρημένων σχημάτων is justified.
CHAPTER 20
Syllogisms in the third figure with two problematic premisses
39°4. In the third figure there can be an inference either with
both premisses problematic or with one. When both premisses
are problematic, and when one is problematic, one assertoric, the
conclusion is problematic. When one is problematic, one apodeic-
tic, if the latter is affirmative the conclusion is neither apodeictic
nor assertoric; if it is negative there may be an assertoric
conclusion; ‘possible’ in the conclusion must be understood as
= ‘not impossible’.
14. (A) Both premisses universal
AcAcl¢ valid, by conversion.
19. EsAcOs valid, by conversion.
23. E-E'I* valid, by transition from Es to A* and conversion.
28. (B) One premiss particular
When one premiss is particular, the moods that are valid corre-
spond to the valid moods of pure syllogisin in this figure. (a)
Both premisses affirmative. A*IcIv valid, by conversion.
I. το. 38541 — 20. 39238 363
35. IcAclI¢ similarly valid.
36. (5) A negative major and an affirmative minor give a
conclusion (EcIcOc, OcAcI*), by conversion.
38. (c) Two negative premisses give a conclusion (EcOcls,
OcE-I:), by complementary conversion.
52. (C) Both premtsses particular
Nothing follows ; this shown by contrasted instances.
3977-8. kai Grav... ὑπάρχειν. For the justification of this
v. Ch. 21.
8-11. ὅταν δ᾽... πρότερον. For the justification of this v.
ch. 22. καθάπερ... πρότερον refers to 38213-16 (the corresponding
combinations in the second figure).
IX-I12. ληπτέον Se... ἐνδεχόμενον, i.e. the only sort of possi-
bility:that can be proved by any combination of a negative
apodeictic with a problematic premiss is possibility in the sense
in which 'possible' — 'not impossible' (cf. 33529-33), not in the
strict sense in which it means 'neither impossible nor necessary',
(cf. 32218-21). ὁμοίως = ‘as with the corresponding combinations
in the second figure".
23-8. εἰ δ᾽... ἀντιστροφῆς. A. says here that premisses of
the form E-E* can be made to yield a conclusion ‘by converting
the premisses’, ie. by complernentary conversion (cf. 32329-b1).
By this means we pass from E«E* to AcAs, the combination
already seen in 414-19 to be valid.
In #27 Waitz reads, with n, ἐὰν μεταληφθῇ τὸ ἐνδέχεσθαι μὴ
ὑπάρχειν, assuming that μεταληφθῇ means ‘is changed’; and this
derives some support from Al's commentary (243. 23)—pe7a-
ληφθείσης δὲ τῆς ἐλάττονος eis τὴν καταφατικὴν évBexouévqv—and
the corresponding remark in P. 229. 26. But the usual sense of
μεταλαμβάνειν in A. is ‘to substitute’ (cf. Bonitz, Index), and μή
is therefore not wanted.
28-31. εἰ δ᾽... συλλογισμός, Le. ‘the valid syllogisms in this
figure with two problematic premisses of different quantity
correspond to the valid syllogisms with two assertoric premisses
of different quantity’. Thus we have A-Is, IcAc, EcIv, and OcAc
corresponding to Datisi, Disamis, Ferison, Bocardo. But in
addition, owi:1g to the possibility of complementary conversion of
problematic premisses (32229—6:), A. allows E«*O* and O°E* to be
valid (4338-52). He says nothing of AcOs and IcEs, but these he
would regard as valid for the same reason.
36-8. ὁμοίως δὲ... ἀντιστροφῆς. The validity of EsI*e would
364 COMMENTARY
be proved thus: By conversion of the minor premiss, ‘For all
C, not being A is contingent, For some C, being B is contingent’
becomes ‘For all C, not being A is contingent, For some B, being
C is contingent', from which it follows that for some B not being
A is contingent. The validity of OcA« would be proved thus: By
complementary conversion, followed by simple conversion, of the
major premiss, and by changing the order of the premisses, 'For
some C, not being A is contingent, For all C, being B is contingent’
becomes ‘For all C, being B is contingent, For some A, being C
is contingent’, from which it follows that for some A being B
is contingent, and therefore that for some B being A is contingent.
br. καθάπερ ἐν rois πρότερον, ie. in the case of EcEs, OcA«
(223-8, 36-8).
3-4. kai yàp . . . μηδενὶ ὑπάρχειν, 1.6. there are cases in which
A must belong to B, and cases in which it cannot, so that neither
a negative nor an affirmative problematic conclusion can follow
from premisses of this form.
4-6. ὅροι τοῦ ὑπάρχειν... μέσον λευκόν. Le. it is possible
that some white things should be, and that some should not be,
animals, it is possible that some white things should be, and that
some should not be, men; and in fact every man is necessarily an
animal. On the other hand, it is possible that some white things
should be, and that some should not be, horses, it is possible that
some white things should be, and that some should not be, men;
but in fact it is necessary that 2o man should be a horse. Thus
I:I*, I*O*, Ocle, O«O* in the third figure prove nothing.
CHAPTER 21
Syllogisms in the third figure with one problematic and one assertoric
premiss
39>7. If one premiss is assertoric, one problematic, the con-
clusion is problematic. The same combinations are valid as were
named in the last chapter.
10. (A) Both premisses universal
(a) Both premisses affirmative: AAcIP valid, by conversion.
x6. A*AI* valid, by conversion.
x7. (b) Major premiss negative, minor affirmative: EAcOp,
I. 20. 395t —21. 39^22 365
23. (d) Both premisses negative (and minor premiss prob-
lematic>: a conclusion follows (EE*O»), by conversion.
26. (B) One premiss particular
(a) Both premisses affirmative: a conclusion follows (AlIcIP,
A*IIe, IA-Ie, IcAIP), by conversion.
27. (b) Universal negative and particular affirmative: a con-
clusion follows (except when the minor premiss is an assertoric
negative (IcE)> (EI«*O», EcIOc, IEcI¢), by conversion.
3x. (c) Universal affirmative (assertoric minor) and particular
negative (problematic major»: OcAOP valid, by reductio ad im-
possibtle.
40?r. (C) Both premisses particular
Two particular premisses prove nothing.
39^ro. τοῖς πρότερον. This refers to the treatment in ch. 20
of arguments in the third figure with two problematic premisses.
It is not, however, strictly true that the same combinations are
valid when one premiss is assertoric, one problematic, as when
both are problematic. In two respects the conditions are different.
A. (rightly) does not consider ‘For all B, not being A is con-
tingent' convertible into ‘For all A, not being B is contingent’
(36535—37231); and he does think it convertible into ‘For all B,
being A is contingent’ (32229->1). For these reasons the valid
combinations do not exactly correspond ; while OcE* is valid (by
conversion to I-A*), neither OE* nor O°E is so.
14-16. ὅτε yàp . . . ἐνδεχόμενον, 19-22 γίνεται γάρ . . . ἐνδε-
xópevov, cf. ch. 15, especially 33525-31.
22. τὸ στερητικόν. ABCd have τὸ ἐνδεχόμενον στερητικόν. n
has τὸ στερητικόν, and both Al. (246. 11-16) and P. (231. 24-6) have
this reading, and say that ἐνδεχόμενον must be understood; their
comments are no doubt the reason why that word appears in
most of the MSS. The shorter reading prima facie covers the
combination AcE as well as AE‘, and the words in the next line
ἢ kai ἄμφω ληφθείη στερητικά prima facie cover the case EcE as
well as EE‘; but AcE and E‘E are invalidated by the fact that
in the third figure the minor premiss must be affirmative (to
avoid illicit major). AE* and EE*, on the other hand, can be
validated by complementary conversion of Es into A‘. There is
therefore no doubt that the interpretation given by Al. and P.
366 COMMENTARY
premiss are valid, but that when they are (i.e. when this premiss
is problematic) they can be validated by complementary con-
version of the minor premiss (δι᾽ αὐτῶν μὲν τῶν κειμένων οὐκ ἔσται
συλλογισμός, ἀντιστραφέντων δ᾽ ἔσται, 523-5).
25. καθάπερ ἐν τοῖς πρότερον, i.e. by complementary con-
version AE‘, EE* are reduced to the valid moods AA‘, EA‘, as
EcE¢ was reduced to A«A* in 426-8.
26-39. Εἰ δ᾽... ὑπάρχειν. A. considers here premisses
differing in quantity. (x) If both premisses are affirmative, the
conclusion is validated by reduction to the first figure (627-31).
This covers Alc, IcA, AcI, IA«. (2) So too if the universal premiss
is negative, the particular premiss affirmative (ib.). Prima facie
this covers EIv, IcE, E-I, IE*. But of these IcE (though A. does
not say so) is invalidated by the fact that in the third figure the
minor premiss must (to avoid illicit major) be affirmative (IE*
escapes this objection by complementary conversion of Ἐπ).
(3) If the universal premiss is affirmative, the particular premiss
negative, the conclusion will be got (so A. says) by reductio ad
impossibile (P31-3). Prima facie this covers the cases AOs, OcA,
AcO, OAs. But the only case specifically mentioned is OcA
(533-9), and it is this case A. has in view in saying that validation
is by reductio ; for it is validated by a reductio in A^ AA? (3o117-
23). AOc can in fact be validated by complementary conversion
of Ov. A*O is in fact invalid, since in the third figure the minor
premiss must be affirmative. A. says nothing of OA‘, which in
fact cannot be validated in any way.
A. says nothing of case (4), in which both premisses are nega-
tive. In fact EO* is reducible by complementary conversion to
the valid mood EIv. OcE and E*O are invalid because in the third
figure the minor premiss must be affirmative; OE- is invalid just
as is OA* above, to which it is equivalent by complementary
conversion.
30-1. ὥστε φανερὸν... συλλογισμός. This follows from the
fact that in the first figure if one premiss is problematic the con-
clusion is so too (br4—16).
37. τοῦτο yap δέδεικται πρότερον, cf. 3021723.
4072-3. ἀπόδειξις δ᾽... ὅρων. The MSS., AL, and P. have ἐν
τοῖς καθόλου, which would be a reference to the discussion of
moods with two universal premisses (39510-25); but A. did not
in fact condemn any of these, and could not, in the course of so
short a chapter, have forgotten that he had not. Al.'s supposition
(248. 33-7) that τοῖς καθόλου means τοῖς δι᾿ ὅλου ἐνδεχομένοις,
premisses both of which are problematic, is quite unconvincing.
I. 21. 39525— 4033 367
Maier (2a. 202 n. 1) suspects the whole sentence; but it would
not be in A.'s manner to dismiss these moods without giving
a reason. The most probable hypothesis is that A. wrote év rois
πρότερον, and that, the last word having been lost or become
illegible, a copyist wrote καθόλου, on the model of such passages
as 38P28-9, 4obrr—12. ἐν τοῖς πρότερον will refer to 3952-6; the
example given there will equally well serve A.’s purpose here.
CHAPTER 22
Syllogisms in the third figure with one problematic and one apodeictic
premiss
40*4. If both premisses are affirmative, the conclusion is
problematic. When they differ in quality, if the affirmative
is apodeictic the conclusion is problematic; if the negative is
apodeictic, both a problematic and an assertoric conclusion, but
not an apodeictic one, can be drawn.
II. (A) Both premisses universal
(a) Both premisses affirmative: A"A-IP valid, by conversion.
16. A*A"I* valid, by conversion.
x8. (b) Major premiss negative, minor affirmative: EcA^Oc
valid, by conversion.
25. E^A*O and E*AcOp valid, by conversion.
33. (c) Major premiss affirmative, minor negative: A^E-IP
valid, by transition from Es to As.
35. AcE" proves nothing; this shown by contrasted instances.
39. (Β) One premiss particular
(a) Both premisses affirmative: a problematic conclusion fol-
lows (A^I-Ip, IcA*Ip, A-InIc, I^A-I-), by conversion.
bz. (b) (Major premiss negative, minor affirmative.» (a) Affir-
mative premiss apodeictic: a problematic conclusion follows
(EcI»Oe, OcA^O»).
4. (8) Negative premiss apodeictic: an assertoric conclusion
follows (E^I*O, O^A*O).
8. (c) Major premiss affirmative, minor negative. (a) Negative
premiss problematic and universal: I*E*I* valid, by conversion.
xo. (£) Negative premiss apodeictic and universal: [Ἐπ proves
nothing; this shown by contrasted instances, as for AcE".
I2. It is now clear that all the syllogisms in this figure are
imperfect, and are completed by means of the first figure.
368 COMMENTARY
40?15-16. οὕτω γὰρ. .. σχήματος, cf. 3640-62 (A^IcIr).
18-38. πάλιν ἔστω. . . ἄνθρωπος. Of combinations of pre-
misses (both universal) differing in quality, A. examines first
(1319-32) those with a negative major premiss, then (233-8) those
with a negative minor. He does not discuss the combinations
of two negative premisses; but his treatment of them would have
corresponded to his treatment of those with an affirmative major
and a negative minor. E^E-* is valid because it is reducible, by
complementary conversion of Es, to EA‘; E«E^ is invalid
because its minor premiss is incurably negative, and in the third
figure the minor must be affirmative to avoid illicit major.
21-3. kai yàp . . . ἐνδεχόμενον, ‘because the negative premiss
here, like the affirmative (minor) premiss in πᾷς (211—16) and the
affirmative (major) premiss in AA" (216-18) is problematic’. The
ydp clause, which gives the reason for what follows, not for what
goes before, is a good example of the 'anticipatory' use of ydp.
Cf. Hdt. 4.79 'Hyiv yàp καταγελᾶτε, ὦ Σκύθαι, ὅτι βακχεύομεν καὶ
ἡμέας ὁ θεὸς λαμβάνει: νῦν οὗτος ὁ δαίμων καὶ τὸν ὑμέτερον βασιλέα
λελάβηκε, and other instances cited in Denniston, The Greek
Particles, 69-70.
23-5. Ste yàp . . . ἐνδεχόμενον. The combination in question,
E*An, reduces, by conversion of the minor premiss, to E-I^ in
the first figure, which was in 3639-52 shown to yield only a
problematic conclusion.
30-2. Ste δ᾽... μὴ ὑπάρχειν. The combination in question,
Ends, reduces, by conversion of the minor premiss, to E^I* in the
first figure, which was in 3634-9 shown to yield an assertoric
conclusion, and a fortiori yields a conclusion of the form It is not
impossible that some S should not be P. ἀνάγκη here (432) only
means ‘it follows’; the conclusion is not apodeictic ; cf. 36710 n.
34-5. μεταληφθείσης . . . πρότερον, ie. by complementary
conversion of the minor premiss (cf. 32329-r).
b2-8. καὶ ὅταν... συμπίπτειν. The first rule stated here (52-3)
prima facie includes I^E*; but the rule in 58-ro also prima facie
includes it. Again, the rule in ^3-8 prima facie approves I*E^,
which the rule in >ro-1r condemns; and in fact [Ἐπ᾿ proves
nothing, since in the third figure the minor premiss cannot be
negative unless it is problematic and therefore convertible by
complementary conversion into an affirmative. Finally, AcO®,
which prima facie falls under the rule in 53-8, is invalid for the
same reason. Clearly, then, 52-3, 3-8 are not meant to cover so
much as they appear to cover. Now in >8 A. expressly passes to
the cases in which the major premiss is affirmative, the minor
I. 22. 40215—br12 369
negative. All is made clear by realizing that in 52-8 A. has in
mind only the cases in which the major premiss is negative, the
minor affirmative; thus A. is not there thinking of the cases
I^Es, IcE^, AcO».
4-6. ὁ yàp αὐτὸς τρόπος .. . ὄντων. E^I«O is in fact validated
just as E^A*O was (225-32), by conversion ; but O^A«*O is validated
by reductio ad smposstbile.
8-11. ὅταν δὲ... ἔσται. καθόλου ληφθέν is unnecessary, since
Απρο is valid, as well as I"Ec, and AcO® invalid, as well as IE».
But καθόλου ληφθέν has the support of Al. and P., and of all the
MSS.
11-I2. δειχθήσεται δὲ... ὅρων, cf. 35-8. It is contingent that
some men should be asleep, no man can be a sleeping horse; but
every sleeping horse must be asleep. On the other hand, it is
contingent that some men should be asleep, no man can be a
waking horse ; and in fact no waking horse can be asleep. There-
fore IcE" cannot prove either a negative or an affirmative con-
clusion.
CHAPTER 23
Every syllogism ts in one of the three figures, and reducible to a
universal mood of the first figure
40^17. We have seen that the syllogisms in all three figures are
reducible to the universal moods of the first figure; we have now
to show that every syllogism must be so reducible, by showing
that it is proved by one of the three figures.
23. Every proof must prove either an affirmative or a negative,
either universal or particular, either ostensively or from a hypo-
thesis (the latter including reducto ad impossibile). If we can
prove our point about ostensive proof, it will become clear also
about proof from an hypothesis.
30. If we have to prove A true, or untrue, of B, we must
assume something to be true of something. To assume A true of
B would be to beg the question. If we assume A true of C, but
not C true of anything, nor anything other than A true of C, nor
anything other than A true of A, there will be no inference;
nothing follows from the assumption of one thing about one other.
37. If in addition to 'C is A’ we assume that A is true of some-
thing other than B, or something other than B of A, or something
other than B of C, there may be a syllogism, but it will not prove
A true of B ; nor if C be assumed true of something other than B,
and that of something else, and that of something else, without
establishing connexion with B.
4985 B b
370 COMMENTARY
41*2. For we stated that nothing can be proved of anything
else without taking a middle term related by way of predication
to each of the two. For a syllogism is from premisses, and a
syllogism relating to this term from premisses relating to this
term, and a syllogism connecting this term with that term from
premisses connecting this term with that; and you cannot get
premisses leading to a conclusion about B without affirming or
denying something of B, or premisses proving A of B if you do
not take something common to A and B but affirm or deny
separate things of each of them.
13. You can get something common to them, only by predi-
cating either A of C and C of B, or C of both, or both of C, and
these are the figures we have named; therefore every syllogism
must be in one of these figures. If more terms are used connecting
A with B, the figure will be the same.
21. Thus all ostensive inferences are in the aforesaid figures;
it follows that reductio ad impossibile will be so too. For all such
arguments consist of (2) a syllogism leading to a false conclusion,
and (δ) a proof of the original conclusion by means of a hypothesis,
viz. by showing that something impossible follows from assuming
the contradictory of the original conclusion.
26. E.g. we prove that the diagonal of a square is incommen-
surate with the side by showing that if the opposite be assumed
odd numbers must be equal to even numbers.
32. Thus reductio uses an ostensive syllogism to prove the false
conclusion ; and we have seen that ostensive syllogisms must be
in one of the three figures ; so that reductio is achieved by means of
the three figures.
37. So too with a/] arguments from an hypothesis; in all of
them there is a syllogism leading to the substituted conclusion,
and the original conclusion is proved by means of a conceded
premiss or of some further hypothesis.
br. Thus all proof must be by the three figures; and therefore
all must be reducible to the universal moods of the first figure.
4018-19. διὰ τῶν... συλλογισμῶν. In 2951-25 A. has shown
that all the valid moods of the three figures can be reduced to the
universal moods of the first figure (Barbara, Celarent). Maier
(2 a. 217 n.) objects that it is only the moods of the pure syllogism
that were dealt with there, and that A. could not claim that all
the moods of the modal syllogism admit of such reduction; he
wishes to reject καθόλου here and in 4155. But throughout the
treatment of the modal syllogism A. has consistently maintained
I. 23. 40*18— 4153 371
that the modal syllogisms are subject to the same conditions,
mutatis mutandis, as the pure, and there can be no doubt that
he would claim that they, like pure syllogisms, are all reducible
to Barbara or Celarent. Both Al. and P. had καθόλου, and it
would be perverse to reject the word in face of their agreement
with the MSS.
25. ἔτι ἢ δεικτικῶς ἢ ἐξ ὑποθέσεως. Cf. 29*31-2n. A.
describes an argument as ἐξ ὑποθέσεως when besides assuming the
premisses one supposes something else, in order to see what con-
clusion follows when it is combined with one or both of the
premisses. Reductio ad impossibile is a good instance of this. For
A.’s analysis of ordinary reasoning ἐξ ὑποθέσεως (other than
reductio) cf. 50416-28.
33-4171. εἰ δὲ... συλλογισμός. A. lays down (1) (233-7) what
we must have in addition to 'C is A', in order to get a syllogism
at all. We must have another premiss containing either C or A.
He mentions the cases in which C is asserted or denied of some-
thing, or something of C, or something of A, but omits by
inadvertence the remaining case in which 4 is asserted or denied
of something). (2) (P37—41?2) he points out what we must have in
addition to 'C is A’, to prove that B is A. We cannot prove this
if the other premiss is of the form 'D is A’, ‘A is D','C is D', or
'DisC'.
41?2-4. ὅλως yap . . . κατηγορίαις. A. has not made this
general statement before, but it is implied in the account he gives
in chs. 4-6 of the necessity of a middle term in each of the three
figures. rats κατηγορίαις is to be explained by reference to 214-16.
22-b3. ὅτι δὲ καὶ ol els τὸ ἀδύνατον. . . σχημάτων. For the
understanding of A.’s conception of reductio ad wmpossibile, the
present passage must be compared with 50716-38. In both
passages reduciio is compared with other forms of proof ἐξ
ὑποθέσεως. The general nature of such proof is that, desiring to
prove a certain proposition, we first extract from our opponent
the admission that if a certain other proposition can be proved,
the original proposition follows, and then we proceed to prove
the substituted proposition (τὸ μεταλαμβανόμενον, 41439). The
substituted proposition is said to be proved syllogistically, the
other not syllogistically but ἐξ ὑποθέσεως. Similarly reductio falls
into two parts. (1) Supposing the opposite of the proposition
which 1s to be proved, and combining with it a proposition known
to be true, we deduce syllogistically a conclusion known to be
untrue. (2) Then we infer, not syllogistically but ἐξ ὑποθέσεως,
the truth of the proposition to be proved. That the ὑπόθεσις
372 COMMENTARY
referred to is not the supposition of the falsity of this proposition
(which is made explicitly in part (1)) is shown (a) by the fact
that both in 41?32—4 and in 50%29~32 it is part (2) of the proof that
is said to be ἐξ ὑποθέσεως, and (b) by the fact that in 50%32-8
reductio is said to differ from ordinary proof ἐξ ὑποθέσεως in that
in it the ὑπόθεσις because of its obviousness need not be stated.
It is, in other words, of the nature of an axiom. A. nowhere makes
it perfectly clear how be would have formulated this, but he
comes near to doing so when he says in 41?24 τὸ δ᾽ ἐξ ἀρχῆς ἐξ
ὑποθέσεως δεικνύουσιν, ὅταν ἀδύνατόν τι συμβαίνῃ τῆς ἀντιφάσεως
τεθείσης. This comes near to formulating the hypothesis in the
form ‘that from which an impossible conclusion follows cannot
be true’. But another element in the hypothesis is brought out
in An. Post. 77*22-5, where A. says that reductio assumes the law
of excluded middle; i.e. it assumes that if the contradictory of
the proposition to be proved is shown to be false, that proposition
must be true.
The above interpretation of the words τὸ δ᾽ ἐξ ἀρχῆς ἐξ ὑποθέσεως
δεικνύουσιν is that of Maier (2 a. 238 n.). T. Gomperz in A.G.P.
xvi (1903), 274-5, and N. M. Thiel in Die Bedeutung des Wortes
Hypothesis bei Arist. 26-32 try, in vain as I think, to identify
the ὑπόθεσις referred to with the assumption of the contradictory
of the proposition to be proved.
26-7. olov ὅτι ἀσύμμετρος... τεθείσης. The proof, as stated
by Al. in 260. 18-261. 19, is as follows: If the diagonal BC of a
square ABDC is commensurate with the side AB, the ratio of
BC to AB will be that of one number to another (by Euc. El.
IO. 5, ed. Heiberg). Let the smallest numbers that are in this
ratio be e, f. These will be prime to each other (by Euc. 7. 22).
Then their squares i, & will also be prime to each other (by
Euc. 7. 27). But the square on the diagonal is twice the size of
the square on the side; 7 = 2k. Therefore 1 is even. But the half
of an even square number is itself even. Therefore 1/2 is even.
Therefore & is even. But it is also odd, since 1 and & were prime
to each other and two even numbers cannot be prime to each
other. Thus either both ? and & or one of them must be odd, and
at the same time both must be even. Thus if the diagonal were
commensurate with the side, certain odd numbers would be equal
to even numbers (or rather, at least one odd number must be
equal to an even number). The proof is to be found in Euc. ro,
App. 27 (ed. Heiberg and Menge).
30-1. τοῦτο yap... συλλογίσασθαι, cf. 2957-11.
31-2. τὸ δεῖξαί τι... ὑπόθεσιν, ‘to prove an impossible result
I. 23. 41:326 —55 373
to follow from the original hypothesis', i.e. from the hypothesis
of the falsity of the proposition to be proved. ἡ ἐξ ἀρχῆς ὑπόθεσις
is to be distinguished from τὸ ἐξ ἀρχῆς (434), the proposition
originally taken as what is to be proved.
37-40. ὡσαύτως δὲ... ὑποθέσεως. The interpretation of the
sentence has been confused by Waitz’s assumption that pera-
λαμβάνειν is used in a sense which is explained in Al. 263. 26—36,
'taking a proposition in another sense than that in which it was
put forward', or (more strictly) 'substituting a proposition of the
form ''Á is B" for one of the form “If A is B, C is D"'. Al.
ascribes this sense not to A. but to of ἀρχαῖοι, the older Peri-
patetics, and it is (as Maier points out, 2 a. 250 n.) a Theophrastean,
not an Aristotelian, usage. According to regular Aristotelian
usage μεταλαμβάνειν means ‘to substitute’ (cf. 4839, 4953), and
what A. is saying is this: In all proofs starting from an hypothesis,
the syllogism proceeds to the substituted proposition, while the
proposition originally put forward to be proved is established (x)
by an agreement between the speakers or (2) by some other
hypothesis. Let the proposition to be proved be ‘A is B'. The
speaker who wants to prove this says to his opponent ‘Will you
agree that if C is D, A is B?' (1) If the opponent agrees, the first
speaker proves syllogistically that C is D, and infers non-
syllogistically that A is B. (2) If the opponent does not agree,
the first speaker falls back on another hypothesis: ‘Will you
agree that if E is F, then if C is D, A is B?', and proceeds to
establish syllogistically that E is F and that C is D, and non-
syllogistically that 4 is B. The procedure is familiar in Plato;
cf., for example, Meno, 86 e-87 c, Prot. 355 e. Shorey in 'Συλλο-
γισμοὶ ἐξ ὑποθέσεως in A.’ (A.J.P. x (1889), 462) points out that
A. had the Meno rather specially in mind when he wrote the
Analytics ; cf. 67221, 6924-9, An. Post. 71429.
bg. εἰς τοὺς ἐν τούτῳ καθόλου συλλογισμούς, cf. 40>r8—19 n.
CHAPTER 24
Quality and quantity of the premisses
4156. Every syllogism must have an affirmative premiss and a
universal premiss; without the latter either there will be no
syllogism, or it will not prove the point at issue, or the question
will be begged. For let the point to be proved be that the pleasure
given by music is good. If we take as a premiss that pleasure is
good without adding ‘all’, there is no syllogism ; if we specify one
particular pleasure, then if it is some other pleasure that is
374 COMMENTARY
specified, that is not to the point; if it is the pleasure given by
music, we are begging the question.
13. Or take a geometrical example. Suppose we want to prove
the angles at the base of an isosceles triangle equal. If we assume
the two angles of the semicircle to be equal, and again the two
angles of the same segment to be equal, and again that, when we
take the equal angles from the equai angles, the remainders are
equal, without making the corresponding universal assumptions,
we Shall be begging the question.
22. Clearly then in every syllogism there must be a universal
premiss, and a universal conclusion requires all the premisses to
be universal, while a particular conclusion does not require this.
27. Further, either both premisses or one must be like the
conclusion, in respect of being affirmative or negative, and apodeic-
tic, assertoric, or problematic. The remaining qualifications of
premisses must be looked into.
32. It is clear, too, when there is and when there is not a
syllogism, when it is potential and when perfect, and that if there
is to be a syllogism the terms must be related in one of the
aforesaid ways.
4156. Ἔτι re... εἶναι. Α. offers no proof of this point; he
treats it as proved by the inductive examination of syllogisms
in chs. 4-22. The apparent exceptions, in which two negative
premisses, one or both of which are problematic, give a conclusion,
are not real exceptions. For a proposition of the form ‘B admits
of not being A’ is not a genuine negative (321-3), and can be
combined with a negative to give a conclusion, by being comple-
mentarily converted into ‘B admits of being A’ (32229-b1).
14. ἐν rois διαγράμμασιν, ‘in mathematical proofs’. For this
usage cf. Cat. 14239, Met. 99825.
15-22. €otwoav ... λείπεσθαι. Subject to differences as to the
placing of the letters, the interpretation
given by Al. 268. 6-269. 15 and that given
by P. 253. 28-254. 23 are substantially
the same, viz. the following: A circle
is described having as its centre the
meeting-point of the equal sides (A, B)
Pal of the triangle, and passing through the
ends of the base. Then the whole angle
ee 2 E-FI'(rjv AD) = the whole angle Z 4-A
(r$ B4), they being 'angles of a semi-
circle’. And the angle 7' = the angle 4, they being ‘angles of a
I. 24. 4156-22 375
segment'. But if equals are taken from equals, equals remain;
therefore the angle E — the angle Z.
Waitz criticizes this proof, on the ground that the angles
E--T, Z--A, T, A, being angles formed by a straight line and a
curve, are not likely to have been used in the proof of a proposition
so elementary as the pons asinorum. He therefore assumes a
different construction and proof. He assumes the upper ends of
the two diameters to be joined to the respective ends of the base.
Then the angle A4 4-7" = the angle Β- 4,
they being angles in a semicircle, and the
angle Γ = the angle 4, they being angles
in the same segment. Therefore the angle
A — the angle B. He treats rds EZ in
520 as an interpolation taking its origin
from the ras é£ which was the original p d
reading of the MS. d, τὰς ἐξ being itself
a corrupt reduplication of τὸ ἐξ (ἀρχῆς), SL
which follows immediately.
Heiberg has pointed out (in Abh. zur Gesch. der Math. Wissen-
schaften, xviii (1904), 25-6) that mixed angles (contained by a
straight line and a curve), though in Euclid’s Elements they occur
only in the propositions III. 16 and 31, fall within his conception
of an angle (I, def. 8 "Emimedos δὲ γωνία ἐστὶν ἡ ἐν ἐπιπέδῳ δύο
γραμμῶν ἁπτομένων ἀλλήλων καὶ μὴ ἐπ᾽ εὐθείας κειμένων πρὸς
ἀλλήλας τῶν γραμμῶν κλίσις ; def. 9 "Orav δὲ αἱ περιέχουσαι τὴν
γωνίαν γραμμαὶ εὐθεῖαι ὦσιν, εὐθύγραμμος καλεῖται ἡ γωνία). Further,
the angle of a segment is defined as ἡ περιεχομένη ὑπό τε εὐθείας
kai κύκλου περιφερείας (III, def. 7), in distinction from the angle
in a segment (e.g. ἡ ἐν ἡμικυκλίῳ, An. Post. 94*28, Met. 1051727),
which (as in modern usage) is that subtended at the circum-
ference by the chord of the segment (III, def. 8). We must sup-
pose that A. uses the phrases τὰς τῶν ἡμικυκλίων (γωνίας) x7 and
τὴν τοῦ τμήματος (γωνίαν) 618 in the Euclidean sense, as Al.'s
interpretation assumes. A. refers in one other passage to a mixed
angle—in Meteor. 375524, where τὴν μείζω γωνίαν means the angle
between the line of vision and the rainbow. The use of mixed
angles had probably played a larger part in the pre-Euclidean
geometry with which A. was familiar, though comparatively
scanty traces of it remain in Euclid. The proposition stating the
equality of the mixed 'angles of a semicircle' occurs in ps.-Eucl.
Catoptrica, prop. s.
A.’s use of letters in this passage is loose but characteristic.
A and B are used to denote radii (615) ; for the use of single letters
376 COMMENTARY
to denote lines cf. Meteor. 376211-24, >1, 4, De Mem. 45219-20.
AI, BA are used to denote the mixed angles respectively con-
tained by the radii A, B and the arc I'A which they cut off.
Γ and Δ are used to denote the angles made by that arc with its
chord, and E and Z to denote the angles at the base of the triangle;
for the use of single letters to denote angles cf. An. Post. 94*29,
30, Meteor. 373*12, 13, 376729.
24. xai οὕτως κἀκείνως, i.e. both when both the premisses are
universal and when only one is so.
27-30. δῆλον 8€ . . ἐνδεχομένην. A. gives no reason for this
generalization; he considers it to have been established induc-
tively by his review of syllogisms in chs. 4-22. The generalization
is not quite correct ; for A. has admitted many cases in which an
assertoric conclusion follows from an apodeictic and a problematic
premiss (see chs. 16, 19, 22).
3r. ἐπισκέψασθαι δὲ. .. κατηγορίας. Le. we must consider,
with regard to other predicates—e.g. ‘true’, ‘false’, ‘probable’,
‘improbable’, ‘not necessary’, ‘not possible’, ‘impossible’, ‘true
for the most part’ (cf. 43533-6)—whether, if a conclusion asserts
them, one of the premisses must do so.
33. kai πότε δυνατός. δυνατός is used here to characterize the
syllogisms which are elsewhere called ἀτελεῖς. A syllogism is
δυνατός if the conclusion is not directly obvious as following from
the premisses, but is capable of being elicited by some mani-
pulation of them.
CHAPTER 25
Number of the terms, premisses, and conclusions
41536. Every proof requires three terms and no more; though
(1) there may be alternative middle terms which will connect two
extremes, or (2) each of the premisses may be established by a
prior syllogism, or one by induction, the other by syllogism. In
both these cases we have more than one syllogism.
42*6. What we cannot have is a single syllogism with more than
three terms. Suppose E to be inferred from premisses A, B, C, D.
One of these four must be related to another as whole to part. Let
A be so related to B. There must be some conclusion from them,
which will be either E, C or D, or something else.
14. (x) If E is inferred, the syllogism proceeds from A and B
alone. But then (a) if C and D are related as whole to part, there
will be a conclusion from them also, and this will be E, or A or B,
or something else. If it is (i) E or (ii) A or B, we shall have (i)
I. 24. 41>24—25. 41540 377
alternative syllogisms, or (ii) a chain of syllogisms. If it is (iii)
something else, we shall have two unconnected syllogisms. (b) If
C and D are not so related as to form a syllogism, they have been
assurned to no purpose, unless it be for the purpose of induction
or of obscuring the issue, etc.
24. (2) If the conclusion from A and B is something other than
E, and (a) the conclusion from C and D is either A or B, or some-
thing else, (i) we have more than one syllogism, and (ii) none of
them proves E. If (b) nothing follows from C and D, they have
been assumed to no purpose and the syllogism we have does not
prove what it was supposed to prove.
jo. Thus every proof must have three terms and only three.
32. It follows that it must have two premisses and only two
(for three terms make two premisses), unless a new premiss is
needed to complete a proof. Evidently then if the premisses
establishing the principal conclusion in a syllogistic argument are
not even in number, either the argument has not proceeded
syllogistically or it has assumed more than is necessary.
br. Taking the premisses proper, then, every syllogism proceeds
from an even number of premisses and an odd number of terms;
the conclusions will be half as many as the premisses.
5. If the proof includes prosyllogisms or a chain of middle
terms, the terms will similarly be one more than the premisses
(whether the additional term be introduced from outside or into
the middle of the chain), and the premisses will be equal in
number to the intervals; the premisses will not always be even
and the terms odd, but when the premisses are even the terms
will be odd, and vice versa; for with one term one premiss will
be added.
x6. The conclusions will no longer be related as they were to
the terms or to the premisses; when one term is added, con-
clusions will be added one fewer than the previous terms. For the
new term will be inferentially linked with each of the previous
terms except the last ; if D is added to A, B, C, there are two new
conclusions, that D is A and that D is B.
23. So too if the new term is introduced into the middle; there
is just one term with which it does not establish a connexion.
Thus the conclusions will be much more numerous than the terms
or the premisses.
41536-40. Δῆλον 86 . . . κωλύει. This sentence contains a
difficult question of reading and of interpretation. In >39 d and
the first hand of B have AB καὶ ΒΓ, C and the second hand of A
378 COMMENTARY
(the original reading is illegible) have AB xai ΑΓ, and n, Al., and
P. have AB xai AI καὶ ΒΓ. With that reading we must suppose
the whole sentence to set aside, as irrelevant to A.’s point (that
a syllogism has three termsand no more), the case in which alterna-
tive proofs of the same proposition are given. A. first sets aside
(638-9) the case in which both premisses of each proof are different
from those of the other, as in All N is M (A), All P is N (B),
Therefore all P is M (E), and All O is M (7), All P 150 (4), There-
fore all P is M (E). It then occurs to A. to suggest (in 539) that
there may be three alternative proofs each of which shares one
premiss with each of the other two proofs. Now here, the con-
clusion being identical, the extreme terms in each syllogism are
identical with the extreme terms in each of the other two
syllogisms ; and, each syllogism having one premiss in common
with each of the other two syllogisms, the middle terms must
also be identical. The proofs must differ, then, only in the
arrangement of the terms; they will be proofs in the three figures,
using the same terms. Al. and P. adopt this interpretation.
Two difficulties at once present themselves. (1) If A and 7"
can each serve with the same premiss B to produce the same
conclusion E, they must themselves have identical terms; and
if so, they cannot themselves combine as premisses of a third
syllogism. (2) If we avoid this difficulty by omitting the doubtful
words καὶ AI (or καὶ BI), there still remains the objection that
two syllogisms containing the same terms differently arranged
would be no illustration of what A. is here conceding—the
possibility of the same conclusion being proved by the use of
different middle terms. To avoid this objection, Maier (2 a. 223 n.)
takes the passage quite differently. He reads διὰ τῶν AB xoi ΒΓ,
and supposes these words to refer not to alternative proofs but
to parts of a single proof, such as All N is M (A), AILO is N (B),
All P is O (17), Therefore all P is M (E). The description of such
a sorites, however, as being διὰ τῶν AB xai ΒΓ is unnatural; we
should rather expect διὰ τῶν ABI, the premisses being named
continuously as in 4239. Besides, it seems most unlikely that A.
could have coupled a reference to a single sorites with a reference
to two alternative syllogisms (538-9); it is only in 4281 that he
comes to discuss the single chain of proof with more than one
middle term.
The great variety of readings points to early corruption. Now
in 4231-2 A. goes on to the case in which each premiss of a syllogism
is supported by a prosyllogism ; and this makes it likely that he
has already referred to the case in which one of the premisses is so
I. 25. 4235-30 379
supported. This points to the reading διὰ τῶν AB xoi ATA. A.
will then be saying in 41537-9 ‘if we set aside as irrelevant (1)
the case in which E is proved by two proofs differing in both their
premisses and (2) that in which E is proved by two proofs sharing
one premiss; e.g. when All P is M is proved (a) from All N is M
and All P is N (A and B), and (b) from All N is M, All O is N,
and All P is O (A, Γ, and A)’.
425. xai τὸ Γ, i.e. the conclusion from A and B.
6-8. Ei δ᾽ οὖν... ἀδύνατον, i.e. if anyone chooses to call a
syllogism supported by two prosyllogisms 'one syllogism', we
may admit that in that sense a single conclusion can follow from
more than two premisses; but it does not follow from them in
the same way as conclusion C follows from the premisses A, B,
i.e. directly.
9-12. οὐκοῦν ἀνάγκη . . . ὅρων, i.e. to yield a conclusion, two
of the premisses must be so related that one of them states a
general rule and another brings a particular case under this rule.
This is A.'s first statement of the general principle that syllogism
proceeds by subsumption. That it does so is most clearly true
of the first figure, which alone A. regards as self-evident. τοῦτο yàp
δέδεικται πρότερον is probably a reference to 40530-4120.
18-20. kai εἰ μὲν... συμβαίνει, ie. if C and D prove E, we
have not one but two syllogisms, ABE and CDE ; if C and D
prove A or B, we have merely the case which has already been
admitted in 41-7 to occur without infringing the principle that
a syllogism has three and only three terms, viz. the case in which
a syllogism is preceded by one or two prosyllogisms proving one
or both of the premisses.
23-4. εἰ μὴ ἐπαγωγῆς . . . χάριν, ie. the propositions C, D
may have been introduced not as syllogistic premisses but (a) as
particular statements tending to justify A or B inductively, or
(b) to throw dust in the eyes of one's interlocutor by withdrawing
his attention from A and B, when these are insufficient to prove
E, or (c), as Al. suggests (279. 4), to make the argument apparently
more imposing. Cf. Top. 155>20-4 ἀναγκαῖαι δὲ λέγονται (προτάσεις)
8v ὧν 6 συλλογισμὸς γίνεται. αἱ δὲ mapa ταύτας λαμβανόμεναι
τέτταρές εἰσιν: T) γὰρ ἐπαγωγῆς χάριν τοῦ δοθῆναι τὸ καθόλου, 7j εἰς
ὄγκον τοῦ λόγου, ἢ πρὸς κρύψιν τοῦ συμπεράσματος, ἢ πρὸς τὸ
σαφέστερον εἶναι τὸν λόγον.
28-30. εἰ δὲ μὴ γίνεται... συλλογισμόν. Al. noticed that this
point has been made already with regard to Γ᾿ and 4 (*22-4),
and therefore, to avoid repetition, suggested (28o. 21-4) that AB
should be read for l'A. But in fact this sentence is no mere
380 COMMENTARY
repetition. In 214-24 A. was examining his first main alternative,
that the conclusion from A and B is E. Under this, he examines
various hypotheses as to the conclusion from 7" and 4, and the
last of these is that they have no conclusion. In 324-30 he is
examining his other main alternative, that the conclusion from A
and B is something other than E, and here also he has to examine,
in connexion with this hypothesis, the various hypotheses about
the conclusion from I’ and 4, and again the last of these is that
they have no conclusion.
32-5. Τούτου δ᾽... συλλογισμῶν. From the fact that there
are three and only three terms it follows that there are two and
only two premisses—unless we bring in a new premiss, by con-
verting one of the original premisses, to reduce the argument
from the second or third figure to the first (cf. 24522—6, etc.). This
exception only 'proves the rule', for the syllogism then contains
only the original premiss which is retained and the new premiss
which is substituted for the other original premiss. The sense re-
quires of yàp τρεῖς... προτάσεις to be bracketed as parenthetical.
bg-6. ὅταν δὲ... ΓΔ. Though Al's lemma has μὴ συνεχῶν, his
commentary and quotations (283. 3, 284. 20, 29) show clearly that
he read συνεχῶν, and this alone gives a good sense. If a subject
B is proved to possess an attribute A by means of two middle
terms C, D, this may be exhibited either by means of a syllogism
preceded by a prosyllogism, or as a sorites consisting of a con-
tinuous chain of terms: (1) C is A, D is C, Therefore D is A.
D is A, B is D, Therefore B is A. (2) Bis D, Dis C, C is A,
Therefore B is A. In either case the number of terms exceeds
by one the number of independent premisses ; there are the four
terms A4, C, D, B, and the three independent premisses C is A,
D is C, B is D.
8-10. ἢ yap... ὅρων. In framing the sorites All B is D, All
D isC, All C is A, Therefore all B is A, we may have started with
All D is C, All C is A, Therefore all D is A, or with All B is D,
All D is C, Therefore All B is C, and then brought in the term B
in the first case, or A in the second, ‘from outside’. Or again we
may have started with All B is C, All C is A, Therefore All B
is A, or with All B is D, All D is A, Therefore all B is A, and
brought in the term D in the first case, or the term C in the
second, 'into the middle' (D between B and C, or C between D
and A). In any case, A.’s principle is right, that the number of
stretches from term to term, B-D, D-C, C-A, is one less than
the number of terins.
B. Einarson in A.J.P. lvii (1936), 158 gives reasons for believing
I. 25. 42832 —>26 381
that the usage of παρεμπίπτειν in >8 (as οἱ ἐμπίπτειν and of
éufáAMaÓa:) is borrowed from the language used in Greek mathe-
matics to express the insertion of a proportional mean in an interval.
15-16. ἀνάγκη παραλλάττειν... γινομένης, i.e. the premisses
become odd and the terms even, when the same addition (i.e.
the addition of one) is made to both.
16-26. rà δὲ συμπεράσματα... προτάσεων. The rule for the
simple syllogism was: one conclusion for two premisses (b4-5).
The rule for the sorites is: for each added term there are added
conclusions one fewer than the original terms. A. takes (1)
(P19-23) the case in which we start from All B is A, ΑἹ] C is B,
Therefore all C is A, and add the term D, i.e. the premiss All
DisC. Then we do not get a new conclusion with C as predicate
(πρὸς μόνον τὸ ἔσχατον οὐ ποιεῖ συμπέρασμα, 19-20). But we get
ἃ new conclusion with B as predicate (All D is B) and one with
A as predicate (All D is A). (Similarly if we add a further term
E, i.e. the premiss All E is D, we get three new conclusions—
ANE isC, All E is B, All E is A (ὁμοίως δὲ κἀπὶ τῶν ἄλλων, P23).)
Again (P23-s) suppose we start from All B is A, All C is B,
Therefore all C is A, and introduce a fourth term (2) between
B and A or (3) between C and B. In case (2) we have the premisses
All D is A, All B is D, AUC is B, and we get a new conclusion
with A as predicate (All B is A) and one with D as predicate
(All C is D), but none with B as predicate. In case (3) we have
the premisses All B is A, All D is B, All C is D, and we get a
new conclusion with 4 as predicate (All D is A) and one with
B as predicate (All C is B), but none with C as predicate.
Thus in a sorites 'the conclusions are much more numerous
than either the terms or the premisses' (P25-6). The rule is:
2 premisses, 3 terms, 1 conclusion,
3 premisses, 4 terms, 1-+-2 conclusions,
4 premisses, 5 terms, 1--2--3 conclusions,
and in general 4 premisses, +1 terms, 4 » (n —1) conclusions.
πολὺ πλείω is, of course, correct only when » is greater than 5.
CHAPTER 26
The kinds of proposition to be proved or disproved in each figure
42527. Now that we know what syllogisms are about, and what
kind of thing can be proved, and in how many ways, in each
figure, it is clear what kinds of proposition are hard and what are
easy to prove; that which can be proved in more figures and in
more moods is the easier to prove.
382 COMMENTARY
32. A is proved only in one mood, of the first figure; E in one
mood of the first and two of the second; I in one of the first and
three of the third; O in one of the first, two of the second, and
three of the third.
40. Thus A is the hardest to prove, the easiest to disprove. In
general, universals are easier to disprove than particulars. A is
disproved both by E and by O, and O can be proved in all the
figures, E in two. E is disproved both by A and by I, and this can
be done in two figures. But O can be disproved only by A, I only
by E. Particulars are easier to prove, since they can be proved both
in more figures and in more moods.
43°10. Further, universals can be disproved by particulars and
vice versa; but universals cannot be proved by particulars,
though particulars can by universals. It is clear that it is easier
to disprove than to prove.
16. We have shown, then, how every syllogism is produced,
how many terms and premisses it has, how the premisses are
related, what kinds of proposition can be proved in each figure,
and which can be proved in more, which in fewer, figures.
42527. ᾿Επεὶ δ᾽. . . συλλογισμοί, ie. since we know what
syllogisms aim at doing, viz. at proving propositions of one of the
four forms All B is A, No Bis A, Some B is A, Some B is not A.
32-3. TO μὲν οὖν καταφατικὸν... μοναχῶς, i.e. by Barbara
(25>37-40).
34-5. τὸ δὲ στερητικὸν... διχῶς, i.e. by Celarent (25540-2622),
or by Cesare (2725-9) or Camestres (ib. 9-14).
35-6. τὸ δ᾽ ἐν μέρει... ἐσχάτου, i.e. by Darii (26223-5), or by
Darapti (28418-26), Disamis (2857-11), or Datisi (ib. 11-15).
38-40. τὸ δὲ στερητικὸν . . . τριχῶς, 1.6. by Ferio (26225-3090), by
Festino (27332-6) or Baroco (ib. 36-53), or by Felapton (28226-30),
Bocardo (285r5-21:), or Ferison (ib. 31-5).
43°7- ἦν, cf. 42534.
CHAPTER 27
Rules for categorical syllogisms, applicable to all problems
43*20. We have now to say how we are to be well provided with
syllogisms to prove any given point, and how we are to find the
suitable premisses; for we must not only study how syllogisms
come into being, but also have the power of making them.
25. (1) Some things, such as Callias or any sensible particular,
are not predicable of anything universally, while other things are
I. 26. 42527 — 4337 383
predicable of them; (2) some are predicable of others but have
nothing prior predicable of them ; (3) some are predicable of other
things while other things are also predicable of them, e.g. man of
Callias and animal of man.
32. Clearly sensible things are not predicated of anything else
except per accidens, as we say ‘that white thing is Socrates’. We
shall show later, and we now assume, that there is also a limit in
the upper direction. Of things of the second class nothing can be
proved to be predicable, except by way of opinion; nor can
particulars be proved of anything. Things of the intermediate
class can be proved true of others, and others of them, and most
arguments and inquiries are about these.
Pr. The way to get premisses about each thing is to assume
the thing itself, the definitions, the properties, the attributes
that accompany it and the subjects it accompanies, and the
attributes it cannot have. The things of which it cannot be an
attribute we need not point out, because a negative proposition
is convertible.
6. Among the attributes we must distinguish the elements in
the definition, the properties, and the accidents, and which of
these are merely plausibly and which are truly predicable; the
more such attributes we have at command, the sooner we shall
hit on a conclusion, and the truer they are, the better will be the
proof.
rir. We must collect the attributes not of a particular instance,
but of the whole thing—not those of a particular man, but those
of every man; for a syllogism needs universal premisses. If the
term is not qualified by ‘all’ or ‘some’ we do not know whether the
premiss is universal.
16. For the same reason we must select things on which as a
whole the given thing follows. But we must not assume that the
thing itself follows as a whole, e.g. that every man is every
animal; that would be both useless and impossible. Only the
subject has ‘all’ attached to it.
22. When the subject whose attributes we have to assume is
included in something, we have not to mention separately among
its attributes those which accompany or do not accompany the
wider term (for they are already included; the attributes of
animal belong to man, and those that animal cannot have, man
cannot have); we must assume the thing’s peculiar attributes ;
for some ave peculiar to the species.
29. Nor have we to name among the things on which a genus
follows those on which the species follows, for if animal follows
384 COMMENTARY
on man, it must follow on all the things on which man follows,
but these are more appropriate to the selection of data about man.
32. We must assume also attributes that usually belong to the
subject, and things on which the subject usually follows; for a
conclusion usually true proceeds from premisses all or most of
which are usually true.
36. We must not point out the attributes that belong to every-
thing ; for nothing can be inferred from these.
4329-30. τὰ δ᾽ αὐτὰ... κατηγορεῖται. These are the highest
universals, the categories.
37. πάλιν ἐροῦμεν, An. Post. I. 19-22.
37-43. κατὰ μὲν οὖν τούτων... τούτων. The effect of this is
that the ‘highest terms’ and the ‘lowest terms’ in question cannot
serve as middle terms in a first-figure syllogism, since there the
middle term is subject of one premiss and predicate of the other.
But the ‘highest terms’ can serve as major terms, and the ‘lowest
terms’ as minor terms. And further the ‘highest terms’ can serve
as middle terms in the second figure, and the ‘lowest terms’ as
middle terms in the third. It is noteworthy, however, that A.
never uses a proper name or a singular designation in his examples
of syllogism ; the terms that figure in them are of the intermediate
class—universals that are not highest universals.
39. πλὴν εἰ μὴ κατὰ δόξαν. In view of what A. has said in
429-30, it is clearly his opinion that no predication about any of
the categories can express knowledge. To say that substance
exists or that substance is one is no genuine predication, since
‘existent’ and ‘one’ are ambiguous words not conveying any
definite meaning. But there were people who thought that in
saying ‘substance exists’ or ‘substance is one’ they were making
true and important statements, and it is to this δόξα that A. is
referring. The people he has in view are those about whom he
frequently (e.g. in Met. 99218-19) remarks that they did not
realize the ambiguity of ‘existent’ or ‘one’, viz. the Platonists.
bz. καὶ τοὺς ὁρισμούς. The plural may be used (1) because A.
has to take account of the possibility of the term's being am-
biguous, or (2) because every problem involves two terms, the
subject and the predicate.
13-14. διὰ yàp τῶν καθόλου... συλλογισμός, i.e. syllogism
is impossible without a universal premiss; this has been shown
in ch. 24.
I9. καθάπερ kai προτεινόμεθα, ‘which is also the form in which
we state our premisses’.
I. 27. 43*29— 538 385
25. εἴληπται yàp ἐν ἐκείνοις, ‘for in assigning to things their
genera, we have assigned to them the attributes of the genera’.
26. kai ὅσα μὴ ὑπάρχει, ὡσαύτως. This is true only if μὴ
ὑπάρχει be taken to mean ‘necessarily do not belong’.
29-32. οὐδὲ δὴ... ἐκλογῆς. This rule is complementary to
that stated in 522-9. What it says is that in enumerating the
things of which a genus is predicable, we should not enumerate
the sub-species or individuals of which a species of the genus is
predicable, since it is self-evident that the genus is predicable of
them. We should enumerate only the species of which the genus
is immediately predicable.
36-8. ἔτι τὰ πᾶσιν ἑπόμενα... δῆλον. The reason for this
rule is stated in 44>20-4 (where v. note) ; it is that if we select as
middle term an attribute which belongs to all things, and there-
fore both to our major and to our minor, we get two affirmative
premisses in the second figure, which prove nothing.
CHAPTER 28
Rules for categorical syllogisms, peculiar to different problems
43°39. If we want to prove a universal affirmative, we must
look for the subjects to which our predicate applies, and the
predicates that apply to our subject; if one of the former is
identical with one of the latter, our predicate must apply to our
subject.
43- If we want to prove a particular affirmative, we must look
for subjects to which both our terms apply.
44:2. If we want to prove a universal negative, we must look
for the attributes of our subject and those that cannot belong to
our predicate; or to those our subject cannot have and those that
belong to our predicate. We thus get an argument in the first or
second figure showing that our predicate cannot belong to our
subject.
9. If we want to prove a particular negative, we look for the
things of which the subject is predicable and the attributes the
predicate cannot have; if these classes overlap, a particular
negative follows.
rr. Let the attributes of A and E be respectively B, .. . By,
Z,... 2, the things of which A and E are attributes P, . . . I,,
H,... H,, the attributes that A and E cannot have 4, . . . 4,»
17. “Then if any I" (say I) is identical with a Z (say Z,), (1)
4985 cc
386 COMMENTARY
since all E is Z,, all E is I, (2) since all Γ᾽, is A and all E is T,
all E is A.
19. If I, is identical with H,, (1) since all 77, is A, all H, is A,
(2) since all H, is A and is E, some E is A.
21. If 4, is identical with Z,, (1) since no 4, is A, no Z, is A,
(2) since no Z, is A and all E is Z,, no E is A.
25. If B, is identical with @,, (1) since no E is O,, no E is B,,
(2) since all A is B, and no E is B,, no E is A.
28. If A, is identical with H,, (1) since no 4, is 4, no H, is A,
(2) since no H, is A, and all H, is E, some E is not A.
30. If B, is identical with H,, (1) since all H, is E, all B, is E,
(2) since all B, is E and all A is B,, all A is E, and therefore some
E is A.
36. We must look for the first and most universal both of the
attributes of each of the two terms and of the things of which it is
an attribute. E.g. of the attributes of E we must look to KZ,
rather than to Z, only; of the things of which A is an attribute
we must look to KT, rather than to Γ᾽, only. For if A belongs to
KZ, it belongs both to Z, and to E ; but if it does not belong to
KZ, it may still belong to Z,. Similarly with the things of which
A is an attribute; if it belongs to KT, it must belong to I, but
not vice versa.
b6. It is also clear that our inquiry must be conducted by means
of three terms and two premisses, and that all syllogisms are in
one of the three figures. For all E is shown to be A when Γ and Z
have been found to contain a common member. This is the
middle term and we get the first figure.
rr. Some E is shown to be A when I, and H, are the same;
then we get the third figure, with H, as middle term.
12. No E is shown to be A, when 4, and Z, are the same; then
we get both the first and the second figure—the first because (a
negative proposition being convertible) no Z, is A, and all E is
Z,,; the second because no A is 4, and all E is 4,.
16. Some E is shown not to be A when 4, and H, are the same;
this is the third figure—No H, is A, All H, is E.
19. Clearly, then, (1) all syllogisms are in one or other of the
three figures; (2) we must not select attributes that belong to
everything, because no affirmative conclusion follows from con-
sidering the attributes of both terms, and a negative conclusion
follows only from considering an attribute that one has and the
other has not.
25. All other inquiries into the terms related to our given
terms are useless, e.g. (1) whether the attributes of each of the
I. 28. 4432-11 387
two are the same, (2) whether the subjects of A and the attributes
E cannot have are the same, or (3) what attributes neither can
have. In case (1) we get a second-figure argument with two
affirmative premisses; in case (2) a first-figure argument with a
negative minor premiss; in case (3) a first- or second-figure
argument with two negative premisses; in no case is there a
syllogism.
38. We must discover which terms are the same, not which are
different or contrary; (1) because what we want is an identical
middle term ; (2) because when we can get a syllogism by finding
contrary or incompatible attributes, such syllogisms are reducible
to the aforesaid types.
4524. Suppose B, and Z, contrary or incompatible. Then we
can infer that no E is A, but not directly from the facts named,
but in the way previously described. B, will belong to all 4 and
to no E; so that B, must be the same as some @. (If B, and ΠῚ
are incompatible attributes, we can infer that some E is not A,
by the second figure, for all A is B,, and no E is B,; so that B,
must be the same as some €" (which is the same thing as B, and
H,'s being incompatible).]
17. Thus nothing follows directly from these data, but if B,
and Z, are contrary, B, must be identical with some © and that
gives rise to a syllogism. Those who study the matter in this way
follow a wrong course because they fail to notice the identity of
the B's and the O's.
44'2-4. ᾧ μὲν... παρεῖναι. The full reading which I have
adopted (following the best MSS.) is much preferable to that
of Al. (preferred by Waitz), which has 6 for d in #2 and omits
εἰς rà ἑπόμενα, ὃ δὲ δεῖ μὴ ὑπάρχειν. Al.’s reading is barely intel-
ligible, and its origin is easily to be explained by haplography.
7-8. γίνεται yap . . . μέσῳ. The second alternative (24-6)
clearly produces a syllogism in Camestres. The first alternative
(32-4) at first sight produces a second-figure syllogism (Cesare)
rather than one in the first figure. But A. has already observed
that itis not necessary to select things of which the major or minor
term is not predicable; it is enough to select things that are not
predicable of τὲ, because a universal negative proposition is con-
vertible (4355-6). Thus he thinks of the data No P is M, AIL S
is M, as immediately reducible to No M is P, All 5 is M, which
produces a syllogism in the first figure (Celarent).
9-1ι. ἐὰν δὲ... ὑπάρχειν. Similarly here A. thinks of the
data No P is M, All M is S, as reduced at once to No M is P,
388 COMMENTARY
All M is S, yielding a syllogism in the third figure (Felapton) ;
for of course he does not recognize our fourth figure, to which the
original data conform.
11-35. Μᾶλλον δ᾽... μέρος. A.’s meaning can be easily
followed if we formulate his data (#12-17): All A is B,... B,,
AlID,...IQisA,NoAis4;...4,, Al E is Z, ... 2, All
HQ... Hy is E, No E is €... @,; each of the letters B, Γ, 4,
Z, H, O stands for a whole group of terms. In ?17-35 A. shows
that a conclusion with E as subject and A as predicate follows
if any of the following pairs has a common member—T' and Z,
I' and H, 4 and Z, B and 6, 4 and H, B and H. In >25-37 he
shows that nothing follows from the possession of a common
member by the remaining pairs—B and Z, Γ and 6, 4 and 6.
εἰ δὲ τὸ Γ καὶ τὸ Η ταὐτόν (419-20) must be interpreted in the
light of the more careful phrase εἰ ταὐτό τί ἐστι τῶν Γ τινὶ τῶν Ζ
(517); and so with the corresponding phrases in 321-2, 25, 28,
30-1, P26-8, 29-30, 34-5.
17. εἰ μὲν οὖν... Z. The sense requires us to read ἐστι for
ἔσται.
22. ἐκ προσυλλογισμοῦ. The prosyllogism is No 4, is A (since
No A is 4, is convertible, #23), All Z, is 4,, Therefore no Z,
is A ; the syllogism is No Z, is A, All E is Z,, Therefore no E is A.
31. ἀντεστραμμένος ἔσται συλλογισμός. The syllogism is
called ἀντεστραμμένος because (the fourth figure not being recog-
nized) the data are not such as to lead directly to a conclusion
with E as subject and A as predicate; our conclusion must be
converted. .
34-5. τινὶ δ᾽... μέρος. I have adopted B's reading, which was
that of Al. (306. 16) and of P. (287. 10). ἀντιστρέφειν means ‘to be
convertible', and the universal is convertible into a particular
(All A is E into Some E is A), not vice versa. Cf. 31227 διὰ τὸ
ἀντιστρέφειν τὸ καθόλου τῷ κατὰ μέρος, and ib. 31-2, 5154, 5258-9,
67537.
36-5. Φανερὸν odv.. . ἐγχωρεῖ. The primary method of proof
—that in Barbara (#17-19)—consists in finding a subject (L7) of
which our major term (A) is predicable, which is identical with an
attribute (Z4) of our minor term (E). A. now recommends the
person who is trying to prove that all E is A to take the highest or
widest subject of which A is necessarily true (AI), i.e. the xaóAov
which I, falls under), and the highest attribute which necessarily
belongs to E (KZ,, the καθόλου which Z, falls under). We have
then these data—All E is Z,, All Z, is KZ,, All I, is KT, All
ΚΓ, is A; whereas, before we took account of KZ,, KT',, what
I. 28. 44211 —>24 389
we knew was simply that all E is Z, and all I, is A. The brevity
of A.’s account makes it difficult to see why he recommends this
course; but the following interpretation may be offered con-
jecturally. If we find that KZ, is identical with I, or with
KI, then all KZ, is A and (since all Z, is KZ, and all E is Z,)
it follows that all Z, is A and that all E is A; and All KZ, is A
contains implicitly the statements All Z, is A, All E is A,
without being contained by them. It is thus the most pregnant
of the three statements and the one that expresses the truth most
exactly, since (when all three are true) it must be on the generic
character KZ, and not on the specific character Z, or on the
more specific character E that being A depends. If, on the other
hand, we find that we cannot say All KZ, is A, we can still fall
back on the question ‘Is all Z, A?’, and if it is, we shall have
found an alternative answer to our search for a middle term
between E and A. Thus the method has two advantages: (1) it
gives us two possible middle terms, and (2) if KZ, is a true middle
term it is a better one to have than Z,, since it states more
exactly the condition on which being A depends. This is what
A. conveys in ?1-3. The next sentence repeats the point, stating
it, however, with reference to KI, instead of KZ,. If KT,
necessarily has the attribute A, then I, (which is a species of
KT) necessarily has it, and ‘AT’, is A’ is more strictly true, since
it is not qua a particular species of KI’, but qua a species of KT,
that I, is A. If, on the other hand, KT', is not necessarily A,
we may fall back on a species of it, and find that that is neces-
sarily A.
The upshot of the paragraph is that where there is a series of
middle terms between E and A, the preferable one to treat as
the middle term is that which stands nearest to A in generality.
It is more correct to say All KT, is A, All E is KT',, Therefore
all E is A, than to say All I, is A, All E is Γ᾿,» Therefore all
E is A.
Al. takes αὐτό in ^3 to be E, and is able to extract a good sense
from 53-5 on the assumption. But the structure of the paragraph
makes it clear that 53-5 is meant to elucidate 240-: (τοῦ δὲ A...
μόνον), as ^1-3 is meant to elucidate 339-40 (rod μὲν E . . . μόνον).
b8-r9. δείκνυται γὰρ... τῷ H. 58-10 answers to *17—19, >11-12
to 419-21, Pr4-15 to *21-5, Pr6-19 to 328-30. brs-16 gives a new
proof that if 4, and Z, are identical, no E is A, viz.: If all Z,
is A,, (1) since all E is Z,, all E is A,, (2) since no A is 4, and
all E is 4,, no E is A.
20-4. καὶ ὅτι... μὴ ὑπάρχειν. Both Al. and P. interpret
390 COMMENTARY
πᾶσιν as == ἀμφοτέροις, both major and minor term. But it is
hardly possible that A. should have used πᾶσιν so; we must
suppose him to mean what he says, that the attributes that are
common to all things, i.e. such terms as ὄν or ἕν, which stand
above the categories, should never, in the search for a syllogism,
be mentioned among the attributes of the extreme terms. Sup-
pose M is such a term. We cannot then get an affirmative con-
clusion, since All A is M, All E is M, proves nothing (as was
shown in 27818-20), and we could get a negative conclusion only
by making the false assumption that M is untrue of all or some
A or E.
That this, and not the interpretation given by ΑἹ. and P., is
correct is confirmed by the fact that the point ἐμόν make, that
no use can be made of any attribute that belongs to both major
and minor term, is made as a new point just below, in 526-7:
29-36. εἰ μὲν yap... συλλογισμός. (1) If B, is identical with
Z,, then since all A is B,, all Ais Z,. But from All A is Z, and
All E is Z, nothing follows. (2) If I, is identical with O,, then
since all I, is A, all 9, is A. But from All ©, is A and No E is
©, nothing follows. (3) If 4, is identical with 6,, then (a) since
no 4, is A, no 6, is A; but from No 0, is A and No E is 6,
nothing follows; (8) Since no A is 4,, no A is €,; but from No
A is €, and No E is @, nothing follows.
38. Δῆλον 86 . . . ληπτέον, i.c. καὶ ὅτι ληπτέον ἐστὶν ὁποῖα ταὐτά
ἐστι. ὅτι, though our only ancient evidence for it is the lemma of
Al. (which, as often, has ὅτι xac instead of the more correct xai ὅτι),
is plainly required by the sense.
4574-9. olov εἰ... Θ. A. here points out that from the data
‘All A is B,, All E is Z,’ (the permanent assumptions stated in
4412-15), 'B, is contrary to (or incompatible with) Z,', expressed
in thet form, we cannot infer that no E is A (since there is no
middle term entering into subject-predicate relations with A
and with E). But, he adds, we can get the conclusion No E is A
if we rewrite the reasoning thus: If no Z, is By, (1) since all E is
Z,, no E is B,, (2) since all A is B, and no E is B,, no E is A. In
fact, he continues, since no E is B,, B, must be one of the Θ΄ 5
(the attributes no E can have)—which suggests an alternative
way of reaching the conclusion No E is A, viz. that which has
been given in 44?25-7.
9-16. πάλιν ci... ὑπάρχειν. A. (if the section be A.'s) now
turns to consider the case in which B, (a predicate of A) and H,
(a subject of which E is predicable) are incompatible. Then, he
says, it can be inferred that some £ is not A, and this, as in the
I. 28. 44529 — 45216 391
case dealt with in *4-9, is done by a syllogism in the second
figure.
At this point a difficult question of reading arises. In *12 n,
the first hand of B, and Al. (315. 23) read τῷ δὲ E οὐδενί.
ACd, the second hand of B, and P. (294. 23-4) read τῷ δὲ H
ovdevi, probably as a result of Al.’s having offered this reading
conjecturally (316. 6). Waitz instead reads τῷ δὲ E od τινί (in
the sense of τινὲ οὔ; for the form cf. 24219, 26532, 59510, 63526-7).
With n's reading the reasoning will be: if no H, is B,, (1) since
all H, is E, no E is B,, (2) since all A is B, and no E is B,, some
E is not A (second figure). With Al.'s conjecture the reasoning
will be: If no H, is B,, (1) since all A is B,, no H, is A (second
figure), (2) since no H, is A and all H, is E, some E is not A.
With Waitz’s conjecture the reasoning will be: If no Hj, is B,,
(1) since all H, is E, some E is not B,, (2) since all A is B, and
some £ is not B,, some E is not A (second figure).
n's reading is clearly.at fault in two respects; the inference that
no E is B, involves an illicit minor, and the appropriate inference
from All A is B, and No E is B, is not Some E is not A, but No
E is A. Either of the conjectures avoids these errors.
But now comes a further difficulty. The clause, as emended
in either way, will not support the conclusion ὥστ᾽ ἀνάγκη ro B
ταὐτόν τινι εἶναι τῶν € (the same as one of the attributes E cannot
have). With either reading all that follows is that B, is an attri-
bute which some E does not possess. Al. recognizes the difficulty,
and points out (316. 18-20) that what really follows is not that B,
is identical with one of the O's, but that H, is identical with one
of the A's. A. has in 44?28-30 and P16-17 pointed out that this is
the assumption from which it follows that some E is not A.
On the other hand, the unemended reading in 4512, if what it says
were true, would justify the conclusion that B, is identical with
one of the 6’s.
Thus each of the three readings would involve A. in an elemen-
tary error with which it is difficult to credit him. Now it must
be noted that the next paragraph makes no reference to the
assumption that B, and H, are incompatible; it refers only to
the assumption that B, and Z, are incompatible, which was
dealt with in #4-9. I conclude that 39-16 are not the work of A.,
but of a later writer who suffered from excess of zeal and lack of
logic.
392 COMMENTARY
CHAPTER 29
Rules for reductio ad impossibile, hypothetical syllogisms, and
modal syllogisms
45°23. Like syllogism, reductio ad impossibile is effected by
means of the consequents and antecedents of the two terms. The
same things that are proved in the one way are proved in the
other, by the use of the same terms.
28. If you want to prove that No E is A, suppose some E to be
A; then, since All A is B and Some E is A, Some E is B; but ex
hypothesi none was. So too we can prove that Some E is A, or the
other relations between E and A. Reductio is always effected by
means of the consequents and antecedents of the given terms.
36. If we have proved by reductio that No E is A, we can by
the use of the same terms prove it ostensively; and if we have
proved it ostensively, we can by the use of the same terms prove
it by reductio.
b4. In every case we find a middle term, which will occur in the
conclusion of the reductio syllogism ; and by taking the opposite
of this conclusion as one premiss, and retaining one of the original
premisses, we prove the same main conclusion ostensively. The
ostensive proof differs from the veductto in that in it both premisses
are true, while in the reductio one is false.
12. These facts will become clearer when we treat of reducto ;
but it is already clear that for both kinds of proof we have to look
to the same terms. In other proofs from an hypothesis the terms
of the substituted proposition have to be scrutinized in the same
way as the terms of an ostensive proof. The varieties of proof
from an hypothesis have still to be studied.
21. Some of the conclusions of ostensive proof can be reached in
another way ; universal propositions by the scrutiny appropriate
to particular propositions, with the addition of an hypothesis. If
the P" and the H were the same, and E were assumed to be true
only of the H's, all E would be A; if the 4 and the H were the
same, and E were predicated only of the H's, no E would be A.
28. Again, apodeictic and problematic propositions are to be
proved by the same terms, in the same arrangement, as assertoric
conclusions ; but in the case of problematic propositions we must
assume also attributes that do not belong, but are capable of
belonging, to certain subjects.
36. It is clear, then, not only that all proofs can be conducted
in this way, but also that there is no other. For every proof has
I. 29. 45727 —°8 393
been shown to be in one of the three figures, and these can only
be effected by means of the consequents and antecedents of the
given terms. Thus no other term can enter into any proof.
The object of this chapter is to show (1) that the same con-
clusions can be proved by reductio ad impossibile as can be
proved ostensively ; (2) that for a proof by reductio, no less than
for an ostensive one, what we must try to find is an antecedent
or consequent of our major term which is identical with an
antecedent or consequent of our minor (ie. we must use the
method described in ch. 28). Incidentally A. remarks (1) that
the same scrutiny of antecedents and consequents is necessary
for arguments from an hypothesis—i.e. where, wanting to prove
that B is A, we assume that B is A if D is C, and then set
ourselves to prove that D is C—with the proviso that in this case
it is the antecedents and consequents of D and C, not of B and A,
that we scrutinize (45515—-19) ; (2) that identities which, according
to the method described in ch. 28, yield a particular conclusion,
will with the help of a certain hypothesis yield a universal con-
clusion (ib. 21-8) ; and (3) that the same scrutiny is applicable to
modal as to pure syllogisms (ib. 28-35).
45°27. καὶ 8 διὰ τοῦ ἀδυνάτου, kai δεικτικῶς. In his treat-
ment of the moods of syllogism, A. has generally used reductio ad
impossibile as an alternative proof of something that can be
proved ostensively. But there were two exceptions to this. The
moods Baroco (27236—53) and Bocardo (28515-20) were proved by
reductto, without any ostensive proof being given (though yet
another mode of proof of Bocardo is suggested in 2852o-1). But
broadly speaking A.'s statement is true, that the same premisses
will give the same conclusion by an ostensive proof and by a
reductio.
28-33. olov St r6 Α΄... ὑπῆρχεν. A. shows here how the con-
clusion (a) of a syllogism in Camestres (All A is B, No E is B,
Therefore no E is A) and (5) of a syllogism in Darapti (All H is 4,
All H is E, Therefore some E is A) can be proved by reductio, from
the same premisses as are used in the ostensive syllogism.
54-8. ὁμοίως δὲ... ὅρων. A. now passes from the particular
cases dealt with in ?28—53 to point out that by the use of the same
middle term we can always construct (a) a reductio and (b) an
ostensive syllogism to prove the same conclusion. (a) The way to
construct a reductto is to find ‘a term other than the two terms
which are our subject-matter' (i.e. which we wish to connect or dis-
connect) 'and common to them' (i.e. entering into true predicative
394 COMMENTARY
relations with them), ‘which will become a term in the conclu-
sion of the syllogism leading to the false conclusion'. E.g. if
we want to prove that some C is not A, we can do this if we can
find a term B such that no B is A and some C is B. Then by
taking one of these premisses (No B is A) and combining with it
the supposition that all C is A, we can get the conclusion No
C is B. Knowing this to be false, we can infer that the merely
supposed premiss was false and that Some C is not A is true.
(b) To get an ostensive syllogism, we have only to return to the
original datum whose opposite was the conclusion of the reductio
syllogism (ἀντιστραφείσης ταύτης τῆς προτάσεως, 56) (i.e. to assume
that some C is B), and combine with it the other original datum
(No B is A), and we get an ostensive syllogism in Ferio proving
that some C is not A.
12-13. Ταῦτα μὲν ov... λέγωμεν, i.e. in ii. 14.
15-19. ἐν δὲ τοῖς ἄλλοις... ἐπιβλέψεως. Arguments κατὰ
μετάληψιν are those in which the possession of an attribute by
a term is proved by proving its possession of a substituted attri-
bute (τὸ μεταλαμβανόμενον, 41239). Arguments κατὰ ποιότητα, Says
Al. (324. 19-325. 24), are those that proceed ἀπὸ τοῦ (1) μᾶλλον
xai (2) ἧττον kai (3) ὁμοίου, all of which ‘accompany quality’.
(x) may be illustrated thus: Suppose we wish to prove that happi-
ness does not consist in being rich. We argue thus: 'If something
that would be thought more sufficient to produce happiness than
wealth is not sufficient, neither is that which would be thought
less sufficient. Health, which seems more sufficient than wealth,
is not sufficient. Therefore wealth is not.' And we prove that
health is not sufficient by saying 'No vicious person is happy,
Some vicious people are healthy, Therefore some healthy people
are not happy’. A corresponding proof might be given in mode
(2). (3) May be illustrated thus: 'If noble birth, being equally
desirable with wealth, is good, so is wealth. Noble birth, being
equally desirable with wealth, is good' (which we prove by saying
'Everything desirable is good, Noble birth is desirable, Therefore
noble birth is good’), ‘Therefore wealth is good.’
Arguments κατὰ ποιότητα are thus one variety of arguments
xarà μετάληψιν, since a substituted term is introduced. In all
such arguments, says A. (if the text be sound), the σκέψις, i.e. the
search for subjects and predicates of the major and minor term,
and for attributes incompatible with the major or minor term
(43539-44?17), takes place with regard not to the terms of the
proposition we want to prove, but to the terms of the proposition
substituted for it (as something to be proved as a means to proving
I. 29. 45^12-34 395
it). The reason for this is that, whereas the logical connexion
between the new term and that for which it is substituted is
established δι’ ὁμολογίας ἢ τινος ἄλλης ὑποθέσεως, the substituted
proposition is established by syllogism (41.38-- 1).
Maier (2 a. 282-4) argues that the expressions xarà μετάληψιν,
κατὰ ποιότητα are quite unknown in A.’s writings, and that οἷον...
ποιότητα is an interpolation by a Peripatetic familiar with
Theophrastus’ theory of the hypothetical syllogism, in which, as
we may learn from Al., these expressions were technical terms
(for a full account of Theophrastus’ theory see Maier, 2 a. 263-87).
But since A. here uses the phrase ἐν rois μεταλαμβανομένοις, it
can hardly be said that he could not have used the phrase xara
μετάληψιν, and it would be rash to eject οἷον... ποιότητα in face
of the unanimous testimony of the MSS., AL, and P.
19-20. ἐπισκέψασθαι δὲ... ὑποθέσεως. A. nowhere discusses
this topic in general, but reductio ad impossibile is examined in
li. 11-14.
22-8. ἔστι δὲ... ἐπιβλεπτέον. Le. the assumption that I
(a subject of the major term A) is identical with H, (a subject of
the minor term £), which in 44?19-21 proved that some E is A,
will, if we add the hypothesis that only H,'s are E, justify the
conclusion All E is A. ((1) AL I, is A, All H, is I, Therefore
all H, is A; (2) All H, is A, All E is H,, Therefore all E is A.)
And the assumption that 4, (an attribute incompatible with A)
is identical with H,, which in 44?28-3o proved that Some E is
not A, will, if we add the hypothesis that only H,'s are E, justify
the conclusion No E is A. ((1) No A, is A, All H, is 4,, Therefore
no H,is A; (2) No H, is A, All E is H,, Therefore no E is A.)
Therefore it is useful to examine whether only the H,’s are E,
in addition to the connexions of terms mentioned in 4412-35
(καὶ οὕτως ἐπιβλεπτέον, 45528).
28-31. τὸν αὐτὸν δὲ τρόπον. . . συλλογισμός, This refers
to the method prescribed in ch. 28, i.e. to the use of the terms
designated 4-60 in 44412~-17.
32-4. δέδεικται γὰρ... συλλογισμός. This was shown in the
chapters on syllogisms with at least one problematic premiss
(chs. 14-22).
24. ὁμοίως δὲ... κατηγοριῶν, i.e. propositions asserting that
it is δυνατόν, od δυνατόν, οὐκ ἐνδεχόμενον, ἀδύνατον, οὐκ ἀδύνατον, οὐκ
ἀναγκαῖον, ἀληθές, οὐκ ἀληθές, that E is A (De Int. 22411-13).
Such propositions are to be established, says A., ὁμοίως, i.e. by
the same scrutiny of the antecedents and consequents of E and
A, and of the terms incompatible with E or A (4339-44335).
396 COMMENTARY
CHAPTER 30
Rules proper to the several sciences and arts
46*3. The method described is to be followed in the establish-
ment of all propositions, whether in philosophy or in any science;
we must scrutinize the consequents and antecedents of our two
terms, we must have an abundance of these, and we must pro-
ceed by way of three terms; if we want to establish the truth we
must scrutinize the antecedents and consequents really connected
with our subject and our predicate, while for dialectical syllogisms
we must have premisses that command general assent.
10. We have described the nature of the starting-points and
how to hunt for them, to save ourselves from looking at all that
can be said about the given terms, and limit ourselves to what is
appropriate to the proof of A, £, J, or O propositions.
17. Most of the suitable premisses state attributes peculiar to
the science in question; therefore it is the task of experience to
supply the premisses suitable to each subject. E.g. it was only
when the phenomena of the stars had been sufficiently collected
that astronomical proofs were discovered ; if we have the facts we
can readily exhibit the proofs. If the facts were fully discovered
by our research we should be able to prove whatever was provable,
and, when proof was impossible, to make this plain.
28. This, then, is our general account of the selection of pre-
misses; we have discussed it more in detail in our work on
dialectic.
46*5. περὶ ἑκάτερον, i.e. about the subject and the predicate
between which we wish to establish a connexion.
8. ἐκ τῶν κατ᾽ ἀλήθειαν διαγεγραμμένων ὑπάρχειν, i.e. from the
attributes and subjects (τὰ ὑπάρχοντα καὶ οἷς ὑπάρχει, *5) which
have been catalogued as really belonging to the subject or
predicate of the conclusion.
16. καθ᾽ ἕκαστον... ὄντων. The infinitive is explained by the
fact that δεῖ is carried on in A.'s thought from 44 and 211.
19. λέγω δ᾽ olov τὴν ἀστρολογικὴν μὲν ἐμπειρίαν (sc. δεῖ παρα-
δοῦναι τὰς) τῆς ἀστρολογικῆς ἐπιστήμης.
29-30. δι᾽ ἀκριβείας... διαλεκτικήν, i.c. in the Topics, parti-
cularly in 1. 14. It is, of course, only the selection of premisses
of dtalectical reasoning that is discussed in the Topics; the nature
of the premisses of scientific reasoning is discussed in the Posterior
Analytics.
I. 30. 46*5~30 397
CHAPTER 31
Division
46°31. The method of division is but a small part of the method
we have described. Division is a sort of weak syllogism ; for it
begs the point at issue, and only proves a more general predicate.
But in the first place those who used division failed to notice this,
and proceeded on the assumption that it is possible to prove the
essence of a thing, not realizing what it 7s possible to prove by
division, or that it is possible to effect proof in the way we have
described.
39. In proof, the middle term must always be less general than
the major term; division attempts the opposite—it assumes the
universal as a middle term. E.g. it assumes that every animal is
either mortal or immortal. Then it assumes that man is an
animal. What follows is that man is either mortal or immortal,
but the method of division takes for granted that he is mortal,
which is what had to be proved.
*x2. Again, it assumes that a mortal animal must either have
feet or not have them, and that man is a mortal animal; from
which it concludes not (as it should) that man is an animal with
or without feet, but that he is one with feet.
zo. Thus throughout they take the universal term as middle
term, and the subject and the differentiae as extremes. They
never give a clear proof that man is so-and-so; they ignore the
resources of proof that are at their disposal. Their method cannot
be used either to refute a statement, or to establish a property,
accident, or genus, or to decide between contradictory proposi-
tions, e.g. whether the diagonal of a square is or is not com-
mensurate with the side.
29. For if we assume that every line is either commensurate or
incommensurate, and that the diagonal is a line, it follows that it
must be either commensurate or incommensurate ; but if we infer
that it is incommensurate, we beg the question. The method is
useful, therefore, neither for every inquiry nor for those in which
it is thought most useful.
A. resumes his criticism of Platonic διαίρεσις as a method of
proof, in An. Post. ii. s. In An. Post. 9625-9756 he discusses
the part which division may play in the establishment of
definitions.
Maier (2 b. 77 n. 2) thinks that this chapter sits rather loosely
398 COMMENTARY
between two other sections of the book (chs. 27-3o on the mode
of discovery of arguments and chs. 32-45 on the analysis of them).
He claims that A. states in 46234—9, "22-5 that definitions are not
demonstrable and that this presupposes the proof in An. Post.
ii. 5-7 that this is so. 46522—5 does not in fact say that definitions
are not demonstrable, but only that the method of division does
not demonstrate them; but 234-7 seems to imply that A. thinks
definitions not to be demonstrable, and Maier may be right in
inferring ch. 31 to be later than the proof of this fact in An. Post.
ii. He is, however, wrong in thinking that the chapter has little
connexion with what precedes; it is natural that A., after ex-
pounding his own method of argument (the syllogism), should
comment on what he,regarded as Plato's rival method (division).
46°31-2. Ὅτι δ᾽... ἰδεῖν. The tone of the chapter shows that
μικρόν τι μόριόν ἐστι means ‘is only a small part’. ἡ διὰ τῶν γενῶν
διαίρεσις is the reaching of definitions by dichotomy preached and
practised in Plato’s Sophistes (219 a—237 a) and Politicus (258 b-
267 c).
34. συλλογίζεται δ᾽... ἄνωθεν, i.e. what the Platonic method
of division does prove is that the subject possesses an attribute
higher in the scale of extension than the attribute to be proved.
37-8. ὥστ᾽ οὔτε... εἰρήκαμεν. This sentence yields the best
sense if we read 6 τι in 437 with Al. and P. For διαιρούμενοι we
should read διαιρουμένους, with the MS. n, or διαιρουμένοις. The
MSS. of P. vary between διαιρουμένους and διαιρουμένοις, and in. Al.
335. 11 the best MS. corrected διαιρουμένης (probably a corruption
of διαιρουμένοις by itacism) into διαιρουμένους. The variants are best
explained by supposing διαιρουμένοις to have been the original
reading.
6 τι ἐνδέχεται συλλογίσασθαι διαιρουμένοις. What it is possible
to prove is, as A. proceeds to explain, a disjunctive proposition,
not the simple proposition which the partisans of division
think they prove by it. οὕτως ὡς εἰρήκαμεν refers to A.’s own
method, described in chs. 4-30.
39-2. ἐν μὲν οὖν rais ἀποδείξεσιν... ἄκρων. In Barbara,
the only mood in which a universal affirmative (such as a
definition must be) can be proved, the major term must be at
least as wide as the middle term, and is normally wider.
b22-4. τέλος δέ. . . «eva, As meaning is expressed more
fully in An. Post. 9124-7 τί yàp κωλύει τοῦτο ἀληθὲς μὲν τὸ πᾶν
εἶναι κατὰ τοῦ ἀνθρώπου, μὴ μέντοι τὸ τί ἐστι μηδὲ τὸ τί ἦν εἶναι
δηλοῦν; ἔτι τί κωλύει ἢ προσθεῖναί τι ἣ ἀφελεῖν ἢ ὑπερβεβηκέναι
τῆς οὐσίας;
I. 31. 46831 —537 399
36-7. οὔτ᾽ ἐν οἷς... πρέπειν, i.e. in the finding of definitions,
the use to which Plato had in the Sopiustes and Politscus put the
method of division. Cf. *35-7.
CHAPTER 32
Rules for the choice of premisses, middle term, and figure
46°40. Our inquiry will be completed by showing how syllogisms
can be reduced to the afore-mentioned figures, and that will
confirm the results we have obtained.
47710. First we must extract the two premisses of the syllo-
gism (which are its larger elements and therefore easier to extract),
see which is the major and which the minor, and supply the miss-
ing premiss, if any. For sometimes the minor premiss is omitted,
and sometimes the minor premisses are stated but the major
premisses are not given, irrelevant propositions being introduced.
18. So we must eliminate what is superfluous and add what is
necessary, till we get to the two premisses. Sometimes the defect
is obvious; sometimes it escapes notice because something follows
from what is posited.
24. E.g., suppose we assume that substance is not destroyed by
the destruction of what is not substance, and that by the destruc-
tion of elements that which consists of them ts destroyed. It
follows that a part of a substance must be a substance ; but only
because of certain unexpressed premisses.
28. Again, suppose that if a man exists an animal exists, and
if an animal exists a substance exists. It follows that if a man
exists a substance exists; but this is not a syllogism, since the
premisses are not related as we have described.
3x. There is necessity here, but not syllogism. So we must not,
if something follows from certain data, attempt to reduce the
argument directly. We must find the premisses, analyse them
into their terms, and put as middle term that which occurs in
both premisses.
40. If the middle term occurs both as predicate and as subject,
or is predicated of one term and has another denied of it, we have
the first figure. If it is predicated of one term and denied of the
other, we have the second figure. If the extreme terms are
both predicated, or one is predicated and one denied, of it, we
have the third figure. Similarly if the premisses are not both
universal.
Ὁ), Thus any argument in which the same term is not mentioned
twice is not a syllogism, since there is no middle term. Since we
400 COMMENTARY
know what kinds of premiss can be dealt with in each figure, we
have only to refer each problem to its proper figure. When it can
be dealt with in more than one figure, we shall recognize the figure
by the position of the middle term.
4772-5. εἰ yàp . . . πρόθεσις. εἰ yap τήν re γένεσιν τῶν συλλο-
γισμῶν θεωροῖμεν points back to chs. 2-26; kai τοῦ εὑρίσκειν ἔχοιμεν
δύναμιν to chs. 27-30; ἔτι δὲ τοὺς γεγενημένους ἀναλύοιμεν εἰς τὰ
προειρημένα σχήματα forward to chs. 32-45, especially to chs.
32-3, 42, 44. It is to this process of analysis of arguments into
the regular forms (the moods of the three figures) that the name
τὰ ἀναλυτικά (A.’s own name for the Prior and Posterior Analytics)
refers. The use of the word ἀναλύειν implies that the student has
before him an argument expressed with no regard to logical form,
which he then proceeds to 'break up' into its propositions, and
these into their terms. This use of ἀναλύειν may be compared
with the use of it by mathematical writers, of the process of dis-
covering the premisses from which a predetermined conclusion
can be derived. Cf. B. Einarson in A.J.P. lvii (1936), 36-9.
There is a second use of ἀναλύειν (probably derived from that
found here) in which it stands for the reduction of a syllogism
in one figure to another figure. Instances of both usages are given
in our Index.
I2. μείζω δὲ... ὧν, Le. the premisses are larger components
of the syllogism than the terms.
16-17. ἢ ταύτας... παραλείπουσιν. At first sight it looks as
if ταύτας meant ‘both the premisses', and δι’ ὧν αὖται περαίνονται
the prior syllogisms by which they are proved; but a reference
to these would be irrelevant, since the manner of putting forward
a syllogism is not vitiated by the fact that the premisses are not
themselves proved. ταύτας must refer to the minor premisses,
and δι᾽ ὧν αὗται περαίνονται to the major premisses by which they
are ‘completed’, i.e. supplemented. So Al. 342. 15-18.
40-hs. ᾿Εὰν μὲν οὖν... ἔσχατον. κατηγορῇ in δὲ (bis), 3 is used
in the sense of 'accuses', sc. accuses a subject of possessing itself,
the predicate, i.e. ‘is predicated’, and κατηγορῆται in hr (as in
An. Post. 7317) in the corresponding sense of ‘is accused’, sc.
of possessing an attribute. In 4754, 5 κατηγορῆται is used in its
usual sense ‘is predicated’. ἀπαρνῆται in "2, 3, 4 is passive.
55-6. οὕτω yap... μέσον, cf. 25532—5, 266348, 28*10—14.
I. 32. 4742 — 33. 47°37 401
CHAPTER 33
Error of supposing that what is true of a subject 1n one respect 15
true of it without qualification
47°15. Sometimes we are deceived by similarity in the position
of the terms. Thus we might suppose that if A is asserted of B,
and B of C, this constitutes a syllogism; but that is not so. It is
true that Aristomenes as an object of thought always exists, and
that Aristomenes is Aristomenes who can be thought about ; but
Aristomenes is mortal. The major premiss is not universal, as it
should have been ; for not every Aristomenes who can be thought
about is eternal, since the actual Aristomenes is mortal.
29. Again, Miccalus is musical Miccalus, and musical Miccalus
might perish to-morrow, but it would not follow that Miccalus
would perish to-morrow ; the major premiss is not universally true,
and unless it is, there is no syllogism.
38. This error arises through ignoring a small distinction—
that between ‘this belongs to that’ and ‘this belongs to all of that’.
47°16. ὥσπερ εἴρηται πρότερον, in 231-5.
17. παρὰ τὴν ὁμοιότητα τῆς τῶν ὅρων θέσεως, ‘because the
arrangement of the terms resembles that of the terms of a syllo-
gism’.
21-9. ἔστω yap... 'Apioropévous. ἀεί ἐστι διανοητὸς ‘Apioro-
μένης.
ὁ Ἀριστομένης ἐστὶ δια-
νοητὸς Ἀριστομένης.
-- ὁ "Apioropévns ἔστιν
ἀεί.
This looks like a syllogism without being one. A. hardly does
justice to the nature of the fallacy. He treats its source as lying
in the fact that the first proposition cannot be rewritten as
πᾶς ὁ διανοητὸς Apiorouévns det ἔστιν, which it would have to be,
to make a valid syllogism in Barbara. But there is a deeper source
than this; for the statement that an Aristomenes can always be
thought of cannot be properly rewritten even as ‘some Aristo-
menes that can be thought of exists for ever’.
The Aristomenes referred to is probably the Aristomenes who
is named as a trustee in A.’s will (D. L. v. 1. 12)—presumably a
member of the Lyceum.
29-37. πάλιν ἔστω. . . συλλογισμός. Miccalus is musical
Miccalus; and it may be true that musical Miccalus will perish
4085 pd
402 COMMENTARY
to-morrow, i.e. that this complex of substance and attribute will
be dissolved to-morrow by Miccalus’ ceasing to be musical; but
it does not follow that Miccalus will perish to-morrow. A. treats
this (634-5) as a second example of confusion due to an indefinite
premiss being treated as if it were universal. But this argument
cannot be brought under that description. The argument he
criticizes is: Musical Miccalus will perish to-morrow, Miccalus
is musical Miccalus, Therefore Miccalus will perish to-morrow.
What is wrong with the argument is not that an indefinite major
premiss is treated as if it were universal, but that a premiss which
states something of a composite whole is treated as if the predicate
were true of every element in the whole. The confusion involved
is that between complex and element, not that between individual
and universal.
The name Miccalus is an unusual one; only two persons of the
name are recognized in Pauly-Wissowa. If the reference is to
any particular bearer of the name, it may be to the Miccalus who
was in 323 B.C. sent by Alexander the Great to Phoenicia and
Syria to secure colonists to settle on the Persian Gulf (Arrian,
An. 7. 19. 5). We do not know anything of his being musical.
CHAPTER 34
Error due to confusion between abstract and concrete terms
47°40. Error often arises from not setting out the terms cor-
rectly. It is true that it is not possible for any disease to be
characterized by health, and that every man is characterized by
disease. It might seem to follow that no man can be characterized
by health. But if we substitute the things characterized for the
characteristics, there is no syllogism. For it is not true that it is
impossible for that which is ill to be well; and if we do not assume
this there is no syllogism, except one leading to a problematic
conclusion—‘it is possible that no man should be well’.
4815. The same fallacy may be illustrated by a second-figure
syllogism,
18. and by a third-figure syllogism.
24. In all these cases the error arises from the setting out of the
terms; the things characterized must be substituted for the
characteristics, and then the error disappears.
Chs. 34-41 contain a series of rules for the correct setting out of
the premisses of a syllogism. To this chs. 42-6 form an appendix.
I. 34. 4842~—23 403
4892-15. οἷον ef... ὑγίειαν. From the true premisses Healthi-
ness cannot belong to any disease, Disease belongs to every man,
it might seem to follow that healthiness cannot belong to any
man ; for there would seem to be a syllogism of the mood recog-
nized in 3017-23 (E^AE^ in the first figure). But the conclusion
is evidently not true, and the error has arisen from setting out
our terms wrongly. If we substitute the adjectives ‘ill’ and ‘well’
for the abstract nouns, we see that the argument falls to the
ground, since the major premiss Nothing that is ill can ever be
well, which is needed to support the conclusion, is simply not
true. Yet (213-15) without that premiss we can get a conclusion,
only it will be a problematic one. For from the true premisses
It is possible that nothing that is ill should ever be well, It
is possible that every man should be ill, it follows that it is
Possible that no man should ever be well; for this argument
belongs to a type recognized in 33*1-5 as valid (EvA*E« in the
first figure).
15-18. πάλιν... νόσον. Here again we have a syllogism which
seems to have true premisses and a false conclusion: It is im-
possible that healthiness should belong to any disease, It is
possible that healthiness should belong to every man, Therefore
it is impossible that disease should belong to any man. But if
we substitute the concrete terms for the abstract, we find that
the major premiss needed to support the conclusion, viz. It is
impossible that any sick man should become well, is simply not
true.
According to the doctrine of 38:316-25 premisses of the form
which A. cites would justify only the conclusions It is possible
that disease should belong to no man, and Disease does not
belong to any man. Tredennick suggests νόσος (sc. ὑπάρχει) for
νόσον (sc. ἐνδέχεται ὑπάρχειν) in *18. But the evidence for νόσον
is very strong, and A. has probably made this slip.
18-23. ἐν δὲ τῷ τρίτῳ σχήματι... ἀλλήλοις. While in the
first and second figures it was an apodeictic conclusion (viz. in
the first-figure example (42-8) No man can be well, in the second-
figure example (16-18) No man can be ill) that was vitiated by
a wrong choice of terms, in the third figure it is a problematic
conclusion that is so vitiated. The argument contemplated is
such an argument as Healthiness may belong to every man,
Disease may belong to every man, Therefore healthiness may
belong to some disease. The premisses are true and the conclusion
false; and (321-3) this is superficially in disagreement with the
principle recognized in 39*14-19, that Every C may be A, Every
404 COMMENTARY
C may be B, justifies the conclusion Some B may be A. But the
substitution of adjectives for the abstract nouns clears up the
difficulty ; for from ‘For every man, being well is contingent, For
every man, being ill is contingent’ it does follow that for something
that is ill, being well is contingent.
CHAPTER 35
Expressions for which there is no one word
48°29. We must not always try to express the terms by a
noun; there are often combinations of words to which no noun is
equivalent, and such arguments are difficult to reduce to syllo-
gistic form. Sometimes such an attempt may lead to the error of
thinking that immediate propositions can be proved by syllogism.
Having angles equal to two right angles belongs to the isosceles
triangle because it belongs to the triangle, but it belongs to the
triangle by its own nature. That the triangle has this property is
provable, but (it might seem) not by means of a middle term.
But this is a mistake; for the middle term is not always to be
sought in the form of a ‘this’; it may be only expressible by a
phrase.
48^31—9. ἐνίοτε δὲ... λεχθέντος. There may be a proposition
which is evidently provable, but for the proof of which there is
no easily recognizable middle term (as there is when we can say
Every B is an A, Every C is a B). In such cases it is easy to fall
into the error of supposing that the terms of a proposition may
have no middle term and yet the proposition may be provable.
We can say Every triangle has its angles equal to two right
angles, Every isosceles triangle is a triangle, Therefore every
isosceles triangle has its angles equal to two right angles. But
we cannot find a name X such that we can say Every X has angles
equal to two right angles, Every triangle is an X. It might seem
therefore that the proposition Every triangle has its angles equal
to two right angles is provable though there is no middle term
between its terms. But in fact it has a middle term; only this
is not a word but a phrase. The phrase A. has in mind would be
‘Figure which has its angles equal to the angles about a point’,
i.e. to the angles made by one straight line standing on another;
for in Met. 1051424 he says διὰ τί δύο ὀρθαὶ τὸ τρίγωνον; ὅτι αἱ περὶ
μίαν στιγμὴν γωνίαι ἴσαι δύο ὀρθαῖς. εἰ οὖν ἀνῆκτο ἡ παρὰ τὴν
πλευράν, ἰδόντι ἂν ἣν εὐθὺς δῆλον διὰ τί. The figure implied is
I. 35. 48*31-7 405
5 a a eS oe E
where CE is parallel to BA. Then ZABC = ZECD, and
ZCAB = LACE, and therefore Z2ABC+ ZCAB+ ZBCA =
LECD-r ZACE+ Z BCA = two right angles.
36-7. ὥστ᾽ οὐκ ἔσται... ὄντος, This is the apparent conclu-
sion from the facts stated in 235-6. The triangle has its angles
equal to two right angles in virtue of itself; i.e. there is no wider
class of figures to which the attribute belongs directly, and there-
fore to triangle indirectly. It might seem therefore that though
the proposition ‘The angles of a triangle are equal to two right
angles’ is provable, it is not by means of a middle term. In fact
it is provable by means of a middle term, but only by that stated
in the previous note, which is a property peculiar to the triangle.
CHAPTER 36
The nominative and the oblique cases
48:40. We must not assume that the major term's belonging
to the middle term, or the latter’s belonging to the minor, implies
that the one will be predicated of the other, or that the two pairs
of terms are similarly related. ‘To belong’ has as many senses as
those which ‘to be’ has, and in which the assertion that a thing is
can be said to be true.
b4. E.g. let A be ‘that there is one science’, and B be 'contra-
ries. A belongs to B not in the sense that contraries are one
science, but in the sense that it is true to say that there is one
science of them.
10. It sometimes happens that the major term is stated of the
middle term, but not the middle term of the minor. If wisdom is
knowledge, and the good is the object of wisdom, it follows that
the good is an object of knowledge; the good is not knowledge,
but wisdom is.
14. Sometimes the middle term is stated of the minor but the
major is not stated of the middle term. If of everything that is a
quale or a contrary there is knowledge, and the good is a quale
and a contrary, it follows that of the good there is knowledge ; the
406 COMMENTARY
good is not knowledge, nor is that which is a quale or a contrary,
but the good is a quale and a contrary.
20. Sometimes neither is the major term stated of the middle
term nor the middle of the minor, while the major (2) may or (b)
may not be stated of the minor. (b) If of that of which there is
knowledge there is a genus, and of the good there is knowledge,
of the good there is a genus. None of the terms is stated of any
other. (a) On the other hand, if that of which there is knowledge
is a genus, and of the good there is knowledge, the good is a genus.
The major term is stated of the minor, but the major is not stated
of the middle nor the middle of the minor.
27. So too with negative statements. ‘A does not belong to B’
does not always mean ‘B is not A’; it may mean ‘of B (or for B)
there is no A’; e.g. ‘of a becoming there is no becoming, but of
pleasure there is a becoming, therefore pleasure is not a becoming'.
Or ‘of laughter there is a sign, of a sign there is no sign, therefore
laughter is not a sign'. Similarly in other cases in which the
negative answer to a problem is reached by means of the fact that
the genus is related in a special way to the terms of the problem.
35- Again, 'opportunity is not the right time; for to God belongs
opportunity, but no right time, since to God nothing is advan-
tageous'. The terms are right time, opportunity, God; but the
premiss must be understood according to the case of the noun.
For the terms ought always to be stated in the nominative, but
the premisses should be selected with reference to the case of each
term—the dative, as with 'equal', the genitive, as with 'double',
the accusative, as with ‘hits’ or ‘sees’, or the nominative, as in ‘the
man 5s an animal’,
In this chapter A. points out that the word ὑπάρχειν, ‘to belong’,
which he has used to express the relation of the terms in a pro-
position, is a very general word, which may stand for ‘be pre-
dicable of’ or for various other relations. Thus (to take his first
example) in the statement τῶν ἐναντίων ἔστι μία ἐπιστήμη, he
treats as what is predicated 'that there is one science'; but
the sentence does not say 'contraries are one science', but 'of
contraries there is one science’ (4854—9).
A. says in 48539-49*s that in reducing an argument to syllo-
gistic form we must pick out the two things between which the
argument establishes a connexion, and the third thing, which
serves to connect them. The names of these three things, in the
nominative case, are the terms. But his emphasis undoubtedly
falls on the second half of the sentence (49*1-5). While these are
I. 36. 48340 — 35 407
the three things we are arguing about, we must not suppose that
the relations between them are always relations of predicability ;
we must take account of the cases of the nouns and recognize
that these are capable of expressing a great variety of relations,
and that the nature of the relations in the premisses dictates the
nature of the relation in the conclusion. A. never evolved a theory
of these relational arguments (of which A = B, B =C, Therefore
A — C may serve as a typical example), but the chapter shows
that he is alive to their existence and to the difficulties involved
in the treatment of them.
48*40. τῷ ἄκρῳ, i.e. to the minor term.
52-3. ἀλλ᾽ ὁσαχῶς .. . τοῦτο, ‘in as many senses as those in
which “Bis A" and "it is true to say that B is A” are used’.
9-8. οὐχ Gore ... ἐπιστήμην. It seems impossible to defend
the traditional reading, and Al. says simply οὐ γάρ ἐστιν ἡ
πρότασις λέγουσα ‘7a ἐναντία pia ἐστὶν ἐπιστήμη᾽ (361. 15). P. has
the traditional reading, but has difficulty in interpreting it.
αὐτῶν, at any rate, seems to be clearly an intruder from »8.
12. τοῦ δ᾽ ἀγαθοῦ ἐστὶν ἡ σοφία. ἐπιστήμη (which most of the
MSS. add after σοφία), though Al. had it in his text and tries hard
to defend it, is plainly an intruder, and one that might easily
have crept into the text. We have the authority of one old and
good MS. (d) for rejecting it.
13-14. τὸ μὲν δὴ ἀγαθὸν οὐκ ἔστιν ἐπιστήμη. A.’s point being
that the middle term is not predicated as an attribute of the minor
term, he ought to have said here τὸ μὲν δὴ ἀγαθὸν οὐκ ἔστι σοφία.
But ἐπιστήμη is well supported (Al. 362. 19-21, P. 336. 23-8), and
the slip is a natural one.
20. ἔστι δὲ μήτε. Bekker and Waitz have ἔστι δὲ ὅτε μήτε, but
if ὅτε were read grammar would require it to be followed by οὔτε.
κατηγορεῖσθαι or λέγεσθαι is to be understood.
24-7. εἰ δ᾽... λέγεται. κατ᾽ ἀλλήλων δ᾽ οὐ λέγεται Means ‘the
major is not predicable of the middle term, nor the middle term
of the minor’. A. makes a mistake here. The major term is
predicated not only of the minor but also of the middle term
(‘that of which there is knowledge is a genus’). A. has carelessly
treated not ‘that of which there is knowledge’ but ‘knowledge’ as
if it were the term that occurs in the major premiss.
33-5. ὁμοίως δὲ... γένος. This refers to arguments in the
second figure (like the two arguments in Cesare in >3o-2, 32-3)
in which ‘the problem is cancelled’, i.e. the proposed proposition
is negated, or in other words a negative conclusion is reached, on
the strength of the special relation (a relation involving the use
408 COMMENTARY
of an oblique case) in which the genus, i.e. the middle term
(which in the second figure is the predicate in both premisses),
stands to the extreme terms. αὐτό (sc. τὸ πρόβλημα) is used care-
lessly for the terms of the proposed proposition.
41. τὰς κλήσεις τῶν ὀνομάτων, ie. their nominatives. Cf.
Soph. El. 17340 ἐχόντων θηλείας ἢ ἄρρενος κλῆσιν (cf. 182218).
4932-5. ἢ yap... πρότασιν, ‘for one of the two things may
appear in the dative, as when the other is said to be equal to it,
or in the genitive, as when the other is said to be the double of
it, or in the accusative, as when the other is said to hit it or see
it, or in the nominative, as when a man is said to de an animal—
or in whatever other way the word may be declined in accordance
with the premiss in which it occurs'.
CHAPTER 37
The various kinds of attribution
49:6. That this belongs to that, or that this is true of that, has
a variety of meanings corresponding to the diversity of the
categories; further, the predicates in this or that category may
be predicated of the subject either in a particular respect or
absolutely, and either simply or compounded ; so too in the case
of negation. This demands further inquiry.
49:6-8. Τὸ δ᾽ ὑπάρχειν . . . διήρηνται, i.e. in saying ‘A belongs
to B' we may mean that A is the kind of substance B is, a quality
B has, a relation B is in, etc.
8. kai ταύτας ἢ πῇ ἢ ἁπλῶς, Le. in saying ‘A belongs to B’
we mean that A belongs to B in some respect, or without quali-
fication.
ἔτι ἢ ἁπλᾶς ἢ συμπεπλεγμένας, e.g. (to take Al.’s examples)
we may say ‘Socrates is a man’ or ‘Socrates is white’, or we may
say ‘Socrates is a white man’; we may say ‘Socrates is talking’ or
‘Socrates is sitting’, or we may say ‘Socrates is sitting talking’.
9-10. ἐπισκεπτέον δὲ... βέλτιον. This probably refers to all
the matters dealt with in this chapter. The words do not amount
to a promise; they merely say that these questions demand
further study.
I. 36. 48541 — 38. 49*14 409
CHAPTER 38
The difference between proving that a thing can be known, and
proving that it can be known to be so-and-so
49°11. A word that is repeated in the premisses should be
attached to the major, not to the middle, term. E.g., if we want
to prove that 'of justice there is knowledge that it is good', 'that
it is good' must be added to the major term. The correct analysis
is: Of the good there is knowledge that it is good, Justice is good,
Therefore of justice there is knowledge that it is good. If we say
‘Of the good, that it ‘is good, there is knowledge’, it would be
false and silly to go on to say ' Justice is good, that it is good'.
22. Similarly if we wanted to prove that the healthy is know-
able qua good, or the goat-stag knowable qua non-existent, or man
perishable gua sensible object.
27. The setting out of the terms is not the same when what is
proved is something simple and when it is qualified by some
attribute or condition, e.g. when the good is proved to be know-
able and when it is proved to be capable of being known to be
good. In the former case we put as middle term ‘existing thing’ ;
in the latter, 'that which is some particular thing'. Let A be
knowledge that it is some particular thing, B some particular
thing,C good. Then we can predicate A of B ; for of some particular
thing there is knowledge that it is that particular thing. And we
can predicate B of C ; for the good is some particular thing. There-
fore of the good there is knowledge that it is good. If 'existing
thing’ were made middle term we should not have been able to
infer that of the good there is knowledge that it is good, but only
that there is knowledge that it exists.
49^11-22. Τὸ δ᾽ ἐπαναδιπλούμενον. . . συνετόν. ‘That the
good is good can be known’ is in itself as proper an expression as
‘The good can be known to be good’, and A. does not deny this.
What he points out is that only the latter form is available as a
premiss to prove that justice can be known to be good. To treat
the former expression as a premiss would involve having as the
other premiss the absurd statement ‘Justice is that the good is
good'.
I4. ἢ f ἀγαθόν. A. is here anticipating. The whole argument
in 312-22 deals with the question in which term of the syllogism
(to prove that there is knowledge of the goodness of justice) 'that
it is good’ must be included. ‘There is knowledge of justice 15 so
410 COMMENTARY
far as it is good’ is a different proposition, belonging to the type
dealt with in 322-5. But here also A.’s point is sound. If we want
to prove that justice in so far as it is good is knowable, we must
put our premisses in the form What is good is knowable in so far
as it is good, Justice is good. For if we begin by saying The good
in so far as it is good is knowable, we cannot go on to say Justice
is good in so far as it is good. This, if not ψεῦδος, is at least οὐ
συνετόν (222).
18. ἡ yap δικαιοσύνη ὅπερ ἀγαθόν, ‘for justice is exactly what
good is’. It would be stricter to say ἡ yap δικαιοσύνη ὅπερ ἀγαθόν
τι (cf. 57-8), ‘justice is identical with one kind of good’, ‘justice
is a species of the genus good’.
23. ἢ τραγέλαφος 1j μὴ Sv, sc. ἐπιστητόν ἐστι. Bekker, with the
second hand of B and of d, inserts 8o£acróv before #. Al. and P.
interpret the clause as meaning 'the goat-stag is an object of
opinion qua not existing', but this is because they thought A.
could not have meant to say that a thing can be known qua not
existing; it is clear that P. did not read δοξαστόν (P. 345. 16-18).
But in fact A. would not have hesitated to say ‘the goat-stag qua
not existing can be known’, sc. not to exist.—The τραγέλαφος was
‘a fantastic animal, represented on Eastern carpets and the like’
(L. and S.); cf. De Int. 16816, An. Post. 9257, Phys. 208430, Ar.
Ran. 937, Pl. Rep. 488 a.
25. πρὸς τῷ ἄκρῳ, to the major, not to the middle term.
27-2. Οὐχ ἡ αὐτὴ ... ὅρους. The point A. makes here is that
a more determinate middle term is needed to prove a subject’s
possession of a more determinate attribute.
37-8. kai πρὸς τῷ ἄκρῳ .. . ἐλέχθη, ‘and if "existent", simply,
had been included in the formulation of the major term’; cf.
925-6.
br. ἐν τοῖς ἐν μέρει συλλογισμοῖς, i.e. ὅταν τόδε τι 7) πῇ ἢ πὼς
σνλλογισθῇ (228).
CHAPTER 39
Substitution of equivalent expressions
49°3. We should be prepared to substitute synonymous ex-
pressions, word for word, phrase for phrase, word for phrase or
vice versa, and should prefer a word to a phrase. If ‘the suppos-
able is not the genus of the opinable’ and ‘the opinable is not
identical with a certain kind of supposabie’ mean the same, we
should put the supposable and the opinable as our terms, instead
of using the phrase narned.
I. 38. 49718 — 39. 4959 411
A. makes here two points with regard to the reduction of
arguments to syllogistic form. (ri) The argument as originally
stated may use more than three terms, but two of those which
are used may be different ways of saying the same thing ; in such
à case we must not hesitate to substitute one word for another,
one phrase for another, or a word for a phrase or a phrase for a
word, provided the meaning is identical. (2) The ἔκθεσις, the
exhibition of the argument in syllogistic form, is easier if words
be substituted for phrases. This is, of course, not inconsistent
with ch. 35, which pointed out that it is not always possible to
find a single word for each of the terms of a syllogism.
4956—9. otov ci... θετέον. A. sometimes uses δοξάζειν and
ὑπολαμβάνειν without distinction, but strictly ὑπολαμβάνειν im-
plies a higher degree of conviction than δοξάζειν, something like
taking for granted. Al. is no doubt right in supposing that A.
means to express a preference for the phrase τὸ δοξαστὸν οὐκ
ἔστιν ὅπερ ὑποληπτόν τι as compared with τὸ ὑποληπτὸν οὐκ ἔστι
γένος τοῦ δοξαστοῦ.
CHAPTER 40
The difference between proving that Bis A and proving that B ts
the A
49°10. Since ‘pleasure is good’ and ‘pleasure is the good’ are
different, we must state our terms accordingly ; if we are to prove
the latter, ‘the good’ is the major term ; if the former, ‘good’ is so.
CHAPTER 41
The difference between ‘A belongs to all of that to which B belongs’
and ‘A belongs to all of that to all of which B belongs’. The ‘setting
out’ of terms is merely illustrative
49°14. It is not the same to say ‘to all that to which B belongs,
A belongs’ and ‘to all that, to all of which B belongs, 4 belongs’.
If ‘beautiful’ belongs to something white, it is true to say ‘beauti-
ful belongs to white’, but not ‘beautiful belongs to all that is
white’.
20. Thus if A belongs to B but not to all B, then whether B
belongs to all C or merely to C, it does not follow that A belongs
to C, still less that it belongs to all C.
22. But if A belongs to everything of which B is truly stated,
412 COMMENTARY
A will be true of all of that, of all of which B is stated ; whileif
A is said (without quantification) of that, of all of which B is
said, B may belong to C and yet A not belong to all C, or to any C.
27. Thus if we take the three terms, it is clear that ‘A is said
of that of which B is said, universally’ means ‘A is said of all the
things of which B is said’; and if B is said of all of C, so is A;
if not, not.
33. We must not suppose that something paradoxical results
from isolating the terms; for we do not use the assumption that
each term stands for an individual thing ; it is like the geometer's
assumption that a line is a foot long when it is not—which he
does not use as a premiss. Only two premisses related as whole
and part can form the basis of proof. Our exhibition of terms
is akin to the appeal to sense-perception ; neither our examples
nor the geometer's figures are necessary to the proof, as the pre-
misses are.
49^14-32. Οὐκ ἔστι... παντός. A.’s object here is to point
out that the premiss which must be universal, in a first-figure
syllogism, is the major. This will yield a universal or a particular
conclusion according as the minor is universal or particular; a
particular major will yield no conclusion, whether the minor be
universal or particular.
Maier points out (2a. 265 n. 2) that this section forms the
starting-point of Theophrastus' theory about syllogisms xará
πρόσληψιν. Cf. Al. 378. 12-379. 11.
In 526 Al. (377. 25-6) and P. (351. 8-10) interpret as if there
were a comma before xara παντός, taking these words with
λέγεται 625. But that would make A. say that if the rnajor premiss
is universal, yet no conclusion need follow (ἢ ὅλως μὴ ὑπάρχειν).
He is really saying that if A is only said to be true of that, of all
of which B is said to be true, B may be true of C (not of all of
that), and yet A may not be true of all C, or may be true of noC.
Waitz correctly removed Bekker’s comma before κατὰ παντός.
In 528 also Waitz did rightly in removing Bekker’s comma
before παντός. The whole point is that the phrase καθ᾽ οὗ τὸ B
κατὰ παντὸς τὸ A λέγεται is ambiguous until we know whether κατὰ
παντός goes with what precedes or with what follows. What A.
says is that we have a suitable major premiss only if A is said
to be true of all that of which B is said, not if A is merely asserted
of that, of all of which B is asserted.
33-5073. Οὐ δεῖ... συλλογισμός. ἐκτίθεσθαι and ἔκθεσις are
used in two distinct senses by A. (1) Sometimes they are used of
I. 41. 49514 — 5083 413
the process of exhibiting the validity of a form of syllogism by
isolating in imagination particular cases (28323, 14, 3050, 11, 12,
bar). (2) Sometimes they are used of the process of picking out
the three terms of a syllogism and affixing to them the letters
A, B, Γ (48*1, 25, 29, 49, ^6, 57835). Al. (379. 14), P. (352. 3-7), and
Maier (2 a. 320 n.) think this is what is referred to here. In favour
of this interpretation is the fact that such an ἔκθεσις τῶν ὅρων is,
broadly speaking, the subject which engages A. in chs. 32-45.
But it is open to certain objections. One is that it is difficult to
see what absurdity or paradox {τι ἄτοπον, 49^33-4) could be sup-
posed to attach to this procedure. Another (which none oí these
interpreters tries to meet) is that it affords no explanation of the
words οὐδὲν yap προσχρώμεθα τῷ τόδε τι εἶναι.
Waitz gives the other interpretation, taking A.’s point to be
that the selection of premisses which are in fact incorrect should
not be thought to justify objection to the method, since the
premisses are only illustrative and the validity of a form of syllo-
gism does not depend on the truth of the premisses we choose to
illustrate it. To this Maier objects that there has been no refer-
ence in the context to the use of examples, so that the remark
would be irrelevant. This interpretation, however, comes nearer
to doing justice to the words οὐδὲν yàp προσχρώμεθα τῷ τόδε τι
εἶναι, since this might be interpreted to mean ‘for we make no
use of the assumption that the particular fact is as stated in our
example’. But that is evidently rather a loose interpretation of
these words.
There is one passage that seems to solve the difficulty—Soph.
El. 178>36-17978 καὶ ὅτι ἔστι τις τρίτος ἄνθρωπος map’ αὐτὸν Kai τοὺς
καθ᾽ ἕκαστον: τὸ γὰρ ἄνθρωπος καὶ ἅπαν τὸ κοινὸν οὐ τόδε τι, ἀλλὰ
τοιόνδε τι ἢ ποσὸν ἢ πρός τι ἢ τῶν τοιούτων τι σημαίνει. ὁμοίως δὲ καὶ
ἐπὶ τοῦ Κορίσκος καὶ Κορίσκος μουσικός, πότερον ταὐτὸν ἢ ἕτερον; τὸ
μὲν γὰρ τόδε τι τὸ δὲ τοιόνδε σημαίνει, ὥστ᾽ οὐκ ἔστιν αὐτὸ
ἐκθέσθαι: οὐ τὸ ἐκτίθεσθαι δὲ ποιεῖ τὸν τρίτον ἄνθρωπον, ἀλλὰ
τὸ ὅπερ τόδε τι εἶναι συγχωρεῖν. οὐ γὰρ ἔσται τόδε τι εἶναι ὅπερ
Καλλίας καὶ ὅπερ ἄνθρωπός ἐστιν. οὐδ᾽ εἴ τις τὸ ἐκτιθέμενον μὴ
ὅπερ τόδε τι εἶναι λέγοι ἀλλ᾽ ὅπερ ποιόν, οὐδὲν διοίσει: ἔσται γὰρ τὸ
παρὰ τοὺς πολλοὺς ἕν τι, οἷον τὸ ἄνθρωπος. Here the ἔκθεσις of man
from individual men, and the ἔκθεσις of ‘musical’ from Coriscus,
is distinguished from the admission that ‘man’ or ‘musical’ is
a τόδε τι, and we are told that it is the latter and not the former
that gives rise to paradoxical conclusions. The same point is
put more briefly in Met. 1078217-21.
Here, then, A. is saying that no one is to suppose that
414 COMMENTARY
paradoxical consequences arise from the isolation of the terms
in a syllogism as if they stood for separable entities. Wc make
no use of the assumption that each term isolated is a rode τι,
an individual thing.
With this usage of ἐκτίθεσθαι may be connected the passages in
which A. refers to the ἔκθεσις of the One from the Many by the
Platonists (Met. 992910, 100310, xo86^ro, 1ogo?17).
37-50?1. ὅλως yap... συλλογισμός, cf. 4249-12 n.
50?2. τὸν μανθάνοντ᾽ ἀλέγοντες. The received text has τὸν
μανθάνοντα λέγοντες, and Waitz interprets this as meaning τὸν
μανθάνοντα τῷ ἐκτίθεσθαι καὶ τῷ αἰσθάνεσθαι χρῆσθαι λέγοντες. This
is clearly unsatisfactory, it is not the learner but the teacher who
uses τὸ ἐκτίθεσθαι, and even if we take the reference to be simply
to τὸ αἰσθάνεσθαι the grammar is very difficult; Phys. 189532
φαμὲν yàp γίγνεσθαι ἐξ ἄλλου ἄλλο καὶ ἐξ ἑτέρου ἕτερον ἢ τὰ ἁπλᾶ
λέγοντες ἢ τὰ συγκείμενα, which Waitz cites, is no true parallel.
I have ventured to write τὸν μανθάνοντ᾽ aAéyovres, ‘in the interests
of the learner’. A. is not averse to the occasional use of a poetical
word; cf. for instance Met. 1090836 rà λεγόμενα... σαίνει τὴν
ψυχήν. Pacius’ πρὸς τὸν μανθάνοντα λέγοντες is probably con-
jectural.
CHAPTER 42
Analysis of composite syllogssms
50*5. We must recognize that not all the conclusions in one
argument are in the same figure, and must make our analysis
accordingly. Since not every type of proposition can be proved
in each figure, the conclusion will show the figure in which the
syllogism is to be sought.
50*5-7. Μὴ AavOaverw . . . ἄλλου. συλλογισμός is here used of
an extended argument in which more than one syllogism occurs.
A. points out that in such an argument some of the conclusions
may have been reached in one figure, some in another, and that
the reduction to syllogistic form must take account of this.
8-9. ἐπεὶ δ᾽... τεταγμένα. All four kinds of proposition can
be proved in the first figure, only negative propositions in the
second, only particular propositions in the third.
I. 41. 4937 — 43. 50°15 415
CHAPTER 43
In discussing definitions, we must attend to the precise point at issue
50711. When an argument has succeeded in establishing or
refuting one element in a definition, for brevity’s sake that element
and not the whole definition should be treated as a term in the
syllogism.
50?11-15. Tous re πρὸς ὁρισμὸν ... θετέον. Al. and P. take
the reference to be to arguments aimed at refuting a definition.
But the reference is more general—to arguments directed towards
either establishing or refuting an element in the definition of
a term. For this use of πρός Waitz quotes parallels in 29*23,
40539, 41*5-9, 39, etc. The object of θετέον is (τοῦτο) πρὸς ὃ
διείλεκται. τοὺς πρὸς ὁρισμὸν τῶν λόγων is an accusativus pendens,
such as is not infrequent at the beginning of a sentence; cf.
52329—30 n. and Kühner, Gr. Gramm., ὃ 412. 3.
CHAPTER 44
Hypothetical arguments are not reducible to the figures
50716. We should not try to reduce arguments ex hypothest to
syllogistic form; for the conclusions have not been proved by
syllogism, they have been agreed as the result of a prior agree-
ment. Suppose one assumes that if there are contraries that are
not realizations of a single potentiality, there is not a single
science of such contraries, and then were to prove that not every
potentiality is capable of contrary realizations (e.g. health and
sickness are not; for then the same thing could be at the same
time healthy and sick). Then that there is not a single potentiality
of each pair of contraries has been proved, but that there is no
science of them has not been proved. The opponent must admit it,
but as a result of previous agreement, not of syllogism. Only the
other part of the argument should be reduced to syllogistic form.
29. So too with arguments ad impossibile. The reductio ad
impossibile should be reduced, but the remainder of the argument,
depending on a previous agreement, should not. Such arguments
differ from other arguments from an hypothesis, in that in the
latter there must be previous agreement (e.g. that if there has
been shown to be one faculty of contraries, there is one science of
contraries), while in the latter owing to the obviousness of the
falsity there need not be formal agreement—e.g. when we assume
416 COMMENTARY
the diagonal commensurate with the side and prove that if it is,
odds must be equal to evens.
39. There are many other arguments ex hypothest. Their
varieties we shall discuss later; we now only point out that and
why they cannot be reduced to the figures of syllogism.
50716. τοὺς ἐξ ὑποθέσεως συλλογισμούς, cf. 41537—40 n., 45>15-
19 n.
19-28. olov εἰ... ὑπόθεσις. Maier (2 a. 252) takes the ὑπόθεσις
to be that if there is a single potentiality that does not admit
of contrary realizations, there is no science that deals with a pair
of contraries. But the point at issue is (as in 4854-9) not whether
all sciences are sciences of contraries, but whether every pair of
contraries is the object of a single science. The whole argument
then is this:
(A) If health and sickness were realizations of a single poten-
tiality, the same thing could be at the same time well
and ill, The same thing cannot be at the same time well
and ill, Therefore health and sickness are not realizations
of a single potentiality.
(B) Health and sickness are not realizations of a single poten-
tiality, Health and sickness are contraries, Therefore not
all pairs of contraries are realizations of a single poten-
tiality.
If not all pairs of contraries are realizations of a single
potentiality, not all contraries aré subjects of a single
science, Not all contraries are realizations of a single poten-
tiality, Therefore not all contraries are subjects of a single
science.
A. makes no comment on (A); the point he makes is that while
(B) is 'presumably' a syllogism, (C) is not. 'Presumably', ie.,
he assumes it to be a syllogism, though he does not trouble to
verify this by reducing the argument to syllogistic form.
In 321 οὐκ ἔστι πᾶσα δύναμις τῶν ἐναντίων is written loosely
instead of the more correct οὐκ ἔστι μία πάντων τῶν ἐναντίων
δύναμις (523).
29-38. Ὁμοίως 86 . . . ἀρτίοις. The nature of a reductio ad
impossibile (on which cf. 4122-63 n.) is as follows: If we want to
prove that if all P is M and some S is not M, it follows that some
S is not P, we say ‘Suppose all S to be P. Then (A) All P is M,
All S is P, Therefore all S is M. But (B) it is known that some
S is not M, and since All S is M is deduced in correct syllogistic
form from All P is M and All S is P, and All P is M is known to
3
I. 44. 50316 — ^2 417
be true, it follows that All S is P is false. Therefore Some S is
not P.'
A. points out that the part of the proof labelled (A) is syllogistic
but the rest is not; it rests upon an hypothesis. But the proof
differs from other arguments from an hypothesis, in that while
in them the hypothesis (e.g. that if there are contraries that are
not realizations of a single potentiality, there are contraries that
are not objects of a single science) is not so obvious that it need
not be stated, in reductio ad impossibile τὸ ψεῦδος is φανερόν, i.e.
it is obvious that we cannot maintain both that all S is M (the
conclusion of (ÀA)) and that some S is not M (our original minor
premiss). Similarly, in the case which A. takes (237-8), if it can
be shown that the commensurability of the diagonal of a square
with the side would entail that a certain odd number is equal to
a certain even number (for the proof cf. 41226—7 n.), the entailed
proposition is so obviously absurd that we need not state its
opposite as an explicit assumption.
40-52. τίνες μὲν οὖν... ἐροῦμεν. This promise is nowhere ful-
filled in A.'s extant works.
CHAPTER 45
Resolution of syllogisms in one figure into another
So^s. When a conclusion can be proved in more than one figure,
one syllogism can be reduced to the other. (4) A negative syllo-
gism in the first figure can be reduced to the second; and an
argument in the second to the first, but only in certain cases.
9. (a) Reduction to the second figure (a) of Celarent,
13. (B) of Ferio.
17. (b) Of syllogisms in the second figure those that are uni-
versal can be reduced to the first, but of the two particular
syllogisms only one can.
19. Reduction to the first figure (a) of Cesare,
21. (B) of Camestres,
25. (y) of Festino,
30. Baroco is irreducible.
43. (B) Not all syllogisms in the third figure are reducible to the
first, but all those in the first are reducible to the third.
35. (a) Reduction (a) of Darii,
38. (B) of Ferio.
gx*x. (b) Of syllogisms in the third figure, all can be converted
into the first, except that in which the negative premiss is par-
ticular. Reduction (a) of Darapti,
3985 Ee
7. (B) of Datisi,
8. (y) of Disamis,
12. (8) of Felapton,
15. (e) of Ferison.
18. Bocardo cannot be reduced.
22. Thus for syllogisms in the first and third figure to be
reduced to each other, the minor premiss in each figure must be
converted.
26. (C) (a) Of syllogisms in the second figure, one is and one is
not reducible to the third. Reduction of Festino.
31. Baroco cannot be reduced.
34. (b) Reduction from the third figure to the second, (a) of
Felapton and (8) of Ferison.
37. Bocardo cannot be reduced.
40. Thus the same syllogisms in the second and third figures
are irreducible to the third and second as were irreducible to the
first, and these are the only syllogisms that are validated in the
first figure by reductio ad impossibile.
50531-2. οὔτε yàp . . . συλλογισμός. The universal affirma-
tive premiss cannot be simply converted, and if it could, and we
tried to reduce Baroco to the first figure by converting its major
premiss simply, we should be committing an illicit major.
34. of δ᾽ ἐν τῷ πρώτῳ πάντες, i.e. all the moods of the first
figure which have such a conclusion as the third figure can prove,
i.e. a particular conclusion.
51?22. τὰ σχήματα, i.e. the first and third figures.
26-33. τῶν δ᾽... καθόλου. Of the moods of the second figure,
only two could possibly be reduced to the third figure, since only
two have a particular conclusion. Of these, Festino is reducible;
Baroco is not, since we cannot get a universal proposition by
converting either premiss (the major premiss being convertible
only per accidens, the minor not at all).
34-5. Kai of ἐκ τοῦ τρίτου... στερητικόν. Of the moods of
the third figure, only three could possibly be reduced to the
second, since only three have a negative conclusion. Of these
Felapton and Ferison are reducible, Bocardo is not.
40-52. Φανερὸν οὖν . . . περαίνονται, i.e. (1) in considering
conversion from the second figure to the third and vice versa, we
find the same moods to be inconvertible as were inconvertible
to the first figure, viz. Baroco and Bocardo ; (2) these are the same
moods which could be reduced to the first figure only by reductio
ad impossibile (27*36—53, 28>15-20).
I. 45. 50°31 — 5162 419
CHAPTER 46
Resolution of arguments involving the expressions ‘ts not A’ and
“5 not- A'
51*s. In the establishment or refutation of a proposition it is
important to determine whether 'not to be so-and-so' and 'to be
not-so-and-so' have the same or different meanings. They do not
mean the same, and the negative of ‘is white’ is not ‘is not-white’,
but 'is not white'.
xo. The reason is as follows: (A) The relation of ‘can walk’ to
'can not-walk', or of 'knows the good' to 'knows the not-good',
is similar to that of 'is white' to 'is not-white'. For 'knows the
good' means the same as 'is cognisant of the good', and 'can walk'
as ‘is capable of walking’; and therefore ‘cannot walk’ the same
as 'is not capable of walking'. If then 'is not capable of walking'
means the same as 'is capable of not-walking', 'capable of walk-
ing' and 'not capable of walking' will be predicable at the same
time of the same person (for the same person is capable of walking
and of not walking) ; but an assertion and its opposite cannot be
predicable of the same thing at the same time.
22. Thus, as 'not to know the good' and 'to know the not-
good’ are different, so are ‘to be not-good' and ‘not to be good’.
For if of four proportional terms two are different, the other two
must be different.
25. (B) Norare ‘to be not-equal' and ‘not to be equal’ the same;
for there is a kind of subject implied in that which is not-equal,
viz. the unequal, while there is none implied in that which merely
is not equal. Hence not everything is either equal or unequal, but
everything either is or is not equal.
28. Again, ‘is a not-white log’ and ‘is not a white log’ are not
convertible. For if a thing is a not-white log, it is a log; but that
which is not a white log need not be a log.
31. Thus it is clear that ‘is not-good’ is not the negation of ‘is
good’. If, then, of any statement either the predicate 'affirma-
tion’ or the predicate ‘negation’ is true, and this is not a negation,
it must be a sort of affirmation, and therefore must have a
negation of its own, which is ‘is not not-good’.
36. The four statements may be arranged thus:
‘Is good’ (A) ‘Is not good’ (B)
“15 not not-good’ (D) ‘Is not-good’ (C).
Of everything either A or B is true, and of nothing are both true;
so too with C and D. Of everything of which C is true, B is true
420 COMMENTARY
(since a thing cannot be both good and not-good, or a white log
and a not-white log). But C is not always true of that of which B
is true; for that which is not a log will not be a not-white log.
5236. Therefore conversely, of everything of which 4 is true,
D is true; for either C or D must be true of it, and C cannot be.
But A is not true of everything of which D is true; for of that
which is not a log we cannot say that it is a white log. Further,
A and C cannot be true of the same thing, and B and D can.
15. Privative terms are in the same relation to affirmative
terms, e.g. equal (A), not equal (B), unequal (C), not unequal (D).
18. In the case of a number of things some of which have an
attribute while others have not, the negation would be true as in
the case above; we can say 'not all things are white' or 'not
everything is white' ; but we cannot say 'everything is not-white'
or 'all things are not-white'. Similarly the negation of 'every
animal is white’ is not ‘every animal is not-white', but ‘not every
animal is white'.
24. Since 'is not-white' and 'is not white' are different, the one
an affirmation, the other a negation, the mode of proving each is
different. The mode of proving that everything of a certain kind
is white and that of proving that it is not-white are the same, viz.
by an affirmative mood of the first figure. That every man is
musical, or that every man is unmusical, is to be proved by
assuming that every animal is musical, or is unmusical. That no
man is musical is to be proved by any one of three negative moods.
39. When A and B are so related that they cannot belong to
the same subject and one or other must belong to every subject,
and Γ᾽ and 4 are similarly related, and F implies A and not vice
versa, (1) B will imply 4, and (2) not vice versa; (3) A and A are
compatible, and (4) B and F are not.
b4. For (1) since of everything either I or 4 is true, and of that
of which B is true, I' must be untrue (since I implies A), 4 must
be true of it.
8. (3) Since A does not imply I, and of everything either I or
4 is true, A and 4 may be true of the same thing.
10. (4) B and I cannot be true of the same thing, since I"
implies A.
12. (2) 4 does not imply B, since 4 and A can be true of the
same thing.
x4. Even in such an arrangement of terms we may be deceived
through not taking the opposites rightly. Suppose the conditions
stated in *39—^2 fulfilled. Then it may seem to follow that 4
implies B, which is false. For let Z be taken to be the negation
I. 46 421
of A and B, and @ that of F and 4. Then of everything either
A or Z is true, and also either lor 8. And ex hyfothes: Γ implies
A. Therefore Z implies ©. Again, since of everything either Z
or B, and either Θ or 4, is true, and Z implies ©, 4 will imply B.
Thus if P implies A, 4 implies B. But this is false; for the
implication was the other way about.
29. The reason of the error is that it is not true that of every-
thing either A or Z is true (or that either Z or B is true of it) ; for
Z is not the negation of A. The negation of good is not ‘neither
good nor not-good' but ‘not good’. So too with land 4; we have
erroneously taken each term to have two contradictories.
The programme stated in 32. 4742-5, εἰ... τοὺς γεγενημένους
(sc. συλλογισμοὺς) ἀναλύοιμεν εἰς τὰ προειρημένα σχήματα, τέλος ἂν ἔχοι
ἡ ἐξ ἀρχῆς πρόθεσις, has, as A. says in 5153-5, been fulfilled in chs.
32-45. Ch. 46 is an appendix without any close connexion with
what precedes. But, as Maier observes (2 a. 324 n. 1), this need not
make us suspect its genuineness, for we have already had in
chs. 32-45 a series of loosely connected notes. Maier thinks
(2 b. 364 n.) that the chapter forms the transition from Am. Pr. 1
to the De Interpretatione. He holds that the recognition of the
axioms of contradiction and excluded middle (51520-2, 32-3) pre-
supposes the discussion of them in the Metaphysics (though in
a more general way they are already recognized in An. Pr. 1 and 2,
Cat., and Top.)—reflection on the axioms having cleared up for
A. the meaning and place of negation in judgement, and ch. 46
being the fruit of this insight. At the same time he considers the
chapter to be earlier than the De Interpretatione, on the grounds
that once A. had undertaken (in the De Interpretatione) a separate
work on the theory of the judgement, it would have been in-
appropriate to introduce one part of the theory into the discussion
of the theory of syllogism, and that the discussion in De Int. 10
presupposes that in the present chapter.
These views cannot be said to be very convincing. It seems to
me that A. might at any time in his career have formulated the
axioms of contradiction and excluded middle as he does here,
since they had already been recognized by Plato; and though
De Int. 1931 has a reference (which may well have been added
by an editor) to the present chapter, the De Interpretatione as
a whole seems to be an earlier work than the Prior Analytics,
since its theory of judgement stands in the line of development
from Sophistes 261 e ff. to the Prior Analytics (cf. T. Case in
Enc. Brit. ii. 511-12). Maier's view (A.G.P. xiii (1900), 23-72)
422 COMMENTARY
that the De Interpretatione is the latest of all A.’s works and was
left unfinished is most improbable, and may be held to have.
been superseded by Jaeger's conclusions as to the trend of A.'s
later thought.
A. first tries to prove the difference between the statement
‘A is not B' and the statement ‘A is not-B', using an argument
from analogy drawn from the assumption that ‘A is B’ is related
to ‘A is not-B' as ‘A can walk’ is related to ‘A can not-walk’,
and as ‘A knows the good’ to ‘A knows the not-good’ (51>10—13).
This in turn he supports by pointing out that the propositions
‘A knows the good’, ‘A can walk’ can equally well be expressed
with an explicit use of the copula 'is'——' A is cognizant of the
good’, ‘A is capable of walking’; and that their opposites can
equally well be expressed in the form ‘A is not cognizant of the
good’, ‘A is not capable of walking’ (613-16). He then points out
that if ‘A is not capable of walking’ meant the same as ‘A is
capable of not walking’, then, since he who is capable of not
walking is also capable of walking, it would be true to say of the
same person at the same time that he is not capable of walking
and that he is capable of it; which cannot be true. A similar
impossible result follows if we suppose ‘A does not know the good’
to mean the same as ‘A knows the not-good' (16-22). He con-
cludes that, since the relation of ‘A is B' to ‘A is not-B' was
assumed to be the same as that of ‘A knows the good’ to ‘A knows
the not-good'—sc. and therefore that of (i) ‘A is not B’ to (ii)
‘A is not-B' the same as that of (iii) ‘A does not know the good’ to
(iv) “A knows the not-good'—and since (iii) and (iv) have been seen
to mean different things, (i) and (ii) mean different things (22-5).
The argument is ingenious, but fallacious. ‘A is B' is related to
‘A is not-B’ not as ‘A can walk’ to ‘A can not-walk’, or as ‘A
knows the good’ to ‘A knows the not-good’, but as ‘A is capable
of walking’ to ‘A is not-capable of walking’, or as ‘A is cognizant
of the good’ to ‘A is not-cognizant of the good’, and thus the
argument from analogy fails.
It is not till b25 that A. comes to the real ground of distinction
between the two statements. He points out here that being
not-equal presupposes a definite nature, that of the unequal, i.e.
presupposes as its subject a quantitative thing unequal to some
other quantitative thing, while not being equal has no such pre-
supposition. In 28-32 he supports his argument by a further
analogy; he argues that (1) ‘A is not good’ is to (2) ‘A is not-
good’ as (3) ‘A is not a white log’ is to (4) ‘A is a not-white log’,
and that just as (3) can be true when (4) is not, (1) can be true
I. 46. 52815 —>13 423
when (2) is not. The analogy is not a perfect one, but A.’s main
point is right. Whatever may be said of the form ‘A is not-B’,
which is really an invention of logicians, it is the case that such
predications as ‘is unequal’, ‘is immoral’ (which is the kind of
thing A. has in mind— note his identification of μὴ ἴσον with ἄνισον
in 25-8) do imply a certain kind of underlying nature in the subject
(ὑπόκειταί τι, 526), while ‘is not equal’, ‘is not moral’ do not.
§2°15-17. Ὁμοίως δ᾽... A. A. means that what he has said
in 51636-52414 of the relations of the expressions 'X is white’,
‘X is not white’, ‘X is not-white’, 'X is not not-white’ can equally
be said if we substitute a privative term like ‘unequal’ for an
expression like ‘not-white’. οὐκ ἴσον, οὐκ ἄνισον here stand not
for ἔστιν οὐκ ἴσον, ἔστιν οὐκ ἄνισον, but for οὐκ ἔστιν ἴσον, οὐκ
ἔστιν ἄνισον.
18-24. Καὶ ἐπὶ πολλῶν δέ... λευκόν. A. now passes from the
singular propositions he has dealt with in 51>s—s52*17 to proposi-
tions about a class some members of which have and others have
not a certain attribute, and says (a) that the fact that ‘not all
so-and-so's are white’ may be true when ‘all so-and-so's are not-
white’ is untrue is analogous (ὁμοίως, 519) to the fact that ‘X is
not a white log’ may be true when ‘X is a not-white log’ is
untrue (24-5); and (b) that the fact that the contradictory of
‘every animal is white’ is not ‘every animal is not-white’ but ‘not
every animal is white’ is analogous (ὁμοίως, 422) to the fact that
the contradictory of ‘X is white’ is not ‘X is not-white’ but
'X is not white’ (5158-10).
29-30. ἀλλὰ τὸ μέν... τρόπος. τοῦ μέν (which n reads) would
be easier, but Waitz points out that A. often has ἃ similar
anacolouthon ; instances in An. Pr. may be seen in 4713, 5o%11 n.,
bs. ‘With regard to its being true to say . . . the same method of
proof applies.'
34-5. εἰ 55] . . . μὴ μουσικὸν εἶναι. It is necessary to read
ἔσται, not ἔστιν. ‘If it is to be true’, i.e. if we are trying to prove
it to be true, Al's words (412. 33) εἰ βουλόμεθα δεῖξαι ὅτι más
ἄνθρωπος κτλ. point to the reading ἔσται.
38. κατὰ τοὺς εἰρημένους τρόπους τρεῖς, i.e. Celarent (25>40-
2652), Cesare (27*5—9), Camestres (ib. 9-14).
39-513. ᾿Απλῶς δ᾽. . . ὑπάρχειν. In 51536-52814 A. has
pointed out that (A) 'X is good’. (B) 'X is not good’, (C) 'X is
not-good', (D) 'X is not not-good' are so related that (1) of any
X, either A or B is true, (2) of no X can both A and B be true,
(3) of any X, either C or D is true, (4) of no X are both C and
D true, (5) C entails B, (6) B does not entail C, (7) A entails D,
424 COMMENTARY
(8) D does not entail A, (9) of no X are both A and C true, (10)
of some X's both B and D are true. He here generalizes with
regard to any four propositions A, B, C, D so related that condi-
tions (1) to (4) are fulfilled, i.e. such that A and B are contra-
dictory and C and D are contradictory. But he adds two further
conditions—not, as above, that C entails B and is not entailed
by it, but that C entails A and is not entailed by it. Given these six
conditions, he deduces four consequences: (1) B implies D (2,
proved 54-8), (2) D does not imply B (2-3, proved ^12-13), (3) A
and D are compatible (55, proved 58-10), (4) B and C are not
compatible (b4, proved >1o-12). The proof of (2) is left to the
end because (3) is used in proving it.
b8. πάλιν ἐπεὶ τῷ A τὸ Γ οὐκ ἀντιστρέφει. τὸ A τῷ I" has
better MS. authority, but (as Waitz points out) it is A.’s usage,
when the original sentence is τῷ Γ τὸ A ὑπάρχει, to make τὸ Γ
the subject of ἀντιστρέφει. Cf. 31232, 51*4, 67530-9, 68922, b26.
P. (382. 17) had τῷ Α τὸ T.
14-34. Συμβαίνει δ᾽... εἰσίν. A. here points out that if we
make a certain error in our choice of terms as contradictories,
it may seem to follow from the data assumed in ?39-5z (viz. (1)
that A and B are contradictories, (2) that Γ᾿ and 4 are contra-
dictories, (3) that I’ entails A) that 4 entails B, which we saw
in br2—13 to be untrue.
The error which leads to this is that of assuming that, if we
put Z — ‘neither A nor B', and suppose it to be the contra-
dictory both of A and of B, and put © = ‘neither I' nor 4’, and
suppose it to be the contradictory both of I" and of 4, we shall go
on to reason as follows: Everything is either A or Z, Everything
is either I or ©, All is A, Therefore (1) all Zis 9. Everything is
either Z or B, Everything is either @ or 4, All Ζ is © ((1) above),
Therefore (2) all 4 is B. The cause of the error, A. points out in
529—353, is the assumption that A and Z (= ‘neither A nor B’),
and again B and Z, are contradictories. The contradictory of
‘good’ is not ‘neither good nor not-good’, but ‘not good’. And the
same error has been made about Γ᾿ and 4. For each of the four
original terms we have assumed two contradictories (for A, B
and Z; for B, A and Z; for I, 4 and 6; for 4, Γ and 8);
but one term has only one contradictory.
27. τοῦτο yàp ἴσμεν, since we proved in h4-8 that if one member
of one pair of contradictories entails one member of another pair,
the other member of the second pair entails the other member of
the first.
28-9. ἀνάπαλιν yap... ἀκολούθησις, cf. 4-8.
I. 46. 5258 — II. 1. 5353 425
BOOK II
CHAPTER 1
More than one conclusion can somelimes be drawn from the same
premisses
52538. We have now discussed (1) the number of the figures,
the nature and variety of the premisses, and the conditions of
inference, (2) the points to be looked to in destructive and con-
structive proof, and how to investigate the problem in each kind
of inquiry, (3) how to get the proper starting-points.
5352. Universal syllogisms and particular affirmative syllogisms
yield more than one conclusion, since the main conclusion is
convertible; particular negative syllogisms prove only the main
conclusion, since this is not convertible.
15. The facts about (1) universal syllogisms may be also stated
in this way: in the first figure the major term must be true of
everything that falls under the middle or the minor term.
25. In the second figure, what follows from the syllogism (in
Cesare) is only that the major term is untrue of everything that
falls under the minor; it is also untrue of everything that falls
under the middle term, but this is not established by the syllogism.
34. (2) In particular syllogisms in the first figure the major is
not necessarily true of everything that falls under the minor. It
is necessarily true of everything that falls under the middle term,
but this is not established by the syllogism.
40. So too in the other figures. The major term is not neces-
sarily true of everything that falls under the minor; it is true of
everything that falls under the middle term, but this is not estab-
lished by the syllogism, just as it was not in the case of universal
syllogisms.
52538-9. Ἐν πόσοις . . . συλλογισμός, cf. I. 4-26.
40-5372. ἔτι δ᾽... μέθοδον, cf. I. 27-31.
5372-3. ἔτι δὲ... ἀρχάς, cf. I. 32-46.
3-53. ἐπεὶ δ᾽... τούτων. In this passage A. considers the prob-
lem, what conclusions, besides the primary conclusion, a syllo-
gism can be held to prove implicitly. He first (A) (*3-14) considers
conclusions that follow by conversion of the primary conclusion.
Such conclusions follow from A, E, or I conclusions, but not from
an O conclusion, since this alone is not convertible either simply
or per accidens. (B) He considers secondly (215-53) conclusions
426 COMMENTARY
derivable from the original syllogism, with regard to terms which
can be subsumed either under the middle or under the minor term
(the latter expressed by ὑπὸ τὸ συμπέρασμα, *17). A. considers first
(1) syllogisms in which the conclusion is universal, (a) in the first
figure. If we have the syllogism All C is A, All B is C, Therefore
all B is A, then if all D is B, it is implicitly proved that all D is
A (321-2). And if all E is C, it follows that all E is A (222-4).
Similar reasoning applies to an original syllogism of the form
NoC is A, All B isC, Therefore no B is A (#24). (b) In the second
figure. If we have the syllogism No B is A, All C is A, Therefore
no C is B, then if all D is C, it is implicitly proved that no D is
B (325-8). If all E is A, it follows that no E is B, but this does not
follow from the original syllogism. That syllogism proved that no
C (and therefore implicitly that no D) is B; but it assumed (that
no B is A, or in other words) that no A is B, and it is from this+
All E is A that it follows that no E is B (329-34).
A. next considers (2) syllogisms in which the conclusion is
particular, and as before he takes first (a) syllogisms in the first
figure. While in 519-24 B was the minor and C the middle term,
he here takes B as middle term and C as minor. Here a term sub-
sumable under C cannot be inferred to be A, or not to be A (un-
distributed middle). A term subsumable under B can be inferred
to be (or not to be) A, but not as a result of the original syllogism
(but as a result of the original major premiss All B is A (or No B
is A)-+the new premiss All D is B) (*34-40).
The commentators make A.'s criticism in *29-34 turn on the
fact that the major premiss of Cesare (No B is A) needs to be
converted, in order to yield by the dictum de omni et nullo the
conclusion that no E is B. But this consideration does not apply
to the syllogisms dealt with in *34-40. Take a syllogism in Darii—
All B is A, Some C is B, Therefore some C is A. Then if all D is
B, it follows from the original major premiss+All D is B,
without any conversion, that all D is A. And there was no
explicit reference in the case of Cesare (529-34) to the necessity of
conversion. I conclude that A.'s point was not that, but that the
conclusion No E is B followed not from the original syllogism, but
from its major premiss.
Finally (5), A. says (440-83) that in the case of syllogisms with
particular conclusions in the second or third figure, subsumption
of a new term under the minor term yields no conclusion (un-
distributed middle), but subsumption under the middle term
yields a conclusion—one, however, that does not follow from the
original syllogism (but from its major premiss), as in the case of
II. 1. 53*7-12 427
syllogisms with a universal conclusion, so that we should either
not reckon such secondary conclusions as following from the
universal syllogisms, or reckon them (loosely) as following from
the particular syllogisms as well (ὥστ᾽ ἢ οὐδ᾽ ἐκεῖ ἔσται ἣ καὶ ἐπὶ
τούτων). I take the point of these last words to be that A. has now
realized that he was speaking loosely in treating (in *21-4) the
conclusions reached by subsumption under the middle term of a
syllogism in Barbara or Celarent as secondary conclusions from
that syllogism ; they, like other conclusions by subsumption under
the middle term, are conclusions not from the original syllogism,
but from its major premiss, i.e. by parity of reasoning.
A. omits to point out that from Camestres, Baroco, Disamis,
and Bocardo, by subsumption of a new term under the middle
term, no conclusion relating the new term to the major term can
be drawn.
7. ἡ δὲ στερητική, i.e. the particular negative.
8-9. τὸ δὲ συμπέρασμα... ἐστιν. This should not be tacked
on to the previous sentence. It is a general statement designed to
support the thesis that certain combinations of premisses estab-
lish more than one conclusion (*4-6), viz. the statement that a
single conclusion is the statement of one predicate about one
subject, so that e.g., the conclusion Some A is B, reached by
conversion from the original conclusion All Bis A or Some Bis A,
is different from the original conclusion (#10-12).
9-12. ὥσϑ᾽ oi μὲν ἄλλοι συλλογισμοὶ . . . ἔμπροσθεν. In
pointing out that the conclusion of a syllogism in Barbara,
Celarent, or Darii may be converted, A. is in fact recognizing the
validity of syllogisms in Bramantip, Camenes, and Dimaris. But
he never treats these as independent moods of syllogism ; they are
for him just syllogisms followed by conversion of the conclusion.
(In pointing out that conclusions in A, E, or I are convertible,
he does not limit his statement to conclusions in the first figure;
he is in fact recognizing that the conclusions of Cesare, Camestres,
Darapti, Disamis, and Datisi may be converted. But here con-
version gives no new result. Take for instance Cesare—No P is
M, AlLS is M, Therefore no S is P. The conclusion No P is S can
be got, without conversion, by altering the order of the premisses
and getting a syllogism in Camestres.)
In 29*19-29 A. pointed out that if we have the premisses (a) No
C is B, All B is A, or (b) No C is B, Some B is A, we can, by
converting the premisses, get No B is C, Some A is B, Therefore
some 4 is not C. Le., he recognizes the validity of Fesapo and
Fresison.
428 COMMENTARY
Thus A. recognizes the validity of all the moods of the fourth
figure, but treats them as an appendix to his account of the first
figure.
CHAPTER 2
True conclusions from false premisses, in the first figure
53°4. The premisses may be both true, both false, or one true
and one false. True premisses cannot give a false conclusion;
false premisses may give a true conclusion, but only of the fact,
not of the reason.
11. True premisses cannot give a false conclusion. For if B is
necessarily the case if A is, then if B is not the case A is not. If,
then, A is true, B must be true, or else A would be both true and
false.
16. If we represent the datum by the single symbol A, it must
not be thought that anything follows from a single fact; there
must be three terms, and two stretches or premisses. A stands for
two premisses taken together.
26. (A) Both premisses universal
We may get a true conclusion (a) when both premisses are
false, (b) when the minor is wholly false, (c) when either is partly
false.
Combinations of fact Inference
30. (a) No Bis A. All B is A. Wholly false.
No C is B. AllC is B. p
All C is A. ..AllCis A. True.
35- All B is A. No B is A. Wholly false.
NoC is B. AIL C is B. τ
No C is A. *. NoC is A. True.
541. Some B is not A. All B is A. Partly false.
Some C is not B. All C is B. »
All C is A. Ὁ AllC is A. True.
Some B is A. No B is A. Partly false.
Some C is not B. AIC is B. 5
No Cis A. -. NoC is A. True.
2. A wholly false major and a true minor will not give a true
conclusion :
6. No B is A. All B is A. Wholly false. Im-
All C is B. ) Impossible. AllCis B. True. ,
AILC is A. | ΝΑΙ ΟῚ A. ,, | Postes
II. All B is A. No B is A. Wholly false. MM
AIL C is B. ) Impossible. AllC is B. True ,
No C is A. | "NoCisA. , | Possible:
II. 1. 5329-12
429
18. (c) (2) A partly false major and a true minor can give a
true conclusion:
Combinations of fact
Some B is A.
All C is B.
AIC is A.
Some B is A.
All C is B.
NoC is A.
23.
Inference
All B is A.
AllC is B.
Ὁ All C is A.
No B is A.
Al C is B.
*. NoC is A.
Partly false.
True.
»
Partly false.
True.
”
28. (b) A true major and a wholly false minor can give a true
conclusion.
Al B is A.
No C is B.
All C is A.
No B is A.
NoC is B.
No C is A.
35-
All Bis A.
AllC is B.
.. All C is A.
No B is A.
AMC is B.
“Ὁ NoC is A.
bz. (c) (B) A true major and a partly
à true conclusion.
All B is A.
Some C is B.
AIL C is A.
No B is A.
Some C is B.
No C is A.
All B is A.
All C is B.
ον All C is A.
No B is A.
All C is B.
.. NoC is A.
True.
Wholly false.
True.
True.
Wholly false.
True.
false minor can give
True.
Partly false.
True.
True.
Partly false.
True.
(B) One premiss particular
17. (a) A wholly false major and a true minor, (b) a partly false
major and a true minor, (c) a true major and a false minor, (d)
two false premisses, can give a true conclusion:
21. (a) No B is A.
Some C is B.
Some C is A.
All B is A.
Some C is B.
Some C is not A.
Some B is A.
Some C is B.
Some C is A.
Some B is A.
Some C is B.
Some C is not A.
All B is A.
NoC is B.
Some C is A.
All B is A.
Wholly false.
Some C is B. True.
..SomeCis A. ,,
No B is A.
Wholly false.
Some C is B. True.
*. Some C is not A. True.
All B is A.
Partly false.
Some C is B. True.
"^. SomeC is A. ,,
'" No Bis A.
Partly false.
Some C is B. True.
*. Some C is not A. True.
All B is A.
True.
Some C is B. False.
*, Some C is A. True,
430 COMMENTARY
Combinations of fact Inference
IO. No B is A. No B is A. True.
NoC is B. Some C is B. False.
Some C is not 4. .. Some C is not A. True.
I9. (d) Some B is A. All B is A. Partly false.
NoC is B. Some C is B. False.
Some C is A. .. Some C is A. True.
26. Some Bis A. No Bis A. Partly false.
No G is B. Some C is B. False.
Some C is not 4. .. Some C is not A. True.
28. No B is A. All B is A. Wholly false.
NoC is B. Some C is B. False.
Some C is A. .. Some C is A. True.
36. All Bis A. No Bis A. Wholly false.
NoC is B. Some C is B. False.
Some C is not A. .. Some C is not A. True.
53^ro. δι᾽ fjv δ᾽ αἰτίαν... λεχθήσεται, Le. in 57840-'17.
23-4. τὸ oóv A... συλληφθεῖσαι, i.e. the A mentioned in >r2-
14 (the whole datum from which inference proceeds), not the 4
mentioned in >21-2 (the major term).
27. ταύτης δ᾽ οὐχ ὁποτέρας ἔτυχεν. ὁποτέρας (for ómorépa) is
rather an extraordinary example of attraction, but has parallels
in A., e.g. An. Post. 7941, 80414, 8139.
28-30. ἐάνπερ ὅλην... ὁποτερασοῦν. All B is A is ‘wholly
false’ when no B is A, and No B is A ‘wholly false’ when all B is
A (54*4-6). Al B is A and No B is A are ‘partly false’ when
some B is A and some is not. Cf. 5645-55 n.
54*7-15. ἂν 55... Tl. The phrases ἡ τὸ AB, ἡ τὸ BI in *8, 12
are abbreviations of ἡ πρότασις ἐφ᾽ fj κεῖται τὸ AB (τὸ BI). Similar
instances are to be found in An. Post. 94231, Phys. 2158, 9, etc.
8-9. kai wavri...A, ‘ie. that all B is A’.
11-14. ὁμοίως δ᾽... ἔσται. A. begins the sentence meaning to
say ‘similarly if A belongs to all B, etc., the conclusion cannot be
true' (cf. *9), but by inadvertence says 'the conclusion will be
false’, which makes the οὐδ᾽ in *11 incorrect ; but the anacoluthon
is a very natural one.
13. kai μηδενὶ 6 τὸ B, τὸ A, ‘ie. that no B is A’.
31-2. olov ὅσα... ἄλληλα, e.g. when B and C are species of
A, neither included in the other.
38. olov rois ἐξ ἄλλου γένους . . . γένος, ‘e.g. when A is a
genus, and B and C are species of a different genus'.
55-6. olov τὸ γένος... διαφοῤᾷ, ‘e.g. when A is a genus, B a
species within it, and C a differentia of it' (confined to the genus
but not to the species).
II. 2. 53°10 — 55915 431
11-12. οἷον τὸ γένος . . . διαφορᾷ, ‘e.g. when A is a genus, B
a species of a different genus, and C a differentia of the second
genus’ (confined to that genus but not to the species).
55*13-14. οἷον τὸ γένος . . . εἴδεσι, ‘e.g. when A is a genus, B
a species of another genus, and C an accident of the various species
of A’ (not confined to A, and never predicable of B).
15. λευκῷ δὲ τινί, In order to correspond with #12 τῷ δὲ Γ τινὶ
μὴ ὑπάρχειν and with 517 τὸ A τινὶ τῷ Γ οὐχ ὑπάρξει, this should
read λευκῷ δὲ τινὶ οὔ, and this should perhaps be read; but it has
no MS. support, and in 56414, an exactly similar passage, λευκῷ δὲ
τινὶ οὔ has very little. It is probable that A. wrote λευκῷ δὲ τινί,
since he usually understands a proposition of the form Some S is
P as meaning Some 5 is P and some is not.
CHAPTER 3
True conclusions from false bremisses, in the second figure
55°3. False premisses can yield true conclusions: (a) when both
are wholly false, (b) when both are partly false, (c) when one is
true and one false.
10. (A) Both premisses universal
Combination of facts Inference
(a) No B is A. All B is 4. Wholly false.
AIL C is A. No C is A. ἊΣ
Νο ( is B. ες NoCis B. True.
14. All Bis A. No Bis A. Wholly false.
No Cis A. All C is A. »
No Cis B. -. NoCis B. True.
16.(c) All Bis A. All Bis A. True.
All C is A. No C is A. Wholly false.
No C is B. -. NoC is B. True.
All B is A. No B is A, Wholly false.
AIL C is A. AllCis A. True.
NoC is B. & NoCisB. ,,
23. Some Bis A. No B is A. Partly false.
AIL C is A. AllC is A. True.
No C is B. A NoCisB. ,,
30. All Bis A. All Bis A. True.
Some C is A. NoC is A. Partly false.
No C is B. “. NoC is B. True.
31. Some B is A. All B is A. Partly false.
NoC is A. NoC is A. True. |
No C is B. “Ὁ NoC is B.
»
(c) All Bis A.
Some C is A.
Some C is not B.
II. No B is A.
Some C is not A.
Some C is not B.
18. No B is A.
NoC is A.
Some C is not B.
25. Al Bis A.
AILC is A.
Some C is not B.
32. (a) All B is A.
.. Some C is not B.
No B is A. True.
432 COMMENTARY
Combinations of facts Inference
38. (b) Some B is A. All B is A. Partly false.
Some C is A. NoCisA. ,,
No C is B. " NoCis B. True.
56*3. Some Bis A. No B is A. Partly false.
Some C is A. AllCisA. ,,
NoC is B. *. NoC is B. True.
5. (B) One premiss particular
No B is A. Wholly false.
Some C is A. True.
*. Some C is not B. True.
All B is A. Wholly false.
Some C is not A. True.
»
Some C is A. False.
*. Some C is not B. True.
All B is A. True.
Some C is not A. False.
*. Some C is not B. True.
No B is A. Wholly false.
All C is A. Some C is A (sc. and some not.) False.
Some C is not B. *. Some C is not B. True.
37: No Bis A, All Bis A. Wholly false.
All C is A. Some C is not A. False.
Some C is not B. ες Some C is not B. True.
5553-10. 'Ev δὲ rà μέσῳ σχήματι... συλλογισμῶν. The vul-
gate text of this sentence purports to name six possibilities. But
of these the sixth (εἰ ἡ μὲν ὅλη ψευδὴς ἡ δ᾽ ἐπί τι ἀληθής) is not
mentioned in the detailed treatment which follows, nor anywhere
in chs. 2-4 except in 2. 5519-28. It is to be noted too that the
phrase emi rt ἀληθής does not occur anywhere else in these chapters,
and that the distinction between a premiss which is ἐπί re ψευδής
and one which is ἐπί τι ἀληθής is a distinction without a difference,
since each must mean an A or E proposition asserted when the
corresponding I or O proposition would be true. Waitz is justified,
therefore, in excising the two clauses he excises. But the whole
structure of the latter part of the sentence, xai εἰ ἀμφότεραι...
ἀληθής ^7—9 is open to suspicion. In all the corresponding sentences
in chs. 2-4 (5326-30, 5q4>17-z1, 5654-9) all the alternatives are
expressed by participial clauses. Further, the phrase ἁπλῶς
ἀληθής ^7 does not occur elsewhere in chs. 2-4. Thus the words
IL. 3. 5553— 56°35 433
from xai εἰ ἀμφότεραί to ἐπί τι ἀληθής betray themselves as a gloss,
meant to fill supposed gaps in the enumeration in 54-7.
If we retain ὅλης in 56, the words ἀμφοτέρων... λαμβανομένων
cover the cases mentioned in >10-16, the words ἐπί τι ἑκατέρας
(‘each partly false’) those in 538-5634, and the words τῆς μὲν
aAnBots . . . τιθεμένης those in 616-23 and in 5645-18, but those in
5523-38 and in 56%18-32 are not covered. By excising ὅλης we
get an enumeration which covers all the cases mentioned down
to 56232. ὅλης must be a gloss, probably traceable to the same
scribe who had inserted it in 54520.
The enumeration still leaves out (as do the εἰ clauses) the cases
mentioned in 56232-55, in which the minor premiss, being parti-
cular, is simply ‘false’ and escapes the disjunction ‘wholly or
partly false’, which is applicable only to universal propositions.
The chapter is made easier to follow if we remember that in this
figure A always stands for the middle, B for the major, I' for the
minor term.
18-19. olov τὸ γένος . . . εἴδεσιν, cf. 54°61-2 n.
20. ἐὰν οὖν ληφθῇ, sc. τὸ ζῷον.
56*14. λευκῷ δὲ τινί. Strict logic would require λευκῷ δὲ τινὶ οὔ,
to correspond to τῷ δὲ Γ revi μὴ ὑπάρχειν, "13. But A. often uses
Some S is P as standing for Some S is P and some is not. Cf.
55°15 n.
27-8. olov τὸ γένος . . . διαφορᾷ, i.e. when B is a species of A,
and C a differentia of A (confined to A but not to B).
35. τῷ δὲ Γ τινὶ ὑπάρχειν. Here, as in 215, τινὲ ὑπάρχειν stands
for τινὲ μὲν ὑπάρχειν τινὶ δ᾽ ov, which is untrue because it contra-
dicts τὸ 4... τῷ Γ ὅλῳ ὑπάρχειν, 833-4.
CHAPTER 4
True conclusions from false premisses, in the third figure
5654. False premisses can give a true conclusion: (2) when both
premisses are wholly false, (6) when both are partly false, (c) when
one is true and one wholly false, (4) when one is partly false and
one true.
9. (A) Both premisses universal
Combination of facts Inference
(a) NoCis A. All C is A. Wholly false.
NoC is B. ANC is B. 53
Some B is A. ἐς Some B is A. True.
4985 Ff
434 COMMENTARY
Combination of facts Inference
14. AIC is A. No C is A. Wholly false.
NoC is B. AIL C is B. 15
Some B is not A. *. Some B is not A. True.
20. (b) Some C is A. AllC is A. Partly false.
Some C is B. All C is B. +
Some B is A. *. Some Bis A. True.
26. | SomeC is not A. NoC is A. Partly false.
Some C is B. All C is B. »
Some B is not A. *. Some B is not A. True.
33. (O All Cis A. NoC is A. Wholly false.
All C is B. AllC is B. True.
Some B is not A. .. Some B is not A, True.
40. | NoCis A. NoCis A. True.
No Cis B. AllC is B. Wholly false.
Some B is not A. *. Some B is not A. True.
571. NoC is A. Ali C is A. Wholly false.
AIL C is B. AlCis B. True.
Some B is A. *. Some B is A. True.
8. AII C is A. AllC is A. True.
No C is B. AllC is B. Wholly false.
Some B is A. *. Some B is A. True.
9. (d) Some C is A. AllC is A. Partly false.
All C is B. AllCis B. True.
Some B is A. *. Some B is A. True.
15. ΑΙ C is A. AllC is A. True.
Some C is B. AllC is B. Partly false.
Some B is A. *. Some B is A. True.
18. SomeCis 4. NoC is A. Partly false.
All C is B. AllC is B. True.
Sore B is not A. *. Some B is not A. True.
23. NoCis A. NoC is A. True.
Some C is B. AllC is B. Partly false.
Some B is not A.
*. Some B is not A. True.
(B) Both premisses particular
29. Here too the same combinations of two false premisses, or
of a true and a false premiss, can yield a true conclusion.
36. Thus if the conclusion is false, one or both premisses must
be false; but if the conclusion is true, neither both premisses nor
even one need be true. Even if neither is true the conclusion may
be true, but its truth is not necessitated by the premisses.
40. The reason is that when two things are so related that if
one exists the other must, if the second does not exist neither will
the first, but if the second exists the first need not ; while on the
other hand the existence of one thing cannot be necessitated both
II. 4. 5657 — 57325 435
by the existence and by the non-existence of another, e.g. B's
being large both by A's being and by its not being white.
*6, For when if A is white B must be large, and if B is large C
cannot be white, then if .4 is white C cannot be white. Now when
one thing entails another, the non-existence of the second entails
the non-existence of the first, so that B's not being large would
necessitate A's not being white; and if A's not being white
necessitated B's being large, B's not being large would necessitate
B's being large; which is impossible.
The reasoning in this chapter will be more easily followed if we
remember that in this figure A stands for the major, B for the
minor, J‘ for the middle term.
5657-8. καὶ ἀνάπαλιν... προτάσεις. ἀνάπαλιν is meant to dis-
tinguish the case in which the major premiss is wholly false and
the minor true from that in which the major is true and the minor
wholly false (P6), and that in which the major is true and the
minor partly false from that in which the major is partly false and
the minor true (P7). xai ὁσαχῶς ἄλλως ἐγχωρεῖ μεταλαβεῖν τὰς
προτάσεις is probably meant to cover the distinction between the
case in which both premisses are affirmative and that in which one
is negative, and between that in which both are universal and that
in which one is particular.
40-5771. ὁμοίως 56 . . . ἄψυχον. The argument in 533-40 was:
* * AL C is A, AILC is B, Some B is not A"' may all be true; for in
fact all swans are animals, all swans are white, and some white
things are not animals. But if we assume falsely that no C is A and
truly that all C is B, we get the true conclusion Some B is not A.’
A. now says that the same terms will suffice to show that a true
conclusion can be got from a true major and a false minor pre-
miss. Waitz is no doubt right in bracketing as corrupt μέλαν-
κύκνος -ἄψυχον, which are not in fact of αὐτοὶ ὅροι as those used just
before (or anywhere else in the chapter). But even without these
words all is not well; for if we take a true major and a false minor,
and say All swans are animals, No swans are white, we can prove
nothing, since the minor premiss in the third figure must be
affirmative. A. probably had in mind the argument No swans are
lifeless, All swans are black, Therefore some black things are not
lifeless—where, if not the terms, at least the order of ideas is much
the same as in h33-4o. But this does not justify the words uéAav-
κύκνος -ἅψυχον ; for A. would have said ἀψυχον-μέλαν-κύκνος.
57*23-5. πάλιν ἐπεὶ... ὑπάρχειν. A. evidently supposes him-
self to have proved by an example that No C is A, Some C is B,
436 COMMENTARY
Some B is not A are compatible, but has not in fact done so. He
may be thinking of the proof, by an example, that Some C is not
A, Some C is B, Some B is not A are compatible (5627-30). The
reference cannot be, as Waitz supposes, to 5441-2.
33-5. οὐδὲν yàp . . . ἔκθεσιν, i.e. whether in fact no S is P or
only some S is P, in either case the same proposition All S is P
will serve as an instance of a false premiss, which yet with another
premiss may yield a true conclusion. The point is sound, but is
irrelevant to what A. has just been saying in 229-33. He has been
pointing out that the same instance will serve to show the possi-
bility of true inference from false premisses when the premisses
differ in quantity as when both are universal. What he should be
pointing out now, therefore, is not that the difference in the state
of the facts between pndevi ὑπάρχοντος and τινὶ ὑπάρχοντος does not
affect the validity of the example, but that the difference between
the false assumption παντὶ ὑπάρχειν and the false assumption τινὶ
ὑπάρχειν does not affect the validity of the example. If the fact is
that οὐδενὶ ὑπάρχει, both the assumption παντὲ ὑπάρχειν and the
assumption τινὶ ὑπάρχειν may serve to illustrate the possibility of
reaching a true conclusion from false premisses.
36-517. Φανερὸν οὖν... τριῶν. This section does not refer,
like the rest of the chapter, specially to the third figure. It dis-
cusses the general question of the possibility of reaching true
conclusions from false premisses. The main thesis is that in such
a case the conclusion does not follow of necessity (*4o). This is of
course an ambiguous statement. It might mean that the truth of
the conclusion does not follow by syllogistic necessity ; but if A.
meant this he would be completely contradicting himself. What
he means is that in such a case the premisses cannot state the
ground on which the fact stated in the conclusion really rests,
since the same fact cannot be a necessary consequence both of
another fact and of the opposite of that other (53-4).
40—^17. αἴτιον δ᾽... τριῶν. A. has said in 526-40 (1) that
false premisses can logically entail a true conclusion, and (2) that
the state of affairs asserted in such premisses cannot in fact
necessitate the state of affairs asserted in the conclusion. He first
(*40->3) justifies the first point, and then justifies the second, in
the following way. An identical fact cannot be necessitated both
by a certain other fact and by the opposite of it (53-6). For if
A's being white necessitates B's being large, and B's being large
necessitates C's not being white, A's being white necessitates C's
not being white (66-9). Now if one fact necessitates another, the
opposite of the latter necessitates the opposite of the former
Π. 457833 027 437
(9-11). Let it be the case that A’s being white necessitates B's
being large. Then B’s not being large will necessitate A’s not being
white. Now if we suppose that A’s not being white (as well as A’s
being white) necessitates B’s being large, we shall have a situation
like that described in 56-9. B's not being large will necessitate A's
not being white; A’s not being white will necessitate B’s being
large; therefore B’s not being large will necessitate B’s being
large. But this is absurd; therefore we must have been wrong in
supposing that A’s not being white, as well as its being white,
necessitates B’s being large. The point is the same as was made
briefly in 53>7-ro, that while false premisses may necessitate a
true conclusion, they cannot state the reason for it, i.e. the facts
on which its truth rests.
bro. τὸ πρῶτον. The subject of μὴ εἶναι must be the state of
affairs asserted in the first proposition (θατέρου of P9) ; but through-
out 66-17 A, B, Γ stand not for propositions but for subject-
terms. I have therefore read τὸ πρῶτον. For the substitution of à
for πρῶτον in MSS. cf. Met. 1047522, and many instances in the MSS.
17. ὡς διὰ τριῶν. In 56-9 A. pointed out that ' A's being white
necessitates B's being large' and 'B's being large necessitates C's
not being white' give the conclusion ' A's being white necessitates
C's not being white’. In 59-17 he has used only two subject-terms,
A and B, not three, and has pointed out that similarly ‘B’s not
being large necessitates A’s not being white’ and ' A's not being
white necessitates B's being large' yield the conclusion 'B's not
being large necessitates B's being large'. Maier (2a. 261 n.) thinks
that ὡς διὰ τριῶν is spurious, because the word to be supplied,
according to A.’s terminology, must be ὅρων (cf. πᾶσα ἀπόδειξις
ἔσται διὰ τριῶν ὅρων (41°36), διὰ τριῶν (65219), τριῶν ὄντων ἕκαστον
συμπέρασμα γέγονε (58233)—the three terms of an ordinary syllo-
gism being in each case referred to), while in fact in 56-9 six terms
(he does not say what these are) are used. He considers that the
word to be supplied is probably ὑποθέσεων, and that the phrase
was used by a Peripatetic or Stoic copyist familiar with the phrase
διὰ τριῶν ὑποθετικὸς συλλογισμός (a syllogism with two hypothetical
premisses and a hypothetical conclusion)—perhaps the same
interpolator who has been at work in 45>16-17 and in 585g. He
may be right, but I see no particular difficulty in the phrase ws
διὰ τριῶν if we suppose A. to have only the subject-terms in
view, which are in fact the only terms to which he has assigned
letters. ὡς διὰ τριῶν will then mean ‘we shall have a situation like
that described in 56-9, but with the two terms A, B, instead of the
three terms A, B,C’.
438 COMMENTARY
CHAPTER 5
Reciprocal proof applied to first-figure syllogisms
57>x8. Reciprocal proof consists in proving one premiss of our
original syllogism from the conclusion and the converse of the
other premiss.
2x. If we have proved that C is A because B is A and C is B,
to prove reciprocally is to prove that B is 4 because C is 4 and B
is C, or that C is B because A is B and C is A. There is no other
method of reciprocal proof; for if we take a middle term distinct
from C and A there is no circle, and if we take as premisses both
the old premisses we shall simply get the same syllogism.
32. Where the original premisses are inconvertible one of our
new premisses will be unproved ; for it cannot be proved from the
original premisses. But if all three terms are convertible, we can
prove all the propositions from one another. Suppose we have
shown (1) that All B is A and AllC is B entail All C is A, (2) that
AIL C is A and All B is C entail All B is A, (3) that All A is B and
AllC is A entail AIL C is B. Then we have still to prove that all
B isC and that all A is B, which are the only unproved premisses
we have used. We prove (4) that all A is B by assuming that all
C is B and all A is C, and (5) that all B is C by assuming that all
Α is C and all B is A.
58:6. In both these syllogisms we have assumed one unproved
premiss, that all A is C. If we can prove this, we shall have proved
all six propositions from each other. Now if (6) we take the pre-
misses All B is C and All A is B, both the premisses have been
proved, and it follows that all 4 is C.
12. Thus it is only when the original premisses are convertible
that we can effect reciprocal proof ; in other cases we simply assume
one of our new premisses without proof. And even when the
terms are convertible we use to prove a proposition what was
previously proved from the proposition. All B is C and All A is
B are proved from All A is C, and it is proved from them.
Syllogism Reciprocal proof
2i. NoBis A. No Cis 4.
All C is B. All BisC.
J. NoC is A. Ὁ No B is A.
26. All of that, none of which is A, is B.
No Cis A,
«Ὁ All C is B.
II. 5. 5718 — 5832 439
Syllogism Reciprocal proof
36. All Bis A. The universal premiss cannot be proved reci-
Some C is B. procally, nor can anything be proved from
.. Some C is A. the other two propositions, since these are
both particular.
52, All 4 is B.
Some C is A.
.. Some C is B.
6. No Bis A. The universal premiss cannot be proved.
Some C is B.
.. Some C is not A.
Some of that, some of which is not 4, is B.
Some C is not A.
ες Some C is B.
57^18-20. Τὸ δὲ κύκλῳ... λοιπήν. The construction would
be easier if we had λαβεῖν in ?zo, or if the second τοῦ in Pr9 were
omitted; but either emendation is open to the objection that it
involves A. in identifying τὸ δείκνυσθαι (passive) with τὸ συμπε-
ράνασθαι (middle). The traditional text is possible: ‘Circular and
reciprocal proof means proof achieved by means of the original
conclusion and by converting one of the premisses simply and
inferring the other premiss.'
24. kai τὸ Α τῷ B. The sense and the parallel passage P25-7
show that these words should be omitted.
25-6. ἢ εἰ [ὅτι]... ὑπάρχον. ὅτι must be rejected as ungram-
matical.
58214-15. ἐν δὲ τοῖς ἄλλοις. . . εἴπομεν refers to 57532-5,
where A. pointed out that when the terms are not simply con-
vertible, the circular proof can be effected only by assuming
something that is unprovable, viz. the converse of one of the
original premisses. He omits to point out that even when the
terms are coextensive, the converse of an À proposition cannot be
inferred from that proposition, though its truth may be known
independently.
22. ἔστω τὸ μὲν B . . . ὑπάρχειν, ‘let it be the case that B
belongs to all C'. Waitz is justified in reading ὑπάρχειν, with all
the best MSS. Cf. *3o (where it is read by all the MSS.) and L. and
S. s.v. εἰμί, A. VI. b.
25. ἔστω must be read, not ἔσται.
26-32. εἰ δ᾽... τῷ Γ ὑπάρχειν. Of the valid moods of syllo-
gism, there are nine that have a negative premiss and a negative
conclusion, and in the case of these it is impossible to prove the
affirmative premiss in the way A. adopts in other cases, viz. from
440 COMMENTARY
the conclusion of the original syllogism and the converse of the
other premiss; for an affirmative cannot be proved from two
negatives. Of these nine moods, in three—Baroco, Felapton, and
Bocardo—it is impossible by any means to effect reciprocal proof
of the affirmative premiss; for this is universal, while one or both
of the other propositions are particular. For four of the remaining
moods A. adopts a new method of proof—for Celarent (5826-32),
Ferio (67-12), Festino (33-8), Ferison (5924-9). He says (58>13-
18) that Cesare and Camestres cannot be similarly treated, but in
fact they can. The affinity of the six proofs can be best seen if we
call the minor, middle, and major terms S, M, P in each case.
Celarent
No M is P. All of that, none of which is P, is M.
Al S is M. No S is P.
z^ No Sis P. «Ὁ All S is M.
Cesare
No P is M. All of that, none of which is P, is M.
All S is M. No S is P.
*. No Sis P. «Ὁ ANS is M.
Camestres
All P is M. All of that, none of which is S, is M.
No S is M. (No S is P, ^.) No P is 5.
t NoS is P. -. All P is M.
Ferio
No M is P. Some of that, some of which is not P, is M.
Some S is M. Some S is not P.
*. Some S is not P. ;";, Some S is M.
Festino
No P is M. Some of that, some of which is not P, is M.
Some S is M. Some S is not P.
*. Some S is not P. ες, Some S is M.
Ferison
No M is P. Some of that, some of which is not P, is M.
Some M is S. Some S is not P.
*. Some S is not P. ;. Some S is M.
*. Some M is S.
All the reciprocal proofs fall into one or other of two forms: If
no X is Y, all X is Z, No X is Y, Therefore all X is Z, or If some
X is not Y, some X is Z, Some X is not Y, Therefore some X is Z.
The ‘conversion’ of ‘No M is 7” into ‘All of that, none of which
II. 5. 5856-8 441
is P, is M’ strikes one at first sight as a very odd kind of conver-
sion. But on a closer view we see that what A. is doing is to make
a further, arbitrary, assumption, viz. that M and P, besides being
mutually exclusive, are exhaustive alternatives; i.e. that they are
contradictories. And this is no more arbitrary than the assump-
tion A. makes in the other reciprocal proofs he offers in chs. 5-7,
viz. that All B is A can be converted into All A is B. Throughout
these chapters the proofs that are offered are not offered as proofs
that can be effected on the basis of the original data alone, but
simply as a mental gymnastic.
b6-11. εἰ δὲ... πρότασιν, cf. 226-32 n.
ἡ. δι’ ὃ καὶ πρότερον ἐλέχθη, in 38-52.
7-10. τὴν δ᾽ ἐν μέρει... ὑπάρχειν. The vulgate reading, which
has little MS. support and involves a use οἱ πρόσληψις which is
foreign to A. and belongs to Theophrastus, is no doubt a later
rewriting of the original. P. (who of course was familiar with the
Theophrastean terminology) describes the curious ‘conversion’ as
πρόσληψις (418. 28), and it may be his comment that gave rise to
the insertion of the spurious words into the text. Their absence
from the original text is confirmed by the remark of an anonymous
commentator (189. 43 Brandis), ὑπογράφει οὖν ἡμῖν εἶδος ἕτερον
προτάσεων, ὅπερ ὁ Θεόφραστος καλεῖ κατὰ πρόσληψιν. A. uses
προσλαμβάνειν quite differently, of ordinary conversion (627, 28ὅς,
42°34, 59712, 22). On the later theory see Maier’s learned note,
2a. 265 n. 2.
8. ὥσπερ κἀπὶ τῶν καθόλου, cf. 226-32.
CHAPTER 6
Reciprocal proof applied to second-figure syllogisms
58513. The affirmative premiss cannot be established by a
reciprocal proof, because the propositions by which we should seek
to establish it are not both affirmative (the original conclusion
being in this figure always negative) ; the negative premiss can be
established.
Syllogism Reciprocal proof
18. All Bis A. All A is B.
NoC is A. NoC is B.
.. NoC is B. τς NoC is A.
22. No B is A. NoC is B.
All C is A. All A is C.
“ΝΟ Ὁ is B. .. No Ais B, ". No B is A.
442 COMMENTARY
27. When one premiss is particular, the universal premiss can-
not be proved reciprocally. The particular premiss can, when the
universal premiss is affirmative:
Syllogism Reciprocal proof
All B is A. All A is B.
Some C is not A. Some C is not B.
.. Some C is not B. ες Some C is not A.
33 No Bis A. Some of that, some of which is not B, is A.
Some C is A. Some C is not B.
οἷς Some C is not B. εἰς Some C is A.
58920. τῷ δὲ Γ μηδενί, omitted by AB! C! N, is no doubt a
(correct) gloss; the words can easily be supplied in thought.
There is a similar ellipse in 59*8.
27. προσληφθείσης δ᾽ ἑτέρας ἔσται, i.e. by adding the premiss
If no A is B, no B is A; cf. 59?12-13.
29. διὰ τὴν αὐτὴν αἰτίαν. The reference is to *38-2.
33-8. εἰ δ᾽... ὑπάρχειν, cf. 526-32 n.
35-6. συμβαίνει yàp .. . ἀποφατικήν, i.e. (the original syllo-
gism being No B is A, Some C is A, Therefore some C is not B),
if we take as new premisses No A is B, Some C is not B, we shall
have two negative premisses ; and even if the first of these could
be altered into an affirmative form we should still have one
negative premiss, and therefore cannot prove what we want to
prove, that some C is A.
37. ὡς kai ἐπὶ τῶν καθόλου. A. has not in fact used this method
to prove premisses of the universal moods of the second figure
(though he might have done; cf. #26-32 n.) ; he is thinking of the
use of it to prove the minor premiss of Celarent in the first figure
(526--32).
CHAPTER 7
Reciprocal proof applied to third-figure syllogisms
58°39. Since a universal conclusion requires two universal pre-
misses, but the original conclusion is always in this figure parti-
cular, when both premisses are universal neither can be proved
reciprocally, and when one is universal it cannot be so proved.
59*3- When one premiss is particular, reciprocal proof is some-
times possible :
Syllogism Reciprocal proof
All C is A. All A is C.
Some C is B. Some B is A.
τς Some B is A. τς Some B is C, .. Some C is B.
II. 6. 58520 — 7. 59441 443
Syllogism Reciprocal proof
I5. Some C is A. Some B is A.
All C is B. All B is C.
ες Some B is A. ες Some C is A.
18. Some C is not A. Some B is not A.
Al C is B. All Bis C.
ἐς Some B is not A. εἰς Some C is not A.
24. NoCis A Some of that, some of which is not A, is C.
Some C is B. Some B is not A.
*, Some B is not A. οἷς Some B is C.
(7. Some C is B).
(32. Thus (1) reciprocal proof of syllogisms in the first figure is
effected in the first figure when the original conclusion is affirma-
tive, in the third when it is negative; (2) that of syllogisms in the
second figure is effected both in the second and in the first figure
when the original conclusion is universal, both in the second and
in the third when it is particular; (3) that of syllogisms in the
third figure is effected in that figure; (4) when the premisses of
syllogisms in the second or third figure are proved by syllogisms
not in these figures respectively, these arguments are either not
reciprocal or not perfect.]
5924-31. ὅταν δ᾽... συλλογισμός, cf. 58426—-32 n.
32-41. Φανερὸν οὖν... ἀτελεῖς. The statement that in the
first figure, when the conclusion is affirmative, reciprocal proof is
effected in the first figure refers to the cases in which the original
conclusion is affirmative ; and the statement is correct, since the
proof of both premisses of Barbara and of the minor premiss of
Darii were in the first figure. The statement that in the first
figure, when the conclusion is negative, reciprocal proof is effected
in the third figure refers to Celarent and Ferio ; and the statement
is erroneous, since (x) it overlooks the fact that the proof of the
major premiss of Celarent was in the first figure (58222—6), and (2)
it treats the proof of the minor premisses of Celarent and Ferio
(ib. 26-32, 67-12) as being in the third figure. The statement that
in the second figure, when the syllogism is universal, reciprocal
proof is effected in the first or second figure refers to the cases in
which the original conclusion is universal; and the statement is
correct, since the proof of the minor premiss of Camestres was in
the second figure and that of the major premiss of Cesare in the
first. The statement that in the second figure, when the syllogism
is particular, reciprocal proof is in the second or third figure refers
to Baroco and Festino, and erroneously treats the proof of the
444 COMMENTARY
minor premiss of Festino (5833-8) as being in the third figure.
The statement that all the reciprocal proofs applied to the third
figure are in that figure (1) overlooks the fact that the proof of the
minor premiss of Datisi (596-11) was in the first figure and (2)
treats the proof of the minor premiss of Ferison (#24~9) as being
in the third figure. Thus two types of error are involved: (a) the
errors with regard to the major premiss of Celarent and the minor
premiss of Datisi, and (b) the treatment of the reciprocal proofs of
the minor premisses of Celarent, Ferio, Festino, and Ferison as
being in the third figure. Take one case which will serve for all—
that of Celarent. Here we have No B is A, All C is B, Therefore
no C is A. A. converts the major premiss into All that, none of
which is A, is B (in other words If no X is A, all X is B), adds the
original conclusion No C is A, and infers that all C is B. P. (417.
22-9) describes this as being a proof in the third figure, and an
anonymous scholiast (190217-27 Brandis) gives the reason, viz.
that the major premiss has a single subject with two predicates,
as the two premisses of a third-figure syllogism have. But this is
a most superficial analogy, since the relation between the protasis
and the apodosis of a hypothetical statement is quite different
from that between the premisses of a syllogism. The affinities of
the argument are with a first-figure syllogism, and it is easily
turned into one. The doctrine that there are three kinds of hypo-
thetical syllogism answering to the three figures is one of which
there is no trace in A.
The final statement (5939-41), that reciprocal proofs applied
to the second or third figure, if not effected in the same figure,
either are not κατὰ τὴν κύκλῳ δεῖξιν or are imperfect, at first sight
conflicts with the previous statement that all reciprocal proofs
applied to the third figure are effected in that figure. But the
statements can be reconciled by noting that all the norrnal con-
versions of syllogisms in these figures, viz. those of Camestres,
Baroco, Disamis, and Bocardo (5851822, 27—33, 59215-18, 18-23),
are carried out in the original figure, while those that are not in
the original figure either involve the abnormal conversion men-
tioned in our last paragraph (οὐ παρὰ τὴν κύκλῳ δεῖξιν) (viz. those
of Festino and Ferison, 5833-8, 59?24-31) or are imperfect, invol-
ving a conversion of the conclusion of the new syllogism (viz.
those of Cesare and Datisi, 58»22—7, 596-14).
The errors pointed out in (a4) above might be a mere oversight,
but that pointed out in (b) is a serious one which A. is most
unlikely to have fallen into; and there can be little doubt that the
paragraph is a gloss.
IT. 7. 59832-41 445
CHAPTER 8
Conversion of first-figure syllogisms
59^r. Conversion is proving, by assuming the opposite of the
conclusion, the opposite of one of the premisses; for if the con-
clusion be denied and one premiss remains, the other must be
denied.
6. We may assume either (a) the contrary or (b) the contra-
dictory of the conclusion. A and O, I and E are contradictories ;
A and E, I and O, contraries.
II. (A) Universal syllogisms
(a) All Bis A. All B is A. No C is A.
All C is B. No C is A. All C is B.
^. All C is A. .. NoC is B. εἰ. Some B is not A.
The contrary of the major premiss cannot be proved, since the
proof will be in the third figure.
20. So too if the syllogism is negative.
No B is A. No B is A. All € ts A.
All C is B. Al C is A. All C is B.
-. No € is A. ες NoC is B. .. Some B is A,
25. (b) Here the reciprocal syllogisms will only prove the cod-
tradictories of the premisses, since one of their premisses will be
particular.
All B is A. All B is A. Some C is not A.
All C is B. Some C is not A. All C is B.
τς AUC is A. .. Some C is not B. .. Some B is not A,
32. So too if the syllogism is negative.
No B is A. No B is A. Some C 1s A.
AIL C is B. Some C is A. AIL C is B.
ΤΌ NoC is A. ες Some C is not B. ες Some B is A.
37- (B) Particular syllogisms
(a) If we assume the contradictory of the conclusion, both
premisses can be refuted ;
(b) if the subcontrary, neither.
6051. (a) All Bis A. All B is A. NoC is A.
Some C is B. No C is A. Some C is B.
τς SomeC is A. ©. NoCis B. .. Some B is not A.
446 COMMENTARY
5. (b) All B is A. All B is A. Some C 1s not A.
Some C is B. Some C is not A, Some C is B.
..SomeCis A... Some C is not B, Nothing follows.
which does not disprove
Some C is B.
11. So too with a syllogism in Ferio. Both premisses can be dis-
proved by assuming the contradictory of the conclusion, neither
by assuming the subcontrary.
A. tells us in chs. 8-10 how the moods of the three figures can be
converted, but he does not tell us the point of the proceeding.
Conversion is defined as the construction of a new syllogism having
as premisses one of the original premisses and the opposite of the
original conclusion, and as conclusion the opposite of the other
premiss. Now when the original syllogism is in the second or
third figure and the converse syllogism in the first, the latter may
be regarded as an important confirmation of the former. For A.
always regards a first-figure syllogism as more directly proving its
conclusion than one in the second or third figure, so that if by a
first-figure syllogism we can prove that if the conclusion of the
original syllogism is untrue, one of its premisses must have been
untrue, we confirm the original syllogism. But in these chapters
A. also considers the conversion of a first-figure syllogism into a
second- or third-figure syllogism, that of a second-figure syllogism
into a third-figure syllogism, and that of a third-figure syllogism
into a second-figure syllogism; and such conversion can add
nothing to the conclusiveness of the original syllogism. What then
is the point of such conversion? It is stated in Top. 163329-36,
where practice in the conversion of syllogisms is commended πρὸς
γυμνασίαν καὶ μελετὴν τῶν τοιούτων λόγων, i.e. to give the student
of logic experience in the use of the syllogism. But conversion of
syllogisms has this special importance for A., that it is identical
with the syllogistic part of reductio ad impossibile, which is a really
important method of inference; v. 6118-33.
59^2-3. τὸ üxpov . . . τῷ τελευταίῳ, the major term, the minor
term.
10. οὐ τινί is used here in the sense of the more usual τινὶ οὔ
(i.e. an O proposition) ; cf. 63526.
I5-16. οὐ yap... σχήματος, cf. 29*16—18.
39-60*1. οὐ yap... ἀναιρεῖν. In the case of original syllo-
gisms with two universal premisses (511-36) there were instances
(513-20, 23-4) in which, though the conclusion of the converse
syllogism lacked universality (ἐλλείποντος, 540), it disproved an
II. 8. 5952 — 9. 60227 447
original premiss (since a particular conclusion is contradictory to
an original universal premiss); but when one of the original
premisses is particular, the subcontrary of the original conclusion
will not prove even the contradictory, let alone the contrary, of
either of the original premisses. For (60%5-11) if we combine it
with the universal original premiss we can only infer the swb-
conirary of the particular original premiss; and if we combine it
with that premiss we have two particular premisses and therefore
no conclusion.
CHAPTER 9
Conversion of second-figure syllogisms
60415. (A) Universal syllogisms
The contrary of the major premiss cannot be proved, whether
we assume the contradictory or the contrary of the conclusion ;
for the syllogism will be in the third figure, which cannot prove a
universal. (a) The contrary of the minor premiss can be proved
by assuming the contrary of the conclusion ; (b) the contradictory
by assuming the contradictory.
21. () All Bis A. All B is A. No C is A.
No Cis A. All C is B. All C is B.
J. No C is B. .. All C is A. ἐς Some B is not A.
26. (ὃ) | AU Bis A. All Bis A. No C is A.
No C is A. Some C is B. Some C is B.
No C is B. ες Some C is A. .. Some B is not A.
3x. So too with Cesare.
32. (B) Particular syllogisms
(a) If the subcontrary of the conclusion be assumed, neither
premiss can be disproved ; (δ) if the contradictory, both can.
(a) No B is A. No B is A. Some C is A.
Some C is A. Some C is B. Some C is B.
τς Some C is not B. .'. Some C is not A, Nothing follows.
which does not disprove
Some C is 4.
br.(b) No Bis A. No B is A. Some C is 4.
Some C is A. All C is B. All C is B.
4. Some C ts not B. /. No Cis A. ἐς Some B is 4.
bs. So too with a syllogism in Baroco.
60718. καθόλου δ᾽... συλλογισμός, cf. 29216-18.
27. ἡ μὲν AB . . . ἀντικειμένως, i.e. the contradictory of the
448 COMMENTARY
major premiss will be proved, as it was when the contrary of the
conclusion was assumed (224-6) ; the contradictory of the minor
premiss will be proved, not the contrary, which was what was
proved when the contrary of the conclusion was assumed (222-4).
34. καθάπερ οὐδ᾽ ἐν τῷ πρώτῳ σχήματι, cf. 59539-60*1, 6075-14.
CHAPTER 10
Conversion of third-figure syllogisms
60°6. (a) When we assume the subcontrary of the conclusion,
neither premiss can be disproved; (b) when the contradictory,
both can.
(A) Affirmative syllogisms
(a) AIL C is A. Some B is not A. Some B 1s not A.
AIL C is B. All C is B. ANC is A.
J. Some Bis A. Nothing follows. Nothing follows.
14. So too if one premiss is particular ; (a) if the subcontrary is
taken, either both premisses or the major premiss will be particu-
lar, and neither in the first nor in the second figure does this give
a conclusion ; (5) if the contradictory is taken, both premisses can
be disproved.
20. (b) All C is A. No B is A. No B is A.
AIL C is B. AIL C is B. AIL C is A.
τς Some B is A. /. NoC is A. *. NoC is B.
22. So too if one premiss is particular.
All C is A. No B is A. No Bis A.
Some C is B. Some C is B. All C is A.
ἐς Some B is A. .. SomeC isnot A. ,;. NoC is B.
25. (B) Negative syllogisms
(a) NoC is A. Some B is A. Some B is A.
All C is B. AII C is B. NoC is A.
ἐν Some B is not A. Nothing follows. Nothing follows.
33.00 — NoCis A. All B is A. All B is A.
AIL C is B. AIL C is B. No C is A.
ἐς Some B isnot A. .. AllC is A. ἐς NoC is B.
37- So too if one premiss is particular.
(b) NoC is A. All B is A. All B is A.
Some C is B. Some C is B. NoC is A.
ἐς Some B is not A... Some C is A. ἐς NoC is B.
6x4x. (a) NoC is A. Some B is A. Some B is A.
Some C is B. Some C is B. NoC is A.
τς Some B is noi A.
Nothing follows.
Nothing follows.
II. 9. 60°34 — ro. 60532 449
5. We see, then, (1) how the conclusion in each figure must be
converted in order to give a new conclusion, (2) when the contrary
and when the contradictory of an original premiss is proved, (3)
that when the original syllogism is in the first figure, the minor
premiss is disproved by a syllogism in the second, the major by one
in the third, (4) that when the original syllogism is in the second
figure, the minor premiss is disproved by one in the first, the major
by one in the third, (5) that when the original syllogism is in the
third figure, the major premiss is disproved by one in the first,
the minor by one in the second.
60517-18. οὕτω δ᾽... μέσῳ, cf. 26217-21, 2754-8, 28-39.
19-20. ἐὰν δ᾽... ἀμφότεραι. Waitz is no doubt right in sug-
gesting that the reading ἀντιστρέφωνται is due to a copyist who
punctuated after instead of before ai προτάσεις. Throughout chs.
8-10 the movement is from the opposite of the concluston.
28. οὕτω yap... συλλογισμός, cf. 2826-30, P1521, 31-5.
31. οὐκ Hv... Γ, cf. 26430-6.
32. οὐκ ἦν... συλλογισμός, cf. 2756-8.
CHAPTER 11
‘Reductio ad impossibile! in the first figure
61°17. Reductio ad impossibile takes place when the contra-
dictory of the conclusion is assumed and another premiss is added.
It takes place in all the figures; for it is like conversion except
that conversion takes place when a syllogism has been formed and
both its premisses have been expressly assumed, while reductio
takes place when the opposite of the conclusion of the reductio
syllogism has not been previously agreed to but is obviously
true.
26. The terms, and the way we take them, are the same; e.g. if
all B is A, the middle term being C, then if we assume Some B is
not A (or No B is A) and All C is A (which is true), Some B will not
be C (or no B will beC). But this is impossible, so that the assump-
tion must be false and its opposite true. So too in the other
figures; wherever conversion is possible, so is reductto.
34. E, I, and O propositions can be proved by reductio in any
figure; A propositions only in the second and third. For to get a
syllogism in the first figure we must add to Some B is not A (or
No B is A) either All A is C or All D is B.
4985 Gg
450
40. Propositions to
be proved
All B is A.
Reductio
All A is C.
Some B is not A.
Some B ts not A.
All D is B.
No B is A.
All D is B.
Ὁ No Dis A.
All A is C.
No Bis A.
by,
7-
COMMENTARY
Remark
Nothing follows.
Nothing follows.
If the conclusion is false,
this only shows that
Some B is A.
yey
Nothing follows.
Thus an A proposition cannot be proved P reductio in the first
figure.
IO. Some B is A. No B 1s A.
All (or Some) C is B.
*. NoC is A (or Some C is not A)
All A is C.
No Bis A.
15.
j
If the conclusion is false,
some B must be A.
᾿ Nothing follows.
17. The assumption some B 15 not A also leads to no conclusion.
Thus it is the contradictory of the conclusion that must be assumed.
19. No Bis A. All A is C.
Some Bis A,
*. Some B is C.
No A is C.
Some Bis A.
*. Some B is not C.
Some B is A.
All C is B (or NoC is B).
All A is C.
All B is A.
*, All BisC.
All Bis A.
AIL C is B.
/. AUC is A.
24.
30.
If the conclusion is false,
no B can be A.
|
|
|
|
If the conclusion is false,
no B can be A.
Nothing follows.
If the conclusion is false,
this only shows that
some B is not A.
If the conclusion is false,
this only shows that
some B is not A.
Thus it is the contradictory of the conclusion that must be assumed.
33. Not all Bis A. All A is C.
All Bis A.
S All BisC.
All Bis A.
AllC is B.
«Ὁ All C is A.
36.
If the conclusion is false,
it follows that some 8
is not A.
|
;
If the conclusion is false,
it follows that some B
is not 4.
II. 11. 61227-31 451
Reductio Remark
37- No A isC. If the conclusion is false,
All Bis A. it follows that some B
^ No BisC. is not 4.
8. All B is A. :
3 a. C 3d B. ) Nothing follows.
39- (1) If the conclusion is
All A is C. false, this proves too
Some Bis A much, viz. that no B
f Sane Bis C. is A, which is not
true; (2) the con-
clusion is not in fact
false.
So too if we were trying to prove that some B is not A (which
= Not all B is A).
62211. Thus it is always the contradictory of the proposition to
be proved, that we must assume. This is doubly fitting ; (1) if we
show that the contradictory of a proposition is false, the proposi-
tion must be true, and (2) if our opponent does not allow the truth
of the proposition, it is reasonable to make the supposition that
the contradictory is true. The contrary is not fitting in either
respect.
Chapters 11-13 deal with reductio ad impossibile, in the three
figures. It is defined as an argument in which 'the contradictory
of the conclusion is assumed and another premiss is added to it'
(61218-21) ; and in this respect it is like conversion of syllogisms
(321-2). But it is said to differ from conversion in that ‘conversion
takes place when a syllogism has been formed and both its pre-
misses have been expressly assumed, while reductio takes place
when the opposite' (ie. the opposite of the conclusion of the
reductio syllogism) ‘has not been previously agreed upon but is
obviously true' (322-5). This is equivalent to saying that pre-
viously to the reductio syllogism no ostensive syllogism has been
formed, so that when A. describes the reductio as assuming the
contradictory of the conclusion, this must mean 'the contra-
dictory of the conclusion we wish to prove’.
What reductio has in common with conversion is that it is an
indirect proof of a proposition, by supposing the contradictory to
be true and showing that from it and a proposition known to be
true there follows a proposition known or assumed to be false.
61427-31. olov ei... ἀντικείμενον. A. here leaves it an open
question whether it is the contradictory (μὴ παντί, ?28) or the
452 COMMENTARY
contrary (μηδενί, ibid.) of the proposition to be proved that is
to be assumed as the basis of the veductio syllogism. But in the
course of the chapter he shows that the assumption of the contrary
of an A or E proposition (bx—ro, 24-33), or the subcontrary of an I
or O proposition (617-18, 39-62*10), fails to disprove the A, E, I,
or O proposition.
54-8. οὐδ᾽ ὅταν... ὑπάρχειν. This is a repetition of what A.
has already said in *4o-^r. The sentence would read more natu-
rally if we had ὥσπερ οὐδ᾽.
6224-7. ἔτι... τῷ B. The received text, ἔτι od mapa τὴν ὑπό-
θεσιν συμβαίνει τὸ ἀδύνατον, gives the wrong sense ‘further, the
impossible conclusion is not the result of the assumption’. The
sense required is rather that ‘the assumption leads to nothing
impossible; for if it did, it would have to be false (since a false
conclusion cannot follow from true premisses), but it is in fact
true; for some B is in fact A’. A. as usual treats Some B is not
A as naturally implying Some B is A. The reading I have adopted
receives support from n.’s οὐδέ and from P.’s paraphrase οὐδὲν
ἄτοπον ἕπεται.
13. ἀξίωμα, ‘assumption’. This sense is to be distinguished
from a second sense, in which it means ‘axiom’. Examples of
both senses are given in our Index.
I5. μὴ τίθησιν is used in the sense of ‘does not admit’, and has as
its understood subject the person one is trying to convince. Cf.
Met. 106310 μηθὲν τιθέντες ἀναιροῦσι τὸ διαλέγεσθαι.
19. θάτερον (sc. τὸ παντί)... ϑάτερον (sc. τὸ μηδενί) answers to
τὴν κατάφασιν... τὴν ἀπόφασιν in "16.
CHAPTER 12
‘Reductio ad imposstbtle’ in the second figure
6220. Thus all forms of proposition except A can be proved by
reductio in the first figure. In the second figure all four forms can
be proved.
Proposition to
be proved Reductio Rosndrh
23. All B is A. E ü m P If the conclusion is false,
-. Some B is not C. all B must be A.
28. AIL C is A. | If the conclusion is false,
No Bis A. it only follows that
.. No BisC. some Bis A.
II. 11. 6157 — 12. 62440 453
Propositions to
be proved Reductio Remark
32. Some B is A. AUC is A. If the conclusion is false,
No Bis A. B tbe. Àd
“No Bis C. SENS SUIS ᾿
46. Some B is not A. Cf. remark in 6151718.
37. No Bis A. No C is A. If the conclusion is false,
Sume iA: no B can be A
.. Some B is not C. i
40. Some B is not A. NoC is A. If the conclusion is false,
All B is 4. it follows that some B
Ὁ No BisC. is not A.
bg. Thus all four kinds of proposition can be proved in this
figure.
62°32-3. ὅτι δὲ... ὑπάρχει τὸ A. Here, in *40, and in 514 the
best MSS. and P. read ὅτι, while Bekker and Waitz with little MS.
authority read ὅτε. There can be no doubt that ὅτι is right; the
construction is elliptical—' with regard to the proposition that’,
‘if we want to prove the proposition that’. Cf. Pl. Crat. 384€ 3,
Prot. 33o e 1, Phaedo 115d2, Laws 688 Ὁ 6.
36-7. radr’ ἔσται. . . σχήματος. ταὐτ᾽ should obviously be
read, for the vulgate ταῦτ᾽. So too in 1o, 23. The reference is to
61517-18.
40. ὅτι δ᾽ οὐ παντί, cf. 232-3 n.
CHAPTER 13
'Reductio ad impossibile! in the third figure
62>s. All four kinds of proposition can be proved in this figure.
Propositions to
be proved Reductio Remark
All Bis A. Some Β ἐς ποί Α. If the conclusion is false,
ALB EE. all B must be A
.. Some C is not A. :
8. No Bis A. If the conclusion is false,
All B is C. this only shows that
*. Some C is not A. some B is A.
If the conclusion is false,
Some B is C. some B must be 4.
Ix. Some B is A. No B is A.
*. Some C is not A.
454 COMMENTARY
Propositions to
be proved Reductio Remark
14. No B is A. apte Β ἐς 4. If the conclusion is false,
All B isC. B ΒΕ Α
.. Some C is A. wear eee
18. All Bis A. If the conclusion is false,
All BisC. this only shows that
ἐς Some C is A. some B is not A.
19. ΘΟ πε ΒΒ. ΠΟΤ: ΑἸΣῈ ἃς οἵ; If the conclusion is false,
ABC some B must not be 4
εἰς Some C is A. 9
23. Some B is A. Cf. remark in 61539-6238.
25. Thus (1) in all cases of reductto what we must suppose true
is the contradictory of the proposition to be proved ; (2) an affirma-
tive proposition can in a sense be proved in the second figure, and
a universal proposition in the third.
62>10-11. ταὐτ᾽ ἔσται... πρότερον. The reference is to 611-
8, 62228—32. For the reading cf. 62536-- n.
14. ὅτι δ᾽. Cf. 2332-3 n.
18. οὐ δείκνυται τὸ προτεθέν. For the proof of this cf. the
corresponding passage on the first figure, 61524—33.
23-4. ταὐτ᾽ ἔσται... προειρημένων. The reference is to the
corresponding passage on the first figure, 61539-6238. For the
reading cf. 62336—7 n.
26-8. δῆλον δὲ... καθόλου, ie. an affirmative conclusion,
which cannot be proved ostensively in the second figure, can be
proved by a reductio in that figure (62423-8, 32-6) ; and a universal
conclusion, which cannot be proved ostensively in the third figure,
can be proved by a reductto in it (6255-8, 11-14).
CHAPTER 14
The relations between ostensive proof and 'reductio ad impossibile
62529. Reductio differs from ostensive proof by supposing what
it wants to disprove, and deducing a conclusion admittedly false,
while ostensive proof proceeds from admitted premisses. Or
rather, both take two admitted propositions, but ostensive proof
takes admitted propositions which form its premisses, while
reductio takes one of the premisses of the ostensive proof and the
contradictory of the conclusion. The conclusion of ostensive
proof need not be known before, nor assumed to be true or to be
false; the conclusion of a reductio syllogism must be already known
II. 13. 6210-28 455
to be false. It matters not whether the main conclusion to be
proved is affirmative or negative; the method is the same.
38. Everything that can be proved ostensively can be proved
by veductio, and vice versa, by the use of the same terms. (A)
When the reductio is in the first figure, the ostensive proof is in
the second when it is negative, in the third when it is affirmative.
(B) When the reductio is in the second figure, the ostensive proof
is in the first. (C) When the veductto is in the third figure, the
ostensive proof is in the first when affirmative, in the second when
negative.
Data Reductio Ostensive proof
(A) First figure Second figure
6357. All A is C. All A is C. All A is C.
No B isC. .. if some B is A, some NoBisC.
BisC. .. No B is A.
But No B isC.
-. No B is A.
I4. All AisC. All A is C. All 4 is C.
Some B is not C. ..ifall Bis A, all BisC. Some B is not C.
But some B isnot C. .. Some B is not A.
ἐς Some B is not A.
16. No AisC. No AisC. No 4150.
All B is C. .. if some B is A, some All B is C.
B is not C. .. No B is A.
But all B is C.
.. No B is A.
No AisC. No AisC. No 4156.
Some B is C. ον if all Bis A,no BisC. Some B is C.
But some B is C. .. Some B is not A.
*. Some B is not A.
Third figure -
18. All Cis A. If no Bis A, then since All C is A.
AIL C is B. all C is B, noC is A. All C is B.
But all C is A. ἐν Some B is A.
.. Some B is A.
23. AllCis A. If no Bis A, then since AllC is A.
Some C is B. allC is B, noC is A. Some C is B.
*. Some B is A.
But all C is A.
ες Some B is A.
Some C is A. If no B is A, then since Some C is A.
All C is B. allC is B, noC is A. All C is B.
But some C is A. ες Some B is A,
*. Some B is A.
456
25.
35.
Data
AUC is A.
All B is C.
AUC is A.
Some B is C.
NoC is A.
All B is C.
NoC is A.
Some B is C.
All C is A.
All B isC.
All C is A.
Some B is C.
No AisC.
All BisC.
No 4156.
Some B is C.
COMMENTARY
Reductio
(B) Second figure
AUC is A.
*. if some B is not A,
some B is not C.
But all B is C.
«Ὁ All B is A.
AUC is A.
*. ifno Bis A, no BisC.
But some B is C.
*. Some B is A.
NoC is A.
*. if some B is A, some
B is not C.
But all B is C.
*. No B is A.
.
NoC is A.
. ifall Bis 4, no BisC.
But some B is C.
*. Some B is not A.
(C) Third figure
If some B is not A,
then since all B isC,
some C is not A.
But all C is A.
*. All B is A.
If no B is A, then since
some B is C, some C
is not A.
But all C is A.
*. Some B is A.
All B is C.
*. if some B is A, some
AisC.
But no A is C.
-. No B is A.
Some B is C.
*. if all B is 4, some A
is C.
But no A is C.
*. Some B is not A.
Ostensive proof
First figure
All C is A.
All B is C.
*. All B is A.
All C is A.
Some B is C.
*. Some B is A.
No C is A.
All B isC.
*, No B is A.
No C is A.
Some B is C.
.. Some B is not A.
First figure
All C is A.
All BisC.
'. All B is A.
All C is A.
Some B is C.
*. Some B is A.
Second figure
No 4 is C.
All B is C.
'. No B is A.
No A isC.
Some B is C.
*. Some B is not 4.
12. Thus any proposition proved by a reduct;o can be proved
ostensively, by the use of the same terms; and vice versa. If we
II. 14. 62632 — 63517 457
take the contradictory of the conclusion of the ostensive syllogism
we get the same new Syllogism which was indicated in dealing
with conversion of syllogisms; and we already know the figures
in which these new syllogisms must be.
6232-3. λαμβάνουσι μὲν οὖν. . . ὁμολογουμένας. μὲν οὖν
introduces a correction. The usage is common in dialogue (Den-
niston, The Greek Particles, 475-8), rare in continuous speech (ib.
478-9) ; for. Aristotelian instances cf. Rhet. 139915, 23.
36-7. ἔνθα Se... ἔστιν. Cf. An. Post. 87414 ὅταν μὲν οὖν F τὸ
συμπέρασμα γνωριμώτερον ὅτι οὐκ ἔστιν, ἡ εἰς TO ἀδύνατον γίνεται
ἀπόδειξις.
41-6377. ὅταν μὲν yàp . . . μέσῳ. There are also negative osten-
sive syllogisms in the third figure answering to reductio syllogisms
in the first, ostensive syllogisms in the third answering to reductio
syllogisms in the second, and negative ostensive syllogisms in the
first answering to reductio syllogisms in the third. E.g.,
Data Reductio Ostensive syllogism
No C is A. If all Bis A, then since all C is B, NoC is A.
AIL C is B. all C is A. AIL C is B.
But no C is 4. ἐν Some B is not A,
.. Some B is not A.
But A.'s statement here is a correct summary of the correspon-
dences he gives in this chapter, which are presumably not meant
to be exhaustive.
41-63*1. ὁ συλλογισμὸς . . . τὸ ἀληθές, the reductio ... the
ostensive proof.
6327. ἔστω yap δεδειγμένον, sc. by reducto.
br2-13. Φανερὸν οὖν... ἀδυνάτου. καὶ δεικτικῶς means 'os-
tensively as well as by reductio’, so that καὶ διὰ τοῦ ἀδυνάτου is
superfluous ; indeed, it makes the next sentence pointless.
16-17. γίνονται yàp . . . ἀντιστροφῆς, i.e. the reductio syllogism
is related to the ostensive syllogism exactly as the converse syllo-
gisms discussed in chs. 8—ro were related to the original syllogisms.
CHAPTER 15
Reasoning from a pair of opposite premisses
63522. The following discussion will show in what figures it is
possible to reason from opposite premisses. Of the four verbal
oppositions, that between I and O is only verbally an opposition,
458 COMMENTARY
that between A and E is contrariety, and those between A and O
and between E and I are true oppositions.
31. There cannot be such a syllogism in the first figure—not an
affirmative syllogism because such a syllogism must have two
affirmative premisses ; not a negative syllogism because opposite
premisses must have the same subject and the same predicate,
but in this figure what is subject of one premiss is predicate of the
other.
40. In the second figure there may be both contradictory and
contrary premisses. If we assume that all knowledge is good and
that none is, it follows that no knowledge is knowledge.
64°4. If we assume that all knowledge is good and that no
medical knowledge is so, it follows that one kind of knowledge is
not knowledge.
7. If no knowledge is supposition and all medical knowledge is
so, it follows that one kind of knowledge is not knowledge.
12. Similarly if the minor premiss is particular.
rS. Thus self-contradictory conclusions can be reached pro-
vided that the extreme terms are either the same or related as
whole to part.
20. In the third figure there cannot be an affirmative syllogism
with opposite premisses, for the reason given above; there may
be a negative syllogism, with or without both premisses universal.
If no medical skill is knowledge and all medical skill is knowledge,
it follows that a particular knowledge is not knowledge.
27. So too if the affirmative premiss is particular ; if no medical
skill is knowledge and a particular piece of medical skill is know-
ledge,a particular knowledge is notknowledge. When the premisses
are both universal, they are contrary; when one is particular,
contradictory.
33. Such mere assumption of opposite premisses is not likely
to go unnoticed. But it is possible to infer one of the premisses by
syllogism from admissions made by the adversary, or to get it in
the manner described in the Topics.
37. There being three ways of opposing affirmations, and the
order of the premisses being reversible, there are six possible
combinations of opposite premisses, e.g. in the second figure AE,
EA, AO, EI; and similarly a variety of combinations in the third
figure. So it is clear what combinations of opposite premisses are
possible, and in what figures.
by, We can get a true conclusion from false premisses, but not
from opposite premisses. Since the premisses are opposed in
quality and the terms of the one are either identical with, or
II. 15. 63526 — 6453 459
related as a whole to part to, those of the other, the conclusion
must be contrary to the fact—of the type 'if S is good it is not
good'.
13. It is clear too that in paralogisms we can get a conclusion
of which the apodosis contradicts the protasis, e.g. that if a certain
number is odd it is not odd; for if we take contradictory premisses
we naturally get a self-contradictory conclusion.
17. À self-contradictory conclusion of the type 'that which is
not good is good' cannot be reached by a single syllogism unless
there is an explicit self-contradiction in one premiss, the premisses
being of the type 'every animal is white and not white, man is an
animal’.
21. Otherwise we must assume one proposition and prove the
opposite one; or one may establish the contrary propositions by
different syllogisms.
25. This is the only way of taking our premisses so that the
premisses taken are truly opposite.
63526. τῷ οὐ τινί = τῷ τινὶ οὔ. Cf. τοῦτο.
64.21--2. διὰ τὴν εἰρημένην αἰτίαν... σχήματος, cf. 63533-5.
23-30. ἔστω γάρ... ἐπιστήμην. A. here seems to treat the
premisses. All A is B, No A is C (723-7) and the premisses Some
A is B, No A is C (827-30) as yielding the conclusion Some C is
not B, which they do not do. But since B and C stand for the
same thing, knowledge, these premisses may be rewritten re-
spectively as No A is B, All A is C and as No A is B, Some A
is C, each of which combinations does yield the conclusion Some
C is not B.
36-7. ἔστι δὲ... λαβεῖν. The methods of obtaining one's pre-
misses in such a way as to convince an incautious opponent, so
that he does not see what he is being led up to, are described at
length in Tof. viii. 1. But they reduce themselves to two main
methods—the inferring of the premisses by syllogism and by
induction (155>35-6).
37-8. ἐπεὶ δὲ... τρεῖς, i.e. AE, AO, IE—not IO, since an I
proposition and an O proposition are only verbally opposed
(635278).
38-53. ἑξαχῶς συμβαίνει... ὅρους. Of the six possible com-
binations AE, AO, IE, EA, OA, EI, A. evidently intends to
enumerate in >1-3 the four possible in the second figure—AE, EA,
AO, EI. τὸ A... μὴ παντί gives us AE, EA, AO; καὶ πάλιν τοῦτο
ἀντιστρέψαι κατὰ τοὺς ὅρους must mean ‘or we can make the uni-
versal premiss negative and the particular premiss affirmative (EI).
460 COMMENTARY
The combinations possible in the third figure (3-4) are of course
EA, OA, EI.
5B. καθάπερ εἴρηται πρότερον, in chs. 2-4.
9-13. ἀεὶ yap... μέρος. A. has shown in 6340-64931 how, by
taking two premisses opposite in quality, with the same predicate
and with subjects identical or related as genus to species (second
figure), or with the same subject and with predicates identical or
related as genus to species (third figure), we can get a conclusion
of the form No 4 is A (illustrated here by εἰ ἔστιν ἀγαθόν, μὴ εἶναι
ἀγαθόν) or Some A is not A.
13-15. δηλὸν δὲ... περιττόν. A paralogism is defined in Top.
IOI*13-15 as an argument that proceeds from assumptions appro-
priate to the science in question but untrue. This A. aptly illus-
trates here by referring to the proof (for which v. 4126-7 n.) that
if the diagonal of a square were commensurate with the side, it
would follow that odds are equal to evens, i.e. that what is odd is
not odd.
15-16. ἐκ yàp τῶν ἀντικειμένων... συλλογισμός, ‘since, as we
saw in Ῥ9-13, an inference from premisses opposite to one another
must be contrary to the fact’.
17-25. Set δὲ... συλλογισμῶν. A. now turns to quite a
different kind of inference, in which the conclusion is not negative
but affirmative—not No A is A or Some A is not A, but All (or
Something) that is not A is A. He puts forward three ways in
which such a conclusion may be reached. (1) (Pzo-:) It may be
reached by one syllogism, only if one premiss asserts contraries of
a certain subject ; e.g. Every animal is white and not white, Man
is an animal, Therefore man is white and not white (from which
it follows that Something that is not white is white). (2) (621-4)
A more plausible way of reaching a similar conclusion is, not to
assume in a single proposition that a single subject has opposite
attributes, but to assume that it has one and prove that it (or
some of it) has the other, e.g. to assume that all knowledge is
supposition, and then to reason ‘No medical skill is supposition,
All medical skill is knowledge, Therefore some knowledge is not
supposition’. (3) (825) We may establish the opposite propositions
by two separate syllogisms.
24. ὥσπερ of ἔλεγχοι γίνονται. Anyone familiar with Plato's
dialogues will recognize the kind of argument referred to, as one
of the commonest types used by Socrates in refuting the theories
of others (particularly proposed definitions).
25~7. ὥστε δ᾽... πρότερον. It is not clear whether this is
meant to sum up what has been said in 515-25 of the methods of
II. 15. 6458-26 461
obtaining a conclusion of the form ‘Not-A is A’, or to sum up the
main results of the chapter as to the methods of obtaining a
conclusion of the form ‘A is not A’. The latter is the more prob-
able, especially in view of the similarity of the language to that in
63°22-8.. ὥστ᾽ εἶναι ἐναντία κατ᾽ ἀλήθειαν τὰ εἰλημμένα means then
‘so that the premisses of a single syllogism are genuinely opposed
to one another’. How, and how alone, this can be done, has been
stated in 63540-6456.
26. οὐκ ἔστιν, sc. λαβεῖν, which is easily supplied from the
. previous rà εἰλημμένα.
CHAPTER 16
Fallacy of 'Petitio principi
64528. Petitio principii falls within the class of failure to prove
the thesis to be proved; but this may happen if one does not
syllogize at all, or uses premisses no better known than the
conclusion, or logically posterior to it. None of these constitutes
petitio principi.
34. Some things are self-evident; some we know by means of
these things. It is petitio principii when one tries to prove by
means of itself what is not self-evident. One may do this (a) by
assuming straight off the point at issue, or (b) by proving it
by other things that are naturally proved by it, e.g. proposition 4
by B, and B byC, when C is naturally proved by A (as when people
think they are proving the lines they draw to be parallel, by means
of assumptions that cannot be proved unless the lines are parallel).
6557. People who do this are really saying ‘this is so, if it is so’;
but at that rate everything is self-evident ; which is impossible.
10. (i) If it is equally unclear that C is A and that B is A, and
we assume the latter in order to prove the former, that in itself
is not a fetifio Principii, though it is a failure to prove. But if B
is identical with C, or plainly convertible with it, or included in
its essence, we have a petitio Principi. For if B and C were con-
vertible one could equally well prove from 'C is A' and 'C is B'
that B is A (if we do not, it is the failure to convert 'C is B’, and
not the mood we are using, that prevents us) ; and if one did this,
one would be doing what we have described above, effecting a
reciprocal proof by altering the order of the three terms.
19. (ii) Similarly if, to prove that C is 4, one assumed that
C is B (this being as little known as that C is A), that would be
a failure to prove, but not necessarily a petitio Principst. But if
462 COMMENTARY
A and B are the same either by being convertible or by A’s being
necessarily true of B, one commits a felitio principit.
26. Petitio principu, then, is proving by means of itself what
is not self-evident, and this is (a) failing to prove, (b) when con-
clusion and premiss are equally unclear either (ii above) because
the predicates asserted of a single subject are the same or (i above)
because the subjects of which a single predicate is asserted are the
same. In the second and third figure there may be pefitio principii
of both the types indicated by (i) and (ii). This can happen in an
affirmative syllogism in the third and first figures. When the
syllogism is negative there is petitio principii when the predicates
denied of a single subject are the same; the two premisses are not
each capable of committing the $et;tio (so too in the second figure),
because the terms of the negative premiss are not interchangeable.
35. In scientific proofs petitio principii assumes true proposi-
tions; in dialectical proofs generally accepted propositions.
64529. τοῦτο δὲ συμβαίνει πολλαχῶς. ἐπισυμβαίνει, which ap-
pears in all the early MSS. except n, is not found elsewhere in any
work earlier than ps.-A. Rhet. ad Al. (142646), and the ἐπι- would
have no point here.
31. καὶ εἰ διὰ τῶν ὑστέρων τὸ πρότερον refers to logical priority
and posteriority. A. thinks of one fact as being prior to another
when it is the reason or cause of the other; cf. An. Post. 7122,
where προτέρων and αἰτίων τοῦ συμπεράσματος are almost synony-
mous.
36-7. μὴ τὸ δι᾽ αὑτοῦ γνωστὸν... ἐπιχειρῇ δεικνύναι is, in
Aristotelian idiom, equivalent to τὸ μὴ δι’ αὑτοῦ γνωστὸν...
ἐπιχειρῇ δεικνύναι. Cf. Met. 1068428 μεταβεβληκὸς ἔσται... εἰς μὴ
τὴν τυχοῦσαν ἀεί, Rhet. 136437 ὃ πάντες αἱροῦνται (κάλλιόν ἐστι) τοῦ
μὴ ὃ πάντες.
65°4-7. ὅπερ ποιοῦσιν. .. παραλλήλων. P. has a particular
explanation of this (454. 5-7) βούλονται yap παραλλήλους εὐθείας
ἀπὸ τοῦ μεσημβρινοῦ κύκλου καταγράψαι δυνατὸν (Óv», xai λαμβά-
νουσι σημεῖον ὡς εἰπεῖν προσπῖπτον περὶ τὸ ἐπίπεδον ἐκείνου, καὶ
οὕτως ἐκβάλλουσι τὰς εὐθείας. But we do not know what authority
he had for this interpretation; the reference may be to any pro-
posed manner of drawing a parallel to a given line (which involves
proving two lines to be parallel) which assumed anything that
cannot be known unless the lines are known to be parallel.
Euclid’s first proof that two lines are parallel (I. 27) assumes only
that if a side of a triangle be produced, the exterior angle is
greater than either of the interior and opposite angles (I. 16), but
IT. 16. 64529 — 65225 463
from 66413-15 otov τὰς παραλλήλους συμπίπτειν... εἰ τὸ τρίγωνον
ἔχει πλείους ὀρθὰς δυεῖν it seems that some geometer known to A.
assumed, for the proof of I. 27, that the angles of a triangle =
two right angles (I. 32), which involves a circulus 1n probando ; and
it is probably to this that τοιαῦτα à . . . παραλλήλων refers. As
Heiberg suggests (AbhA. zur Gesch. d. Math. Wissenschaften, xviii.
19), it may have been this defect in earlier text-books that led
Euclid to state the axiom of parallels (fifth postulate) and to
place I. 16 before the proof that the angles of a triangle = two
right angles. For a full discussion of the subject cf. Heath,
Mathematics in Aristotle, 27-30.
10-25. Εἰ οὖν... δῆλον. A. here points out the two ways in
which $etit:o principi may arise in a first-figure syllogism. Let
the syllogism be All B is A, ΑἹ] Ο is B, Therefore all C is A. (1)
(410-19) There is felitio principi if (a) we assume All B is A when
this is as unclear as All C is A, and (δ) B is (i) identical with C (i.e.
if they are two names for the same thing), or (11) manifestly con-
vertible with C (as a species is with a differentia peculiar to it) or
(iii) B is included in the essential nature ofC (as a generic character
is included in the essence of a species). If B and C are convertible
(this covers cases (i) and (ii)) and we say All B is A, All C is B,
Therefore all C is A, we are guilty of petitio Principi ; for (416-17)
if we converted All C is B we could equally well prove All B is A
by means of the other two propositions—All C is A, All B is C,
Therefore all B is A.
In 415 the received text has ὑπάρχει. ὑπάρχειν is A.’s word for
the relation of any predicate to its subject, and ὑπάρχει is therefore
too wide here. A closer connexion between subject and predicate
is clearly intended, and this is rightly expressed by ἐνυπάρχει, ‘or
if B inheres as an element in the essence of C’. P. consistently
uses ἐνυπάρχειν in his commentary on the passage (451. 18, 454. 21,
23, 455. 17). The same meaning is conveyed by rà ἕπεσθαι τῷ B τὸ
A (‘by A's necessarily accompanying B") in ?22. An early copyist
has assimilated ἐνυπάρχει here to ὑπάρχει in #16. For confusion in
the MSS. between the two words cf. An. Post. 73*37-8 n., 38,
84713, 19, 20.
The general principle is that when one premiss connects identi-
cal or quasi-identical terms, the other premiss commits a petitzo
principi ; it is the nature of a genuine inference that neither of the
premisses should be a tautology, that each should contribute
something to the proof.
viv δὲ τοῦτο κωλύει, ἀλλ᾽ οὐχ ὁ τρόπος (17) is difficult. P.
(455. 2) is probably right in interpreting τοῦτο as τὸ μὴ ἀντιστρέφειν.
464 COMMENTARY
‘If he does not prove ‘B is A’ from ‘C is A’ (sc. and ‘C is B’), it
is his failure to convert ‘C is B’, not the mood he is using, that
prevents his doing so’. Not the mood; for the mood Barbara,
which he uses when he argues ‘B is A, C is B, Therefore C is A’,
has been seen in 5735-5815 to permit of the proof of each of its
premisses from the other premiss and the conclusion, if the terms
are convertible and are converted.
If (A. continues in 518-19) we do thus prove All C is A from All
B is A and ΑἹ] C is B, and All B is A from All C is A and All B is
C (got by converting All C is B), we shall just be doing the useless
thing described above (*1-4)—ringing the changes on three terms
and proving two out of three propositions, each from the two
others, which amounts to proving a thing by means of itself.
(2) *19-25. Similarly we shall have a petitio principit if (a) we
assume All C is B when this is no clearer than All C is A, and (b)
(i) A and B are convertible or (ii) A belongs to the essence of B.
(i) here corresponds to (i) and (ii) above, (ii) to (iii) above.
Thus where either premiss relates quasi-identical terms, the
assumption of the other commits a petitio principit.
20. οὔπω τὸ ἐξ ἀρχῆς, Sc. αἰτεῖσθαί ἐστι, OF αἰτεῖται.
24. εἴρηται, in 64534-8.
26-35. Εἰ οὖν... συλλογισμούς. A. here considers fetitio
principii in the second and third figures, and in negative moods of
the first figure. He begins by summarizing the two ways in which
petitio has been described as arising in affirmative moods of the
first figure—} τῷ ταὐτὰ τῷ αὐτῷ ἢ τῷ ταὐτὸν τοῖς αὐτοῖς ὑπάρχειν.
ταὐτὸν τοῖς αὐτοῖς refers to case (1) (?ro—19), in which an identical
term A is predicated of quasi-identical terms B, C in a premiss
and in the conclusion, ταὐτὰ τῷ αὐτῷ to case (2) (*19-25), in which
quasi-identical terms B, A are predicated of an identical term C
in a premiss and in the conclusion. A study of the paradigms of
the three figures
First figure Second figure Third figure
B is (or is not) A. A is (or is not) B. B is (or is not) A,
C is B. C is not (or is) B. BisC.
.. C is (or is not) A. .. C is not A. .. C is (or is not) A,
shows that (1) can occur in affirmative and negative moods of the
first figure (Barbara, Celarent) and of the third (Disamis, Bocardo),
and (2) in affirmative moods of the first (Barbara, Darii), and in
moods of the second (which are of course negative) (Camestres,
Baroco). It is at first sight puzzling to find A. saying that both
(x) and (2) occur in the second and third figures ; for (1) seems not
II. 16. 65*20-7 465
to occur in the second, nor (2) in the third. But in Cesare (No A is
B, AM C is B, Therefore no C is A), in saying No A is B we are
virtually saying No Bis A, and therefore in the major premiss and
the conclusion may be denying the identical term A of quasi-
identical terms (case 1)). And in Datisi (All B is A, Some B is C,
Therefore some C is A), in saying Some B is C we are virtually
saying Some C is B, and therefore in the minor premiss and the
conclusion may be asserting quasi-identical terms of the identical
term C (case (2)).
Having pointed out the distinction between case (1) and case
(2), A. proceeds to point out that the affirmative form of each can
only occur in the first and third figures (since there are no affirma-
tive moods in the second figure). He designates the negative
forms of both kinds of petitio by the phrase ὅταν rà αὐτὰ ἀπὸ τοῦ
αὐτοῦ. We might have expected him to distinguish from this the
case ὅταν ταὐτὸν ἀπὸ τῶν αὐτῶν, but the distinction is unnecessary,
since in denying an identical term of two quasi-identical ones we
are (since universal negative propositions are simply convertible)
virtually denying them of it. Finally, he points out that in
negative syllogisms the two premisses are not alike capable of
committing a petitio. Since the terms of a negative premiss can-
not be quasi-identical, it is only in the negative premiss that a
petitio can be committed.
27. ὅταν, sc. τοῦτο γένηται.
CHAPTERS 17, 18
Fallacy of false cause
65°38. The objection ‘that is not what the falsity depends on’
arises in the case of reductio ad impossibile, when one attacks the
main proposition established by the reductio. For if one does not
deny this proposition one does not say ‘that is not what the falsity
depends on’, but ‘one of the premisses must have been false’; nor
does the charge arise in cases of ostensive proof, since such a proof
does not use as a premiss the counter-thesis which the opponent is
maintaining.
b4. Further, when one has disproved a proposition ostensively
no one can say 'the conclusion does not depend on the supposi-
tion’ ; we can say this only when, the supposition being removed,
the conclusion none the less follows from the remaining premisses,
which cannot happen in ostensive proof, since there if the premiss
is removed the syllogism disappears.
9. The charge arises, then, in relation to reductio, i.e. when the
4985 Hh
466 COMMENTARY
supposition is so related to the impossible conclusion that the
latter follows whether the former is made or not.”
13. (ri) The most obvious case is that in which there is no
syllogistic nexus between the supposition and the impossible con-
clusion ; e.g. if one tries to prove that the diagonal of the square
is incommensurate with the side by applying Zeno's argument and
showing that if the diagonal were commensurate with the side
motion would be impossible.
21. (2) A second case is that in which the impossible conclusion
is syllogistically connected with the assumption, but the im-
possibility does not depend on the assumption. (a) Suppose that
B is assumed to be A, I^ to be B, and 4 to be I^, but in fact 4 is
not B. If when we cut out A the other premisses remain, the
premiss ‘B is A’ is not the cause of the falsity.
28. (b) Suppose that B is assumed to be A, A to be E, and E to
be Z, but in fact A is not Z. Here too the impossibility remains
when the premiss ‘B is A’ has been cut out.
32. For a reductio to be sound, the impossibility must be con-
nected with the terms of the original assumption ‘B is A’; (a)
with its predicate when the movement is downward (for if it is 4’s
being A that is impossible, the elimination of A removes the false
conclusion), (b) with its subject when the movement is upward
(if it is B's being Z that is impossible, the elimination of B removes
the impossible conclusion). So too if the syllogisms are negative.
66:1. Thus when the impossibility is not connected with the
original terms, the falsity of the conclusion is not due to the
original assumption. But (3) even when it is so connected, may
not the falsity of the conclusion fail to be due to the assumption?
If we had assumed that K (not B) is A, and Γ is Καὶ, and 4 is T,
the impossible conclusion ‘4 is A’ may remain (and similarly if
we had taken terms in the upward direction). Therefore the
impossible conclusion does not depend on the assumption that
B is A. '
8. No; the charge of false cause does not arise when the sub-
stitution of a different assumption leads equally to the impossible
conclusion, but only when, the original assumption being elimi-
nated, the remaining premisses yield the same impossible conclu-
sion. There is nothing absurd in supposing that the same false
conclusion may result from different false premisses ; parallels will
meet if either the interior angle is greater than the exterior, or a
triangle has angles whose sum is greater than two right angles.
16. A false conclusion depends on the first false assumption
on which it is based. Every syllogism depends either on its two
II. 17. 65238 — 28 467
premisses or on more than two. If a false conclusion depends on
two, one or both must be false; if on more—e.g. l'on A and B,
and these on 4 and E, and Z and H, respectively—one of the
premisses of the prosyllogisms must be false, and the conclusion
and its falsity must depend on it and its falsity.
65338—53. To δὲ μὴ παρὰ τοῦτο... ἀντίφησιν. A. makes two
points here about the incidence of the objection 'that is not the
cause of the falsity'. Suppose that someone wishes to maintain
the thesis No C is A, on the strength of the data No B is A, AIL C
is B. (1) He may use a reductio ad impossibile: ‘If some C is A,
then since all C is B, some B will be A. But in fact no B is A.
Therefore Some C is A must be false, and No C is A true.’ Now,
A. maintains, a casual hearer, hearing the conclusion drawn that
some B is A, and knowing that no B is A, will simply say ‘one of
your premisses must have been wrong’ (Pr—-3). Only a second
disputant, interested in contradicting the thesis which was being
proved by the reductio, i.e. in maintaining that some C is A (*4o-
by), will make the objection ‘Some B is A is no doubt false, but
not because Some C is A is false’. (2) The first disputant may
infer ostensively: ‘No B is A, All C is B, Therefore no C is A’,
and this gives no scope for the objection οὐ παρὰ τοῦτο, because
the ostensive proof, unlike the reductio, does not use as a premiss
the proposition Some C is A, which the second disputant is main-
taining in opposition to the first (63-4).
bi-3. τῇ εἰς τὸ ἀδύνατον... ἐν τῇ δεικνούσῃ, sc. ἀποδείξει (cf.
62629).
8-9. ἀναιρεθείσης γάρ. . . συλλογισμός. ἡ θέσις means, as
usual in A. (cf. P14, 6622, 8) the assumption, and 6 πρὸς ταύτην
συλλογισμός is ‘the syllogism related to it’, i.e. based on it.
15-16. ὅπερ εἴρηται... Τοπικοῖς, 1.6. in Soph. El. 167%21-36
(cf. 168b22—5, 181*31—5).
17-19. olov εἰ... ἀδύνατον. Heath thinks that this ‘may point
to some genuine attempt to prove the incommensurability of the
diagonal by means of a real "infinite regression" of Zeno's type'
(Mathematics in Aristotle, 30-3). But it is equally possible that
the example A. takes is purely imaginary.
18-19. τὸν Ζήνωνος Adyov .. . κινεῖσθαι, For the argument
cf. Phys. 233?21-3, 239^5-240*18, 263*4-11.
24-8. olov εἰ... ὑπόθεσιν. If we assume that B is A, Γ is B,
and 4 is I’, and if not only ‘4 is A’ but also ‘4 is B' is false, the
cause of the falsity of ‘4 is A’ is to be found not in the falsity
of ‘Bis A’ but in that of ‘is B' or in that of ‘dis I".
468 COMMENTARY
66*5. τὸ ἀδύνατον, sc. that 4 is A.
5-6. ὁμοίως 86 . . . ὄρους, i.e. if we had assumed that B is
4, and 4 is E, and E is Z, the impossible conclusion ‘B is Z'
might remain.
7. τούτου, the assumption that B is A.
8-15. ἢ τὸ μὴ ὄντος... δυεῖν; For ἢ introducing the answer
to a suggestion cf. An. Post. 9952, Soph. El. 17725, 178431.
13-15. olov τὰς παραλλήλους... δυεῖν. As Heiberg (Abh.
zur Gesch. d. Math. Wissenschaften, xviii. 18-19) remarks, the first
conditional clause refers to the proposition which appears as
Euc. i. 28 (‘if a straight line falling on two straight lines makes the
exterior angle equal to the interior and opposite angle on the
same side of the straight line . . . the straight lines will be parallel’),
while the second refers to Euc. i. 27 (‘if a straight line falling on
two straight lines makes the alternate angles equal, the straight
lines will be parallel, since only in some pre-Euclidean proof
of this proposition, not in the proof of i. 28, can the sum of the
angles of a triangle have played a part. Cf. 6544-7 n.
16-24. Ὁ δὲ ψευδής ... ψεῦδος. Chapter 18 continues the
treatment of the subject dealt with in the previous chapter, viz.
the importance of finding the premiss that is really responsible
for the falsity of a conclusion; if the premisses that immediately
precede the conclusion have themselves been derived from prior
premisses, at least one of the latter must be false.
19-20. ἐξ ἀληθῶν... συλλογισμός refers back to 53*11-25.
CHAPTERS 19, 20
Devices to be used against an opponent in argument
66°25. To guard against having a point proved against us we
should, when the arguer sets forth his argument without stating
his conclusions, guard against admitting premisses containing the
same terms, because without a middle term syllogism is impossible.
How we ought to look out for the middle term is clear, because we
know what kind of conclusion can be proved in each figure. We
shall not be caught napping because we know how we are sustain-
ing our own side of the argument.
33. In attack weshould try to conceal what in defence we should
guard against. (1) We should not immediately draw the conclu-
sions of our prosyllogisms. (2) We should ask the opponent to
admit not adjacent premisses but those that have no common
term. (3) If the syllogism has one middle term only, we should
start with it and thus escape the respondent's notice.
II. 17. 6685 — 20. 66517 469
bg. Since we know what relations of the terms make a
syllogism possible, it is also clear under what conditions refutation
is possible. If we say Yes to everything, or No to one question
and Yes to another, refutation is possible. For from such admis-
sions a syllogism can be made, and if its conclusion is opposite to
our thesis we shall have been refuted.
11. If we say No to everything, we cannot be refuted ; for there
cannot be a syllogism with both premisses negative, and therefore
there cannot be a refutation ; for if there is a refutation there must
be a syllogism, though the converse is not true. So too if we make
no universal admission.
66%25~32 may be compared with the treatment of the same
subject in Top. viii. 4, and 66353-53 with Top. viii. 1-3.
66*27-8. ἐπειδήπερ ἴσμεν . . . γίνεται, cf. 40530-41220.
29-32. ws δὲ δεῖ... λόγον. To take two examples given by
Pacius, (1) if the respondent is defending a negative thesis, he need
not hesitate to admit two propositions which have the same
predicate, since the second figure cannot prove an affirmative
conclusion. (2) If he is defending a particular negative thesis
(Some S is not P), he should decline to admit propositions of the
form All M is P, All S is M, since these will involve the conclusion
All S is P. We shall not be caught napping because we know
the lines on which we are conducting our defence (πῶς ὑπέχομεν
τὸν λόγον). ὑπέχωμεν, ‘how we are to defend our thesis’, would
perhaps be more natural, and would be an easy emendation.
37. ἄμεσα here has the unusual but quite proper sense 'pro-
positions that have no middle term in common'. This reading,
as Waitz observes, is supported by P.’s phrase ἀσυναρτήτους εἶναι
τὰς προτάσεις (460. 28).
bx-3. κἂν δι’ ἑνὸς, . . ἀποκρινόμενον. A. has in mind an
argument in the first figure. If we want to make the argument
as clear as possible we shall either begin with the major and say
‘A belongs to B, B belongs to C, Therefore A belongs to C’, or
with the minor and say 'C is B, B is A, Therefore C is A'. There-
fore if we want to make the argument as obscure as possible we
shall avoid these methods of statement and say either 'B belongs
to C, A belongs to B, Therefore A belongs to C', or 'B is A,
C is B, Therefore C is A’.
4-17. ᾿Επεὶ δ᾽... συλλογισμοῦ. Chapter 20 is really continuous
with that which precedes. A. returns to the subject dealt with
in the first paragraph of the latter, viz. how to avoid making
admissions that will enable an opponent to refute our thesis. An
470 COMMENTARY
elenchus is a syllogism proving the contradictory of a thesis that
has been maintained (bir). Therefore if the maintainer of the
thesis makes no affirmative admission, or if he makes no universal
admission, he cannot be refuted, because a syllogism must have
at least one affirmative and one universal premiss, as was main-
tained in i. 24.
66^9-10. εἰ τὸ κείμενον . . . συμπεράσματι. ἐναντίον is used
here not in the strict sense of ‘contrary’, but in the wider sense
of 'opposite'. A thesis is refuted by a syllogism which proves
either its contrary or its contradictory.
I2-13. οὐ yap... ὄντων, cf. 4156.
I4-15. εἰ μὲν yap... ἔλεγχον. The precise point of this is
not clear. A. may only mean that every refutation is a syllogism
but not vice versa, since a refutation presupposes the maintenance
of a thesis by an opponent. Or he may mean that there is not
always, answering to a syllogism in a certain figure, a refutation
in the same figure, since, while the second figure can prove a
negative, it cannot prove an affirmative, and, while the third
figure can prove a particular proposition, it cannot prove the
opposite universal proposition.
I5-17. ὡσαύτως δέ... συλλογισμοῦ, cf. 4156-27.
CHAPTER 21
How ignorance of a conclusion can coexist with knowledge of the
premisses
66018. As we may err in the setting out of our terms, so may
we in our thought about them. (1) If the same predicate belongs
immediately to more than one subject, we may know it belongs
to one and think it does not belong to the other. Let both B and
C be A, and D be both B and C. If one thinks that all B is A and
all D is B, and that no C is A and all D is C, one will both know
and fail to know that D is A.
26. (2) If A belongs to B, B to C, and C to D, and someone
supposes that all B is A and noC is A, he will both know that all
D is A and think it is not.
3o. Does he not claim, then, in case (2) that what he knows he
does not think? He knows in a sense that A belongs to C through
the middle term B, knowing the particular fact by virtue of his
universal knowledge, so that what in a sense he knows, he main-
tains that he does not even think; which is impossible.
34- In case (1) he cannot think that all B is A and noC is A,
II. 20. 669-17 471
and that all D is B and all D is C. To do so, he must be having
wholly or partly contrary major premisses. For if he supposes
that everything that is B is A, and knows that D is B, he knows
that D is A. And again if he thinks that nothing that is C is A,
he thinks that no member of a class (C), one member of which
(D) is B, is A. And to think that everything that is D has a
certain attribute, and that a particular thing that is B has it not,
is wholly or partly self-contrary.
67*5. We cannot think thus, but we may think one premiss
about each of the middle terms, or one about one and both about
the other, e.g. that all B is A and all D is B, and that no C is A.
8. Then our error is like that which arises about particular
things in the following case. If all B is A and allC is B, all C will
be A. If then one knows that all that is B is A, one knows that
C is A. But one may not know that C exists, e.g. if A is ‘having
angles equal to two right angles', B triangle, and C a sensible
triangle. If one knows that every triangle has angles equal to two
right angles but does not think that C exists, one will both know
and not know the same thing. For 'knowing that every triangle
has this property’ is ambiguous; it may mean having the universal
knowledge, or having knowledge about each particular instance.
It is in the first sense that one knows that C has the property,
and in the second sense that one fails to know it, so that one is
not in two contrary states of mind about C.
21. This is like the doctrine of the Meno that learning is
recollecting. We do not know the particular fact beforehand ; we
acquire the knowledge at the same moment as we are led on to the
conclusion, and this is like an act of recognition. There are things
we know instantaneously, e.g. we know that a figure has angles
equal to two right angles, once we know it is a triangle.
27. By universal knowledge we apprehend the particulars,
without knowing them by the kind of knowledge appropriate to
them, so that we may be mistaken about them, but not with an
error contrary to our knowledge ; wehave the universal knowledge,
we err as regards the particular knowledge.
30. So too in case (1). Our error with regard to the middle
term C is not contrary to our knowledge in respect of the syllo-
gism ; nor is our thought about the two middle terms self-contrary.
33. Indeed, there is nothing to prevent a man's knowing that
all B is A and all C is B, and yet thinking that C is not A (e.g.
knowing that every mule is barren and that this is a mule, and
thinking that this animal is pregnant); for he does not know that
C is A unless he surveys the two premisses together.
472 COMMENTARY
37. A fortiori a man may err if he knows the major premiss
and not the minor, which is the position when our knowledge is
merely general. We know no sensible thing when it has passed
out of cur perception, except in the sense that we have the
universal knowledge and fossess the knowledge appropriate to the
particular, without exercising it.
b3. For ‘knowing’ has three senses—universal, particular, and
actualized—and there are three corresponding kinds of error.
Thus there is nothing to prevent our knowing and being in error
about the same thing, only not so that one is contrary to the
other. This is what happens where one knows both premisses and
has not studied them before. When a man thinks the mule is
pregnant he has not the actual knowledge that it is barren, nor is
his error contrary to the knowledge he has; for the error contrary
to the universal knowledge would be a belief reached by syllogism.
12. A man who thinks (a) that to be good is to be evil is think-
ing (b) that the same thing is being good and being evil. Let
being good be A, being evil B, being good C. He who thinks that
B is the same as C will think that C is B and B is A, and therefore
also that C is A. For just as, if B had been true of that of which C
is true, and A true of that of which B is true, A would have been
true of that of which C is true, so too one who believed the first two
of these things would believe the third. Or again, just as, if C
is the same as B, and B as A,C is the same as A, so too with the
believing of these propositions.
22. Thus a man must be thinking (δ) if he is thinking (a). But
presumably the premiss, that a man can think being good to be
being evil, is false; a man can only think that per accidens (as
may happen in many ways). But the question demands better
treatment.
A.’s object in this chapter is to discuss various cases in which
it seems at first sight as if a man were at the same time knowing
a certain proposition and thinking its opposite—which would be
a breach of the law of contradiction, since he would then be
characterized by opposite conditions at the same time. In every
case, A. maintains, he is no? knowing that B is A and thinking
that B is not A, in such a way that the knowing is opposite to and
incompatible with the thinking.
Maier (ii. a. 434 n. 3) may be right in considering ch. 21 a later
addition, especially in view of the close parallelism between
67*8-26 and An. Post. 71*17-30. Certainly the chapter has no
close connexion with what precedes or with what follows.
II. 21-2 473
A. considers first (6620-6) a case in which an attribute A
belongs directly both to B and to C, and both B and C belong
to all D. Then if some one knows (622; in 524 A. says ‘thinks’,
and the chapter is somewhat marred by a failure to distinguish
knowledge from true opinion) that all B is A and all D is B,
and thinks that no C is A and all DisC, he will be both knowing
and failing to know an identical subject D in respect to its
relation to an identical attribute A. The question is whether
this is possible.
A. turns next (26-34) to a case in which not two syllogisms
but one sorites is involved. If all B is A, and all C is B, and all
D is C, and one judged that all B is A but also that no C is A,
one would at the same time know (A. again fails to distinguish
knowledge from true opinion) that all D is A (because all B is A,
all C is B, and all D is C) and judge that no D is A (because one
would be judging that no C is A and that all D is C). The intro-
duction of D here is unnecessary (it is probably due to the presence
of a fourth term D in the case previously considered) ; the question
is whether one can at the same time judge that B is A and C is B,
and that C is not A. Is not one who claims that he can do this
claiming that he can know what he does not even think? Cer-
tainly he knows in a sense that C is A, because this is involved
in the knowledge that all B is A and all C is B. But it is plainly
impossible that one should know what he does not even judge
to be true.
A. now (534-6738) returns to the first case. One cannot, he
says, at the same time judge that all B is A and all D is B, and
that no C is A and all DisC. For then our major premisses must
be ‘contrary absolutely or in part’, i.e. ‘contrary or contradictory’
(cf. ὅλη ψευδής, ἐπί τι ψευδής in 5421-4). A. does not stop to ask
which they are. In fact the major premisses (All B is A, NoC
is A) are only (by implication) contradictory, since No C is A,
coupled with All D is C and All D is B, implies only that some B
is not A, not that no B is A.
But, A. continues (6755-8), while we cannot be believing all four
premisses, we may be believing one premiss from each pair,
or even both from one pair, and one from the other; e.g. we may
be judging that all B is A and all D is B, and that no C is A.
So long as we do not also judge that all D is C and therefore that
no D is A, no difficulty arises.
The error here, says A. (28-21), is like that which arises when
we know a major premiss All B is A, but through failure to
recognize that a particular thing C is B, fail to recognize that it is
474 COMMENTARY
A; ie. the type of error already referred to in 6626-34. In both
cases the thinker grasps a major premiss but through ignorance
of the appropriate minor fails to draw the appropriate conclusion.
If all C is in fact B, in knowing that all B is A one knows by
implication that all C is A, but one need not know it explicitly,
and therefore the knowledge that all B is A can coexist with
ignorance of C's being A, and even with the belief that no C is
A, without involving us in admitting that a man may be in two
opposite states of mind at once.
This reminds A. (221-30) of a famous argument on the subject
of implicit knowledge, viz. the argument in the Meno (81 b-86 b)
where a boy who does not know geometry is led to see the truth
of a geometrical proposition as involved in certain simple facts
which he does know, and Plato concludes that learning is merely
remembering something known in a previous existence. A. does
not draw Plato's conclusion; no previous actual knowledge, he
says, but only implicit knowledge, is required; that being given,
mere confrontation with a particular case enables us to draw the
particular conclusion.
A. now recurs (410-32) to the case stated in 66520-6, where two
terms are in fact connected independently by means of two middle
terms. Here, he says, no more than in the case where only one
middle term is involved, is the error into which we may fall
contrary to or incompatible with the knowledge we possess. The
erroneous belief that no C is A (ἡ κατὰ τὸ μέσον ἀπατή) is not
incompatible with knowledge of the syllogism All B is A, All
D is B, Therefore all D is A (231-2); nor a forttort is belief that
no C is A incompatible with knowledge that all B is A (332-3).
A. now (2333-7) takes a further step. Hitherto (66534-6735) he
has maintained that we cannot at the same time judge that all
B is A and all D is B, and that no C is A and all D is C, because
that would involve us in thinking both that all D is A and that
no D is A. But, he now points out, it is quite possible to know
both premisses of a syllogism and believe the opposite of the con-
clusion, if only we fail to see the premisses in their connexion;
and a fortiort possible to believe the opposite of the conclusion if
we only know one of the premisses (237-9).
A. has already distinguished between ἡ καθόλου ἐπιστήμη,
knowledge of a universal truth, and ἡ καθ᾽ ἕκαστον (#18, 20), ἡ τῶν
κατὰ μέρος (223), OF ἡ οἰκεία (227), knowledge of the corresponding
particular truths. He now adds a third kind, ἡ τῷ ἐνεργεῖν. This
further distinction is to be explained by the reference in *39-2
to the case in which we have already had perceptual awareness
II. 21. 6618-19 475
of a particular but it has passed out of our ken. Then, says A.,
we have ἡ οἰκεία ἐπιστήμη as well as ἡ καθόλου, but not ἡ τῷ
ἐνεργεῖν; i.e. we have a potential awareness that the particular
thing has the attribute in question, but not actual awareness of
this; that comes only when perception or memory confronts us
anew with a particular instance. Thus we may know that all
mules are barren, and even have known this to be true of certain
particular mules, and yet may suppose (as a result of incorrect
observation) a particular mule to be in foal. Such a belief (bro-11)
is not contrary to and incompatible with the knowledge we have.
Contrariety would arise only if we had a syllogism leading to the
belief that this mule is in foal. A., however, expresses himself
loosely ; for belief in such a syllogism would be incompatible not
with belief in the major premiss (ἡ καθόλου, >11) of the true
syllogism but with belief in that whole syllogism. Belief in both
the true and the false syllogism would be the position already
described m 66524-8 as impossible.
From considering whether two opposite judgements can be
made at the same time by the same person, A. passes (67512-26)
to consider whether a self-contradictory judgement, such as
'goodness is badness', can be made. He reduces the second case
to the first, by pointing out that if any one judges that goodness
is the same as badness, he is judging both that goodness 15 badness
and that badness is goodness, and therefore, by a syllogism in
which the minor term is identical with the major, that goodness is
goodness, and thus being himself in incompatible states. The fact
is, he points out, that no one can judge that goodness is badness,
εἰ μὴ κατὰ συμβεβηκός (023-5). By this A. must mean, if he is
speaking strictly, that it is possible to judge, not that that which
is in itself good may per accidens be bad, but that that which is
in itself goodness may in a certain connexion be badness. But
whether this is really possible, he adds, is a question which needs
further consideration.
The upshot of the whole matter is that in neither of the cases
stated in 6620-6, 26-34 can there be such a coexistence of error
with knowledge, or of false with true opinion, as would involve
our being in precisely contrary and incompatible states of mind
with regard to one and the same proposition.
66>18-19. καθάπερ ἐν τῇ θέσει... ἀπατώμεθα. The reference
is to errors in reasoning due to not formulating our syllogism
correctly—the errors discussed in i. 32-44; cf. in particular
47515317 ἀπατᾶσθαι... παρὰ τὴν ὁμοιότητα τῆς TOv ὅρων θέσεως
(where confusion about the quantity of the terms is in question)
476 COMMENTARY
and similar phrases ib. 40-482, 4927-8, bro-z1, 50%11-13. Error
ἐν τῇ θέσει τῶν ὅρων is in general that which arises because the
propositions we use in argument cannot be formulated in one of
the valid moods of syllogism. The kind of error A. is «ow to
examine: is rather loosely described as κατὰ τὴν ὑπόληψιν. It is
error not due to incorrect reasoning, but to belief in a false pro-
position. The general problem is, in what conditions belief in a
false proposition can coexist with knowledge of true premisses
which entail its falsity, without involving the thinker's being
in two opposites states at once.
26. τὰ ἐκ τῆς αὐτῆς συστοιχίας, Le. terms related as super-
ordinates and subordinates.
32. τῇ καθόλου, sc. ἐπιστήμῃ, cf. 67418.
67?12. ἀγνοεῖν τὸ [ ὅτι ἔστιν. ὑπολάβοι. . . dv tis μὴ εἶναι
τὸ Γ (^14—15) is used as if it expressed the same situation, and ἐὰν
εἰδῶμεν ὅτι τρίγωνον (225) as if it expressed the opposite. Thus A.
does not distinguish between (1) not knowing that the particular
figure exists, (2) thinking it does not exist, (3) not knowing that
the middle term is predicable of it. He fails to distinguish two
situations, (2) that in which the particular figure in question is
not being perceived, and we have no opinion about it (expressed
by (r)), (b) that in which it is being perceived but not recognized
to be a triangle (expressed by (3)). The loose expression (2) is
due to A.'s having called the minor term αἰσθητὸν τρίγωνον
instead of αἰσθητὸν σχῆμα. Thus thinking that the particular
figure is not a triangle (one variety of situation (5)) comes to be
expressed as 'thinking that the particular sensible triangle does
not exist'.
17. δυὸ ὀρθαῖς, sc. ἔχει τὰς γωνίας ἴσας.
23. ἅμα τῇ ἐπαγωγῇ, ‘simultaneously with our being led on
to the conclusion’. For this sense cf. A». Post. 71420 ὅτι δὲ τόδε
τὸ ἐν τῷ ἡμικυκλίῳ τρίγωνόν ἐστιν, ἅμα ἐπαγόμενος ἐγνώρισεν (cf.
Top. 111538). There is no reference to induction; the reasoning
involved is deductive.
27. TH... καθόλου, sc. ἐπιστήμῃ, cf. 66532 n.
29. ἀπατᾶσθαι δὲ τὴν κατὰ μέρος. The MSS. have τῇ, but
τήν must be right—‘fall into the particular error’. Cf. An. Post.
7436 ἀπατώμεθα δὲ ταυτὴν τὴν ἀπατήν.
b2. τῷ καθόλου, sc. ἐπίστασθαι, cf. 66532 n.
23. τοῦτο, i.e. that a man can think the same thing to be the
essence of good and the essence of evil. τὸ πρῶτον, i.e. that a man
can think the essence of good to be the essence of evil (b12).
II. 21. 66526 — 67523 477
CHAPTER 22
Rules for the use of convertible lerms and of alternative terms, and for
the comparison of desirable and undesirable objects
67527. (A) (a) When the extreme terms are convertible, the
middle term must be convertible with each of them. For if A is
true of C because B is A and C is B, then if ΑἹ] C is A is convert-
ible, (a) All C is B, All A is C, and therefore all A is B, and (8)
All A is C, All B is A, and therefore all B is C.
32. (b) If no C is A because no B is A and all C is B, then (a)
if No B is A is convertible, all C is B, no A is B, and therefore
no A isC ; (B) if All C is B is convertible, No B is A is convertible;
(y) if No C is A, as well as All C is B, is convertible, No B is A is
convertible. This is the only one of the three conversions which
starts by assuming the converse of the conclusion, as in the case
of the affirmative syllogism.
6823. (B) (a) If A and B are convertible, and so are C and D,
and everything must be either A or C, everything must be either
B or D. For since what is A is B and what is C is D, and every-
thing is either A or C and not both, everything must be either B
or D and not both ; two syllogisms are combined in the proof.
rr. (b) If everything is either A or B, and either C or D, and
not both, then if 4 and C are convertible, so are B and D. For if
any D is not B, it must be A, and therefore C. Therefore it must
be both C and D; which is impossible. E.g. if 'ungenerated' and
‘imperishable’ are convertible, so are ‘generated’ and ‘perishable’.
16. (C) (a) When all B is A, and all C is A, and nothing else
is A, and all C is B, A and B must be convertible; for since A is
predicated only of B and C, and B is predicated both of itself and
of C, B is predicable of everything that is A, except A itself.
21. (b) When all C is A and is B, and C is convertible with B,
all B must be A, because all C is A and all B isC.
25. (1) When of two opposites A is more desirable than B, and
D similarly is more desirable than C, then if A+C is more desir-
able than B-- D, A is more desirable than D. For A is just as
much to be desired as B is to be avoided; and C is just as much to
be avoided as D is to be desired. If then (a) A and D were equally
to be desired, B and C would be equally to be avoided. And there-
fore A+C would be just as much to be desired as B4+ D. Since
they are more to be desired than B+ D, A is not just as much to
be desired as D.
33. But if (b) D were more desirable than A, B would be less to
478 COMMENTARY
be avoided than C, the less to be avoided being the opposite of the
less to be desired. But a greater good-+a lesser evil are more
desirable than a lesser good-+a greater evil ; therefore B-+ D would
be more desirable than A+C. But it is not. Therefore A is more
desirable than D, and C less to be avoided than B.
39. If then every lover in virtue of his love would prefer that
his beloved should be willing to grant a favour (A) and yet not
grant it (C), rather than that he should grant it (D) and yet not
be willing to grant it (B), A is preferable to D. In love, therefore,
to receive affection is preferable to being granted sexual inter-
course, and the former rather than the latter is the object of love.
And if it is the object of love, it is its end. Therefore sexual
intercourse is either not an end or an end only with a view to
receiving affection. And so with all other desires and arts.
The first part of this chapter (67527-6873) discusses a question
similar to that discussed in chs. 5-7, viz. reciprocal proof. But the
questions are not the same. In those chapters À. was discussing
the possibility of proving one of the premisses of an original
syllogism by assuming the conclusion and the converse of the
other premiss; and original syllogisms in all three figures were
considered. Here he discusses the possibility of proving the
converse of one of the propositions of an original syllogism by
assuming a second and the converse of the third, or the converses
of both the others; and only original syllogisms in the first figure
are considered.
The rest of the chapter adds a series of detached rules dealing
with relations of equivalence, alternativeness, predicability, or
preferability, between terms. The last section (68325-57) is dia-
lectical in nature and closely resembles the discussion in Tof.
iii. 1-4.
67527-8. Ὅταν δ᾽... ἄμφω. This applies only to syllogisms in
Barbara (b28-32). A. says émi τοῦ μὴ ὑπάρχειν ὡσαύτως (32), but
this means only that conversion is possible also with syllogisms
in Celarent ; only in one of the three cases discussed in 534-6841
does the conversion assume the converse of the conclusion, as
in the case of Barbara.
32-6833. kai ἐπὶ τοῦ μὴ ὑπάρχειν... συλλογισμοῦ. If we
start as A. does with a syllogism of the form No B is A, ΑἹ] C is
B, Therefore no C is A, only three conversions are possible: (1)
Al C is B, No A is B, Therefore no A isC; (2) All BisC, NoC is
A, Therefore no A is B; (3) All B is C, No A is C, Therefore no
A is B. 34-6 refers to the first of these conversions. 537-8 is
II. 22. 67527 — 68216 479
dificult. The vulgate reading, «ai ef τῷ Β τὸ Γ ἀντιστρέφει, kai
τῷ A ἀντιστρέφει, gives the invalid inference All B is C, No B is
A, Therefore no A is C. We must read either (a) καὶ εἰ τῷ B τὸ
Γ ἀντιστρέφει, kai τὸ A ἀντιστρέφει (or ἀντιστρέψει), or (b) kai εἰ
τὸ Β τῷ Γ ἀντιστρέφει, καὶ τῷ A ἀντιστρέφει (or ἀντιστρέψει), either
of which readings gives the valid inference (2) above. 238-6841 is
also difficult. The vulgate reading καὶ εἰ τὸ Γ πρὸς τὸ A ἀντι-
στρέφει gives the invalid inference All C is B, No A is C, Therefore
no A is B. In elucidating this conversion, A. explicitly assumes
not All C is B, but its converse (ᾧ yàp τὸ B, τὸ I). The passage
is cured by inserting καί in 538; we then get the valid inference
(3) above. The reading thus obtained shows that τὸ I must be
the subject also of the protasis in ^37, and confirms reading (a)
above against reading (5).
On this interpretation, the statement in 6821-3 must be taken
to mean that only the last of the three conversions starts by
converting the conclusion, as both the conversions of the affirma-
tive syllogism did, in 228-32.
6823-16. Πάλιν εἰ... ἀδύνατον. A. here states two rules. If
we describe as alternatives two terms one or other of which must
be true of everything, and both of which cannot be true of any-
thing, the two rules are as follows: (1) If 4 and B are convertible,
and C and D are convertible, then if A and C are alternative,
B and D are alternative (3-8); (2) If A and B are alternative,
and C and D are alternative, then if A and C are convertible,
'B and D are convertible (411-16). A. has varied his symbols by
making B and C change places. If we adopt a single symbolism
for both rules; we may formulate them thus: If A and B are
convertible, and A and C are alternative, then (1a) if C and D
are convertible, B and D are alternative; (2a) if B and D are
alternative, C and D are convertible; so that the second rule is
the converse of the first.
Between the two rules the MSS. place an example (#8-11):
If the ungenerated is imperishable and vice versa, the generated
must be perishable and vice versa. But, as P. saw (469. 14-17),
this illustrates rule (2), not rule (1), for the argument is plainly
this: (Since ‘generated’ and 'ungenerated' are alternatives, and
so are ‘perishable’ and ‘imperishable’>, if 'ungenerated' and
‘imperishable’ are convertible, so are ‘generated’ and ‘perishable’.
Pacius has the example in its right place, after the second rule,
and since he makes no comment on this we may assume that it
stood so in the text he used.
It remains doubtful whether δύο yap συλλογισμοὶ σύγκεινται
480 COMMENTARY
(#10) should come after dua in *8, as Pacius takes it, or after
ἀδύνατον in *16, as P. (469. 18-470. 3) takes it. On the first hypo-
thesis the two arguments naturally suggested by 36-8 are (1)
Since all A is B and all C is D, and everything is A or C, every-
thing is B or D, (2) Since all A is B and all C is D, and nothing
is both A and C, nothing is both B and D. But the second of
these arguments is clearly a bad one, and the arguments intended
must rather be Since A is convertible with B, and C with D,
(1) What must be A or C must be B or D, Everything must be
A or C, Therefore everything must be B or D, (2) What cannot
be both A and C cannot be both B and D, Nothing can be both
A and C, Therefore nothing can be both B and D.
On the second hypothesis the two arguments are presumably
those stated in ?14-15: (1) Since A and B are alternative, any
D that is not B must be A, (2) Since A and C are convertible,
any D that is A must be C—which it cannot be, since C and D
are alternative; thus all D must be B.
On the whole it seems best to place the words where Pacius
places them, and adopt the second interpretation suggested on
that hypothesis.
16-21. Ὅταν 86 ...A. The situation contemplated here is that
in which B is the only existing species of a genus A which is
notionally wider than B, and C is similarly the only subspecies
of the species B. Then, though A is predicable of C as well as
of B, it is not wider than but coextensive with B, and B will be
predicable of everything of which A is predicable, except A
itself (220-1). It is not predicable of A, because a species is not
predicable of its genus (Cat. 2521). This is not because a genus is
wider than any of its species; for in the present case it is not
wider. It is because τὸ εἶδος τοῦ γένους μᾶλλον οὐσία (Cat. 2522), so
that in predicating the spécies of the genus you would be reversing
the natural order of predication, as you are when you say 'this
white thing is a log' instead of 'this log is white'. The latter is
true predication, the former predication only in a qualified sense
(An. Post. 8341-18).
21-5. πάλιν ὅταν... B. This section states a point which
is very simple in itself, but interesting because it deals with
the precise situation that arises in the inductive syllogism
(915-24). The point is that when all C is A, and all C is B, and
C is convertible with B, then all B is A.
39-41. εἰ δὴ... ἢ τὸ χαρίζεσθαι. With ἕλοιτο we must 'under-
stand’ μᾶλλον.
56-7. καὶ γὰρ... οὕτως, i.e. in any system of desires, and in
II. 22. 68:16 —55 481
particular in the pursuit of any art, there is a supreme object of
desire to which the other objects of desire are related as means
to end. Cf. Eth. Nic. i. 1.
CHAPTER 23
Induction
6858. The relations of terms in respect of convertibility and of
preferability are now clear. We next proceed to show that not
only dialectical and demonstrative arguments proceed by way of
the three figures, but also rhetorical arguments and indeed any
attempt to produce conviction. For all conviction is produced
either by syllogism or by induction.
15. Induction, i.e. the syllogism arising from induction, con-
sists of proving the major term of the middle term by means of
the minor. Let A be ‘long-lived’, B 'gall-less', C the particular
long-lived animals (e.g. man, the horse, the mule). Then all C is
A, and all C is B, therefore if C is convertible with B, all B must
be A, as we have proved before. C must be the sum of αὐ the
particulars ; for induction requires that.
30. Such a syllogism establishes the unmediable premiss; for
where there is a middle term between two terms, syllogism con-
nects them by means of the middle term; where there is not, it
connects them by induction. Induction is in a sense opposed to
syllogism ; the latter connects major with minor by means of the
middle term, the former connects major with middle by means of
the minor. Syllogism by way of the middle term is prior and more
intelligible by nature, syllogism by induction is more obvious to us.
In considering the origin of the use of ἐπαγωγή as a technical
term, we must take account of the various passages in which
A. uses ἐπάγειν with a logical significance. We must note (1) a
group of passages in which ἐπάγειν is used in the passive with a
personal subject. In An. Post. 71220 we have ὅτι δὲ τόδε τὸ ἐν
τῷ ἡμικυκλίῳ τρίγωνόν ἐστιν, ἅμα ἐπαγόμενος ἐγνώρισεν. That
ἐπαγόμενος is passive is indicated by the occurrence in the same
passage (ib. 24) of the words πρὶν δ᾽ ἐπαχθῆναι 7) λαβεῖν συλλογισμὸν
τρόπον μέν τινα ἴσως φατέον ἐπίστασθαι, τρόπον δ᾽ ἄλλον ov. Again
in An. Post. 8155 we have ἐπαχθῆναι δὲ μὴ ἔχοντας αἴσθησιν
ἀδύνατον.
P. interprets ἐπαγόμενος in 71221 as προσβάλλων αὐτῷ κατὰ τὴν
αἴσθησιν (17. 12, cf. 18. 13). But (a) in the other two passages
ἐπάγεσθαι clearly refers to an inferential process, and (b) in the
4985 11
482 COMMENTARY
usage of ἐπάγειν in other authors it never seems to mean ‘to lead
up to, to confront with, facts’, while if we take ἐπάγεσθαι to mean
‘to be led on to a conclusion’, it plainly falls under sense I. 10
recognized by L. and S., ‘in instruction or argument, lead on’,
and has affinities with sense I. 3, ‘lead on by persuasion, influence’.
(2) With this use is connected the use of ἐπάγειν without an
object—An. Post. 91°15 ὥσπερ οὐδ᾽ ὁ ἐπάγων ἀποδείκνυσιν (cf.
ib. 33), 92337 ὡς ὁ ἐπάγων διὰ τῶν καθ᾽ ἕκαστα δήλων ὄντων, Top.
10811 οὐ γὰρ padidy ἐστιν ἐπάγειν μὴ εἰδότας τὰ ὅμοια, 15624 ἐπάγοντα
ἀπὸ τῶν καθ᾽ ἕκαστον ἐπὶ τὸ καθόλου, 157234 ἐπάγοντος ἐπὶ πολλῶν,
Soph. El., 174234 ἐπαγαγόντα τὸ καθόλου πολλάκις οὐκ ἐρωτητέον
ἀλλ᾽ ὡς δεδομένῳ χρηστέον, Rhet. 135658 ἀνάγκη (ἢ) συλλογιζόμενον
7j ἐπάγοντα δεικνύναι ὁτιοῦν. The passages cited under (1) definitely
envisage two persons, of whom one leads the other on to a con-
clusion. In the passages cited under (2) there is no definite
reference to a second person, but there is an implicit reference
to a background of persons to be convinced. This usage is related
to the first as ἐπάγειν in the sense of ‘march against’ is related to
ἐπάγειν in the sense of ‘lead on (trans.) against’ (both found under
L. and S. I. 2b.
(3) In one passage we find ἐπάγειν τὸ καθόλου-- ΤῸΡ. 10810
τῇ καθ᾽ ἕκαστα ἐπὶ τῶν ὁμοίων ἐπαγωγῇ τὸ καθόλου ἀξιοῦμεν ἐπάγειν.
(In Soph. El. 17434, cited under (2), it is possible that τὸ καθόλου
should be taken as governed by ἐπαγαγόντα as well as by ἐρωτη-
Téov.) This should probably be regarded as a development from
usage (2)—írom ‘infer (abs.) inductively’ to ‘infer the universal
inductively’.
(4) In Top. 159718 we find ἐπαγαγεῖν τὸν λόγον, a usage which
plainly has affinities with usages (1), (2), (3)-
(5) There is a usage of ἐπάγεσθαι (middle) which has often been
thought to be the origin of the technical meaning of ἐπαγωγή,
viz. its usage in the sense of citing, adducing, with such words
as μάρτυρας, μαρτύρια, εἰκόνας (L. and S. II. 3). A. has ἐπάγεσθαι
ποιητήν (Met. 9958), and ἐπαγόμενοι καὶ τὸν Ὅμηρον (Part. An.
673*15), but apparently never uses the word of the citation of
individual examples to prove a general conclusion. There is,
however, a trace of this usage in A.’s use of ἐπακτικός, ἐπακτικῶς.
In An. Post. 77533 ἐπακτικὴ πρότασις and in Phys. 21058 ἐπακτικῶς
σκοποῦσιν the reference is to the examination of individual
instances rather than to the drawing of a universal conclusion.
The same may be true of the famous reference to Socrates as
having introduced ἐπακτικοὶ λόγοι (Met. 1078528); for in fact
Socrates adduced individual examples much more often to refute
II. 23 483
a general proposition than he used them inductively, to establish
such a proposition.
Of the passages in which the word ἐπαγωγή itself occurs, many
give no definite clue to the precise shade of meaning intended;
but many do give such a clue. In most passages ἐπαγωγή clearly
means not the citation of individual instances but the advance
from them to a universal; and this has affinities with senses (1),
(2), (3), (4) of ἐπάγειν, not with sense (5). E.g. Top. 105213 ἐπαγωγὴ
ἡ ἀπὸ τῶν καθ᾽ ἕκαστα ἐπὶ τὸ καθόλου ἔφοδος, Am. Post. 8151 ἡ
ἐπαγωγὴ ἐκ τῶν κατὰ μέρος, An. Pr. 68b15 ἐπαγωγή ἐστι... τὸ διὰ
τοῦ ἑτέρου θάτερον ἄκρον τῷ μέσῳ συλλογίσασθαι. But occasionally
ἐπαγωγή seems to mean ‘adducing of instances’ (corresponding to
sense (5) of émáyew)—T op. 108510 τῇ καθ᾽ ἕκαστα ἐπὶ τῶν ὁμοίων
ἐπαγωγῇ τὸ καθόλου ἀξιοῦμεν ἐπάγειν, Soph. El. 174236 διὰ τὴν τῆς
ἐπαγωγῆς μνείαν, Cat. 13537 δῆλον τῇ καθ᾽ ἕκαστον ἐπαγωγῇ, Met.
1048235 δῆλον δ᾽ ἐπὶ τῶν καθ᾽ ἕκαστα τῇ ἐπαγωγῇ ὃ βουλόμεθα λέγειν.
(The use of ἐπαγωγή in 673223 corresponds exactly to that of
ἐπαγόμενος in An. Post. 71421. Here, asin Top. 111538, a deductive,
not an inductive, process is referred to.)
The first of these two usages of ἐπαγωγή has its parallels in
other authors (L. and S. sense 5 a), and has an affinity with the
use of the word in the sense of 'allurement, enticement' (L. and S.
sense 4 a). The second usage seems not to occur in other authors.
Plato's usage of ἐπάγειν throws no great light on that of A.
The most relevant passages are Pol. 278a ἐπάγειν αὐτοὺς ἐπὶ
τὰ μήπω γιγνωσκόμενα (usage (1) of ἐπάγειν), and Hipp. Maj.
289 b, Laws 823a, Rep. 364 c, Prot. 347 e, Lys. 215 c (usage 5).
ἐπαγωγή occurs in Plato only in the sense of ‘incantation’ (Rep.
364 c, Laws 933 d), which is akin to usage (1) of ἐπάγειν rather than
to usage (5).
It is by a conflation of these two ideas, that of an advance in
thought (without any necessary implication that it is an advance
from particular to universal) and that of an adducing of particular
instances (without any necessary implication of the drawing of
a positive conclusion), that the technical sense of ἐπαγωγή as
used by A. was developed. A.'s choice of a word whose main
meaning is just ‘leading on’, as his technical name for induction, is
probably influenced by his view that induction is πιθανώτερον
than deduction (Top. 105#16).
A. refers rather loosely in the first paragraph to three kinds of
argument—demonstrative and dialectical argument on the one
hand, rhetorical on the other. His view of the relations between
the three would, if he were writing more carefully, be stated as
484 COMMENTARY
follows: The object of demonstration is to reach knowledge, or
science ; and to this end (a) its premisses must be known, and (6)
its procedure must be strictly convincing; and this implies that
it must be in one of the three figures of sylogism—preferably in
the first, which alone is for A. self-evidencing. The object of
dialectic and of rhetoric alike is to produce conviction (πίστις);
and therefore (a) their premisses need not be true; it is enough if
they are ἔνδοξοι, likely to win acceptance; and (b) their method
need not be the strict syllogistic one. Many of their arguments
are quite regular syllogistic ones, formally just like those used in
demonstration. But many others are in forms that are likely to
produce conviction, but can be logically justified only if they can
be reduced to syllogistic form; and it is this that A. proposes to
do in chs. 23-7. Thus these chapters form a natural appendix to
the treatment of syllogism in I. 1-II. 22.
The distinction between dialectical and rhetorical arguments
is logically unimportant. They are of the same logical type; but
when used in ordinary conversation or the debates of the schools
A. calls them dialectical, when used in set speeches he calls them
rhetorical.
Conviction, says A. (613-14), is always produced either by
syllogism or by induction; and this statement is echoed in many
other passages. But besides these there are processes akin to
syllogism (εἰκός and σημεῖον, ch. 27) or to induction (παράδειγμα,
ch. 24). And with them he discusses reduction (ch. 25) and
objection (ch. 26), which are less directly connected with his theme
—discusses them because he wants to refer to all the kinds of
argument known to him.
Induction and ‘the syllogism from induction’ (i.e. the syllogism
we get when we cast an inductive argument into syllogistic form)
‘infer that the major term is predicable of the middle term, by
means of the minor term’ (615-17). The statement is paradoxical ;
it is to be explained by noticing that the terms are named with
reference to the position they would occupy in a demonstrative
syllogism (which is the ideal type of syllogism). A. bases his
example of the inductive syllogism on a theory earlier held, that
the absence of a gall-bladder is the cause of long life in animals
(Part. An. 677830 διὸ καὶ χαριέστατα λέγουσι τῶν ἀρχαίων οἱ
φάσκοντες αἴτιον εἶναι τοῦ πλείω ζῆν χρόνον τὸ μὴ ἔχειν χολήν).
A. had his doubts about the completeness of this explanation;
in An. Post. 9954-7 he suggests that it may be true for quadrupeds
but that the long life of birds is due to their dry constitution or to
some third cause. The theory serves, however, to illustrate his
II. 23. 6820-3 485
point. In the demonstrative syllogism, that which explains
facts by their actual grounds or causes, the absence of a gall-
bladder is the middle term that connects long life with the
animal species that possess long life. Thus the inductive syllogism
which aims at showing not why certain animal species are long-
lived but that all gall-less animals are long-lived, is said to prove
the major term true of the middle term (not, of course, its own
middle but that of the demonstrative syllogism) by means of the
minor (not its own minor but that of the demonstrative syllogism).
Now if instead of reasoning demonstratively ‘All B is A, All C is
B, Therefore all C is A’, we try to prove from All C is A, AIC
is B, that all B is A, we commit a fallacy, from which we can
save ourselves only if in addition we know that all B is C (b23 εἰ
οὖν ἀντιστρέφει τὸ Γ τῷ B καὶ μὴ ὑπερτείνει τὸ μέσον, i.e. if B, the
μέσον of the demonstrative syllogism, is not wider than C).
68>20. ἐφ᾽ à δὲ Γ τὸ καθ᾽ ἕκαστον μακρόβιον. In 527-9 A.
says that, to make the inference valid, Γ᾿ must consist of all
the particulars. Critics have pointed out that in order to prove
that all gall-less animals are long-lived it is not necessary to
know that all long-lived animals fall within one or another of the
species examined, but only that all gall-less animals do. Accord-
ingly Grote (Arist. 187 n. b) proposed to read dxoAov for μακρό-
βιον, and M. Consbruch (Arch. f. Gesch. d. Phil. v (1892), 310)
proposed to omit μακρόβιον. Grote's emendation is not probable.
Consbruch’s is more attractive, since μακρόβιον might easily be
a gloss; and it derives some support from P.'s paraphrase, which
says (473. 16-17) simply τὸ Γ οἷον κόραξ xai ὅσα τοιαῦτα. λέγει οὖν
ὅτι ὁ κόραξ καὶ ὁ ἔλαφος ἄχολα μακρόβιά εἰσιν. But P.’s change of
instances shows that he is paraphrasing very freely, and therefore
that his words do not throw much light on the reading. The
argument would be clearer if μακρόβιον, which is the major term A,
were not introduced into the statement of what I" stands for.
But the vulgate reading offers no real difficulty. In saying é$'
ᾧ δὲ Γ τὸ καθ᾽ ἕκαστον μακρόβιον, A. does not say that I stands for
all μακρόβια, but only that it stands for the particular μακρόβια
in question, those from whose being μακρόβια it is inferred that all
ἄχολα are μακρόβια.
21-3. τῷ δὴ Γ΄... τῷ Γ. The structure of the whole passage
b21-7 shows that in the present sentence A. must be stating the
data All C is A, All C is B, and in the next sentence adding
the further datum that 'All C is B' is convertible, and drawing the
conclusion All B is A. Clearly, then, he must not, in this sentence,
state the first premiss in a form which already implies that all
486 COMMENTARY
B is A, so that πᾶν yap τὸ ἄχολον μακρόβιον cannot be right; we
must read I’ for dyoAov. Finding μακρόβιον (which is what A
stands for) substituted by A. for A in >22, an early copyist has
rashly substituted dyoAov for D; but I survives (though deleted)
in n after ἄχολον, and Pacius has the correct reading. Instead of
the colon before and the comma after πᾶν... μακρόβιον printed
in the editions, we must put brackets round these words.
Tredennick may be right in suggesting the omission of way...
μακρόβιον, but I hesitate to adopt the suggestion in the absence
of any evidence in the MSS.
24-9. δέδεικται yap... πάντων. A. has shown in ?21-4 that
if all C is A, and all C is B, and C (τὸ ἄκρον of 526, i.e. the term
which would be minor term in the corresponding demonstrative
syllogism All B is A, AllC is B, Therefore all C is A) is convertible
with B (θάτερον αὐτῶν of 526), A will be true of all B (rà ἀντι-
στρέφοντι of 526, the term convertible with C). But of course to
require that C must be convertible with B is to require that C
must contain all the things that in fact possess the attribute B.
26. τὸ ἄκρον, i.e. C, the minor term of the afodeictic syllogism.
In 534, 35 τὸ ἄκρον is A, the major term of both syllogisms.
27-8. Set δὲ... συγκείμενον, ‘we must presume C to be the
class consisting of αἰ the particular species of gall-less animals’.
For νοεῖν with double accusative cf. L. and S. s.v. νοέω I. 4.
Jt may seem surprising that A. should thus restrict induction
(as he does, though less deliberately, in 69*17 and in An. Post.
92338) to its least interesting and important kind; and it is
certain that in many other passages he means by it something
quite different, the intuitive induction by which (for instance)
we proceed from seeing that a single instance of a certain geo-
metrical figure has a certain attribute to seeing that every
instance must have it. It is certain too that in biology, from
which he takes his example here, nothing can be done by the
mere use of perfect induction ; imperfect induction is what really
operates, and only probable results can be obtained. The present
chapter must be regarded as a tour de force in which A. tries at
all costs to bring induction into the form of syllogism ; and only
perfect induction can be so treated. It should be noted too that
he does not profess to be describing a proof starting from observa-
tion of particular instances. He knows well that he could not
observe all the instances, e.g., of man, past, present, and future.
The advance from seeing that this man, that man, etc., are both
gall-less and long-lived has taken place before the induction here
described takes place, and has taken place by a different method
II. 23. 6824-37 487
(imperfect induction). What he is describing is a process in
which we assume that all men, all horses, all mules are gall-less
and long-lived and infer that all gall-less animals are long-lived.
And while he could not think it possible to exhaust in observation
all men, all horses, all mules, believing as he does in a limited
number of fixed animal species he might well think it possible
to exhaust all the classes of gall-less animals and find that they
were all long-lived. The induction he is describing is not one
from individuals to their species but from species to their genus.
This is so in certain other passages dealing with induction (e.g.
Top. 105413-16, Met. 1048435-64), but in others induction from
individual instances is contemplated (e.g. Top. 1033-6, 105%25-9,
Rhet. 1398*32-*19). In describing induction as proceeding from
τὸ καθ᾽ ἕκαστον to τὸ καθόλου he includes both passage from indi-
viduals to their species and passage from species to their genus.
30-1. Ἔστι δ᾽... προτάσεως, i.e. such a syllogism establishes
the proposition which cannot be the conclusion of a demonstrative
syllogism but is its major premiss, neither needing to be nor
capable of being mediated by demonstration.
36-7. ἡμῖν δ᾽... ἐπαγωγῆς, i.e. induction, starting as it does
not from general principles which may be difficult to grasp but
from facts that are nearer to sense, is more immediately con-
vincing. Nothing could be more obvious than the sequence of
the conclusion of a demonstration from its premisses, but the
difficulty in grasping its premtsses may make us more doubtful
of the truth of its conclusion than we are of the truth of a con-
clusion reached from facts open to sense.
CHAPTER 24
Argument from an example
68538. It is example when the major term is shown to belong
to the middle term by means of a term like the minor term. We
must know beforehand both that the middle term is true of the
minor, and that the major term is true of the term like the minor.
Let A be evil, B aggressive war on neighbours, C that of Athens
against Thebes, D that of Thebes against Phocis. If we want to
show that C is A, we must first know that B is A; and this we
learn from observing that e.g. Dis A. Then we have the syllogism
‘Bis A, C is B, Therefore C is A’.
6927. That C is B, that D is B, and that D is A, is obvious;
that B is A is proved. by means of D. More than one term like C
may be used to prove that B is A.
488 COMMENTARY
13. Example, then, is inference from part to part, when both
fall under the same class and one is well known. Induction
reasons from all the particulars and does not apply the conclusion
to a new particular ; example does so apply it and does not reason
from all the particulars.
The description of παράδειγμα in the’ first sentence of the
chapter would be very obscure if that sentence stood alone.
But the remainder of the chapter makes it clear that by παράδειγμα
A. means a combination of two inferences. If we know that two
particular things C (τὸ τρίτον) and D (τὸ ὅμοιον τῷ τρίτῳ) both have
the attribute B (τὸ μέσον), and that D also has the attribute A
(τὸ ἄκρον or πρῶτον) (6927-10), we ean reason as follows: (1) D is
A, D is B, Therefore B is A, (2) Bis A, C is B, Therefore C is A.
The two characteristics by which A. distinguishes example from
induction (69216—19) both imply that it is not scientific but purely
dialectical or rhetorical in character; in its first part it argues
from one instance, or from several, not from all, and in doing so
commits an obvious fallacy of illicit minor; and to its first part,
in which a generalization is reached, it adds (in its second part)
an application to a particular instance. Its real interest is ποῖ,
like that of science, in generalization, but in inducing a particular
belief, e.g. that a particular aggressive war will be dangerous to
the country that wages it.
68538. τὸ ἄκρον, ie. the major term (A); so in 69*13, 17. τὸ
ἄκρον ib. 18 is the minor term (C).
69:2: Θηβαίους πρὸς Φωκεῖς. This refers to the Third Sacred
War, in 356—346, referred to also in Pol. 1304212. The argument
is one such as Demosthenes might have used in opposing the
Spartan attempt in 353 to induce Athens to attack Thebes in
the hope of recovering Oropus (cf. Dem. "Yep τῶν Μεγαλοπολιτῶν)
12-13. ἡ πίστις... ἄκρον. Waitz argues that if τὸ ἄκρον here
meant the major term, i.e. if the proposition referred to were that
the major term belongs to the middle term, A. would have said
ἡ πίστις γίνοιτο τοῦ ἄκρου πρὸς τὸ μέσον. That is undoubtedly A.'s
general usage, the term introduced by πρός being the subject of
the proposition referred to; cf. 26217, 27226, 28417, >s, 40539, 4141,
45°5, 5834. Waitz supposes therefore that A. means the proof
. that the middle term belongs to the minor. But there is no proof
of this; it is assumed as self-evident (68539-40, 6937-8). A. must
mean the proof connecting the middle term (as subject) with the
major (as predicate) ; cf. 217-18.
17. ἐδείκνυεν, i.e. ‘shows, as we saw in ch. 23’.
II. 24. 68538 —69*17 489
CHAPTER 25
Reduction of one problem to another
69°20. Reduction occurs (1) when it is clear that the major
term belongs to the middle term, and less clear that the middle
term belongs to the minor, but that is as likely as, or more likely
than, the conclusion to be accepted; or (2) if the terms inter-
mediate between the minor and the middle term are few; in any
of these cases we get nearer to knowledge.
24. (1) Let A be ‘capable of being taught’, B ‘knowledge’, I
‘justice’. B is clearly A; if ‘is B' is as credible as, or more
credible than, '7' is A’ we come nearer to knowing that Tis A,
by having taken in the premiss ‘B is A’.
29. (2) Let 4 stand for being squared, E for rectilinear figure,
Z for circle. If there is only one intermediate between E and Z,
in that the circle along with certain lunes is equal to a rectilinear
figure, we shall be nearer to knowledge.
34. When neither of these conditions is fulfilled, that is not
reduction; and when it is self-evident that Γ is B, that is not
reduction, but knowledge.
ἀπαγωγή (simpliciter) is to be distinguished from the more
familiar ἀπαγωγὴ εἰς τὸ ἀδύνατον, but has something in common
with it. In both cases, wishing to prove a certain proposition
and not being able to do so directly, we approach the proof of it
indirectly. In reductio ad impossibile that happens in this way:
having certain premisses from which we cannot prove what we
want to prove, by a first-figure syllogism (which alone is for
A. self-evidencing), we ask instead what we could deduce if the
proposition were not true, and find we can deduce something
incompatible with one of the premisses In reductio (simpliciter)
it happens in this way: we turn away to another proposition
which looks at least as likely to be accepted by the person with
whom we are arguing (ὁμοίως πιστὸν ἢ μᾶλλον τοῦ συμπεράσματος,
421) or likely to be proved with the use of fewer middle terms
(ἂν ὀλίγα ἢ τὰ μέσα, *22), and point out that if it be admitted, the
other certainly follows. If our object is merely success in argu-
ment and if our adversary concedes the substituted proposition,
that is enough. If our object is knowledge, or if our opponent
refuses to admit the substituted proposition, we proceed to try to
prove the latter.
This type of argument might be said to be semi-demonstrative,
490 COMMENTARY
semi-dialectical, inasmuch as it has a major premiss which is
known, and a minor premiss which for the moment is only
admitted. It plays a large part in the dialectical discussions of
the Topics (e.g. 1598-23, 160%11-14). But it also plays a large
part in scientific discovery. It was well recognized in Greek
mathematics; cf. Procl. m Eucl. 212. 24 (Friedlein) ἡ δὲ ἀπαγωγὴ
μετάβασίς ἐστιν ἀπ᾿ ἄλλου προβλήματος 7) θεωρήματος ἐπ᾽ ἄλλο, οὗ
γνωσθέντος ἢ πορισθέντος καὶ τὸ προκείμενον ἔσται καταφανές. In
fact it may be said to be the method of mathematical discovery,
as distinct from mathematical proof.
It is in form a perfect syllogism, but inasmuch as an essential
feature of it is that the minor premiss is not yet known, it belongs
properly not to the main theory of syllogism (to which it is
indifferent whether the premisses are known or not), but to the
appendix (chs. 23-7) of which this chapter forms part. Maier
(ii a. 453 n. 2) suggests that it may be a later addition to this
appendix, and that perhaps its more proper place would be
between chs. 21 and 22. But it seems to go pretty well in its
present place, along with the discussion of the other special types
of argument—induction, example, objection, and enthymeme.
The method is described clearly by Plato (who does not use
the word ἀπαγωγή, but describes the method as that of proof ἐξ
ὑποθέσεως) in Meno 86 e-87 c. It is from there that A. takes his
example, ‘virtue is teachable if it is knowledge’; and Plato also
anticipated A. (23o-4) in taking an example from mathematics.
69?21-2. ὁμοίως δὲ... συμπεράσματος. The premiss will be
no use unless it is more likely to be admitted than the conclusion.
I suppose A. means that it must be a proposition which no one
would be less likely to admit, and some would be more likely to
admit, than the conclusion.
28-9. διὰ τὸ προσειληφέναι. . . ἐπιστήμην. The MSS. have
AT'; but προσλαμβάνειν is used regularly of the introduction of a
premiss (285, 29*16, 42434, etc.), and A. could not well say ‘we
get nearer to knowing that C is A by having brought in the know-
ledge that C is A'. Nor can it be 'the knowledge that C is B';
for this is only believed, not known (221-2). It must be the know-
ledge that B is A; by recognizing this fact, which we had not
recognized before, we get nearer to knowing that C is A, since
we have grasped the connexion of A with one of the middle terms
which connect it with C.
30-4. olov εἰ... εἰδέναι. If we are trying to show that the
circle can be squared, we simplify our problem by stating a premiss
which can easily be proved, viz. that any rectilinear figure can
II. 25. 69*21-34 491
be squared. We then have on our hands a slightly smaller task
(though still a big enough one!), viz. that of linking the subject
‘circle’ and the predicate ‘equal to a discoverable rectilinear
figure’, by means of the middle term ‘equal, along with a certain
set of lunes’ (i.e. figures bounded by two arcs of circles), to a dis-
coverable rectilinear figure’.
This attempt to square the circle is mentioned thrice elsewhere
in A.—in Soph. El. 171>12 rà yàp ψευδογραφήματα οὐκ ἐριστικά....
οὐδέ γ᾽ εἴ τί ἐστι ψευδογράφημα περὶ ἀληθές, olov τὸ ‘Inmoxpdtous 7) 6
τετραγωνισμὸς 6 διὰ τῶν μηνίσκων, ib. 17232 οἷον ὁ τετραγωνιομὸς ó
μὲν διὰ τῶν μηνίσκων οὐκ ἐριστικός, and Phys. 185514 ἅμα δ᾽ οὐδὲ
λύειν ἅπαντα προσήκει, ἀλλ᾽ ἣ ὅσα ἐκ τῶν ἀρχῶν τις ἐπιδεικνὺς
ψεύδεται, ὅσα δὲ μή, οὔ, οἷον τὸν τετραγωνισμὸν τὸν μὲν διὰ τῶν
τμημάτων γεωμέτρικοῦ διαλῦσαι. There has been much discussion
as to the details of the attempt. The text of Soph. El. 171>15
implies that it was different from the attempt of Hippocrates of
Chios; but there is enough evidence, in the commentators on the
Physics, that it was Hippocrates that attempted a solution by
means of lunes, and Diels is probably right in holding 7j ὁ 7erpa-
γωνισμὸς 6 διὰ τῶν μηνίσκων to be a (correct) gloss, borrowed
from 17222, on τὸ ' Imrokpárovs.
I have discussed the details at length in my notes on Phys.
185*16, and there is a still fuller discussion in Heath, Hist. of
Gk. Math. i. 183-200, and Mathematics 1n. Aristotle, 33-6. Re-
ferences to modern literature are given in Diels, Vors.5 i. 396; to
these may be added H. Milhaud in A.G.P. xvi (1903), 371-5.
CHAPTER 26
Objection
69737. Objection is a premiss opposite to a premiss put forward
by an opponent. It differs from a premiss in that it may be par-
ticular, while a premiss cannot, at least in universal syllogisms.
An objection can be brought (a) in two ways and (8) in two figures ;
(a) because it may be either universal or particular, (b) because
it is opposite to our opponent's premiss, and opposites can be
proved in the first or third figure, and in these alone.
bs. When the original premiss is that all B is A, we may object
by a proof in the first figure that no B is A, or by a proof in the
third figure that some B is not A. E.g., let the opponent’s premiss
be that contraries are objects of a single science ; we may reply (i)
‘opposites are not objects of a single science, and contraries are
492 COMMENTARY
opposites’, or (ii) ‘the knowable and the unknowable are not
objects of a single science, but they ave contraries’.
15. So too if the original premiss is negative, e.g. that con-
traries are not objects of a single science, we reply (i) ‘all opposites
are objects of a single science, and contraries are opposites', or
(ii) ‘the healthy and the diseased are objects of a single science,
and they are contraries’.
19. In general, (i) if the objector is trying to prove a universal
proposition, he must frame his opposition with reference to the
term which includes the subject of his opponent's premiss; if he
says contraries are not objects of a single science, the objector
replies ‘opposites are’. Such an objection will be in the first
figure, the term which includes the original subject being our
middle term.
24. (ii) If the objector is trying to prove a particular proposi-
tion, he must take a term tncluded 1m the opponent's subject, and
say e.g. ‘the knowable and the unknowable are not objects of a
single science’. Such an objection will be in the third figure, the
term which is included in the original subject being the middle
term.
28. For premisses from which it is possible to infer the opposite
of the opponent’s premiss are the premisses from which objections
must be drawn. That is why objections can only be made in these
two figures ; for in these alone can opposite conclusions be drawn,
the second figure being incapable of proving an affirmative.
32. Besides, an objection in the second figure would need
further proof. If we refuse to admit that A belongs to B, because
C does not belong to A, this needs proof; but the minor premiss of
an objection should be self-evident.
38. The other kinds of objection, those based on consideration
of things contrary or of something like the thing, or on common
opinion, require examination ; so does the question whether there
can be a particular objection in the first figure, or a negative one
in the second.
This chapter suffers from compression and haste. Objection is
defined as ‘a premiss opposite to a premiss’ (for ἐναντία in 69°37
must be used in its wider sense of ‘opposite’, in which it includes
contradictories as well as contraries). The statement that
ἔνστασις is a premiss opposed to a premiss is to be taken seriously ;
ἐνίστασθαι is ‘to get into the way’ of one's opponent, to block him
by denying one of his premisses, instead of waiting till he has
framed his syllogism and then offering a counter-syllogism (Rhet.
II. 26 493
1402*31, 1403*26, 141855). In Top. 160%39—"10 A. contrasts ἔνστασις
with ἀντισυλλογισμός, to the advantage of the former; it has the
merit of pointing out the πρῶτον ψεῦδος on which the opponent's
contemplated argument would rest (Soph. El. 17923, cf. Top.
160b36).
But ἔνστασις is not merely the stating of one proposition in
opposition to another. It involves a process of argument ; and
the proposition it opposes, while it is described throughout as
a premiss, is itself thought of as having been established by a
syllogism. For it is only on this assumption that we can explain
the reason A. gives for saying that objections can only be carried
out in the first and third figures, viz. that only in these can
opposites be proved, or in other words that the second figure
cannot prove affirmative propositions (P3-5, 29-32). A. must
mean that ἔνστασις is the disproving of a premiss (which the
opponent might otherwise use for further argument) by a proof
in the same figure in which that premiss was proved.
A. places three arbitrary restrictions on the use of ἔνστασις.
(1) He restricts it to the refutation of universal premisses, on the
ground that only such occur in the original syllogism, or at least
in syllogisms proving a universal (239-hr). This restriction is
from the standpoint of formal logic unjustifiable, but less so from
the standpoint of a logic of science, since syllogisms universal
throughout are scientifically more important than those that
have one premiss particular. (2) He insists, as we have seen, that
the objection must be carried out in the same figure in which the
original syllogism was couched, and that for this reason it cannot
be in the second figure. But he should equally, on this basis, have
excluded the third figure. This can prove conclusions in I and
in O, but these form no real contradiction. (3) While he is justi-
fied, on the assumption that the second figure is excluded, in
limiting to the first figure the proof of the contrary of a universal
proposition, he is unjustified in limiting to the third figure, and
to the moods Felapton and Darapti, the proof of its contradictory
(55-19).
Removing all these limitations, he should have recognized that
an A proposition can be refuted in any figure (by Celarent or
Ferio; Cesare, Camestres, Festino, or Baroco; Felapton, Bocardo,
or Ferison); an E proposition in the first or third figure (by
Barbara or Darii; Darapti, Disamis, or Datisi) ; an I proposition
in the first or second figure (by Celarent, Cesare, or Camestres) ;
an O proposition in the first (by Barbara).
If we allow A. to use the third figure while inconsistently
494 COMMENTARY
rejecting the second, his choice of moods—Celarent to prove the
contrary of an A proposition (69-12), Felapton to prove its con-
tradictory (>12-15), Barbara to prove the contrary of an E pro-
position (brs-17), Darapti to prove its contradictory (>17-18)—is
natural enough; only Celarent will prove the contrary of an A
proposition, only Barbara that of an E proposition; Felapton
is preferred to Ferio, Bocardo, and Ferison, and Darapti to Darii,
Disamis, and Datisi, because they have none but universal
premisses.
The general principles A. lays down for ἔνστασις (19-28) are
that to prove a universal proposition a superordinate of the sub-
ject should be chosen as middle term, and that to prove a parti-
cular proposition a subordinate of the subject should be chosen.
This agrees with his choice of moods; for in Celarent and Barbara
the minor premiss is All 5 is M, and in Felapton and Darapti it
is All M is S.
Maier (2 a. 455-6) considers that A. places a fourth restriction
on évoracts—that an objection must deny the major premiss from
which the opponent has deduced the πρότασις we are attacking,
so that the opposed syllogisms must be (to take the case in which
we prove the contrary of our opponent’s proposition) of the form
All M is P, All S is M, Therefore all S is P—No M is P, All
S is M, Therefore no S is P. He interprets ἀνάγκη πρὸς τὸ καθόλου
τῶν προτεινομένων τὴν ἀντίφασιν εἰπεῖν (P2071) as meaning ‘he must
take as his premiss the opposite of the universal proposition from
which as a major premiss the opposed πρότασις was derived’. If
the article in τὸ καθόλου is to be stressed, this interpretation must
be accepted ; for if A. is thinking of S as having only one super-
ordinate, the opposed syllogisms must be related as shown
above. It is, however, quite unnecessary to ascribe this further
restriction to A. What the words in question mean is ‘he must
frame his contradiction with a view to the universal (i.e. some
universal) predicable of the things put forward by the opponent’
(i.e. of the subject of his πρότασις). For A. goes on to say 'e.g., if
the opponent claims that no contraries are objects of a single
science, he should reply that opposites (the genus which includes
both contraries and contradictories) are'—without suggesting that
the opponent has said ‘No opposites are objects of a single science,
and therefore no contraries are’. In fact an ἔνστασις would be
much more plausible if it did not start by a flat contradiction
of the opponent's original premiss, but introduced a new middle
term; and A. can hardly have failed to see this. This interpreta-
tion is confirmed by what A. says about the attempt to prove
II. 26. 69521-37 495
a particular ‘objecting’ proposition (24-5). There the objector
must frame his objection ‘with reference to that, relatively to
which the original subject was universal’ (ie. to a (not the)
subordinate of the subject, as in the former case to a super-
ordinate of it).
Maier argues (ii. a. 471-4) that the treatment of ἔνστασις here
presupposes the treatment in Rhet. 2. 15. He thinks, in particular,
that the vague introductory definition of ἔνστασις, as ‘a premiss
opposite to a premiss', is due to the fact that in the Rhetortc
ἔνστασις not involving a counter-syllogism is recognized as well
as the kind (which alone is treated in the present chapter) which
does involve one. But his argument to show that the present
chapter is later than the context in which it is found is not con-
vincing, though his conclusion may be in fact true. The kind of
ἔνστασις dealt with in the present chapter turns out to be a per-
fectly normal syllogism ; its only pecularity is that it is a syllogism
used for a particular purpose, that of refuting a premiss which
one's opponent wishes to use. And in this respect, that it is
a particular application of syllogism, it is akin to the other
processes dealt with in this appendix to Ax. Pr. II (chs. 23-7).
69^21-2. οἷον εἰ... μίαν. The sense requires the placing of a
comma before πάντων, not after it as in Bekker and Waitz ; cf. 516.
24-5. πρὸς 6... πρότασις. πρὸς 6 = mpós τοῦτο πρὸς 6, ‘the
objector must direct himself to the term by reference to which
the subject of his opponent’s premiss is universal’.
31. διὰ γὰρ τοῦ μέσου... καταφατικῶς, cf. 2847-0.
32-7. ἔτι δὲ... ἔστιν. This further reason given for objection
not being possible in the second figure is obscure. It is not clear,
at first sight, whether in 534 αὐτῷ means A or B, nor whether
τοῦτο means (1a) ‘that A is not C’ or (15) ‘that B is not C' or
(za) ‘that “B is not A" follows from “A is not C’’’, or (2b)
‘that ''B is not A" follows from “B is not C" '. Interpretations
1a and 15 would involve A. in the view that negative proposi-
tions cannot be self-evident, but this interpretation is ruled
out by three considerations. (1) A. definitely lays it down in
An. Post. i. 15 that negative propositions can be self-evident. (2)
He has already used negative premisses, as of course he must do,
for the ἔνστασις in the first or third figure to an affirmative
proposition (65-15). (3) He says in 636 that the reason why an
ἔνστασις in the second figure is less satisfactory than one in the
first or third is that the other premiss should be obvious, i.e. that
if we state the ἔνστασις briefly, by stating one premiss, it should
be clear what the 'understood' premiss is. Thus interpretation
496 COMMENTARY
2a or 2b must be right. Of the two, 2a is preferable. For if
to All B is A we object No 4 isC, it is, owing to the change both
of subject and of predicate, by no means clear what other premiss
is to be supplied, while if we object No B isC, it is clear that the
missing premiss must be All A is C. |
36-7. διὸ καὶ... ἔστιν. Cook Wilson argued (in Trans. of the
Oxford Philol. Soc. 1883-4, 45-6) that this points to an earlier
form of the doctrine of enthymeme than that which is usual in
the Prior Analytics and the Rhetoric; that A. recognized at this
early stage an analogy between ἔνστασις and the argument from
signs, in that while ἔνστασις opposes a particular statement to a
universal and a universal statement to a particular, σημεῖον sup-
ports a universal statement by a particular and a particular
statement by a universal.
Wilson cannot be said to have established his point. The
present sentence does not refer to any general analogy between
ἔνστασις and σημεῖον, but only to the fact that because of ob-
scurity the second figure is unsuitable for both purposes.
The sentence is unintelligible in its traditional position. It
might be suggested that it was originally written in the margin,
and was meant to come after καταφατικῶς in P31. The fact that
the second figure is essentially negative is in effect the reason
given in 702357 for the invalidity of proof by signs in that figure.
But even so the sentence can hardly be by A. For A. does not
in fact hold that the second figure alone is unsuitable for σημεῖον.
He mentions in the next chapter σημεῖα in all three figures
(70*11—28). It is true that he describes σημεῖα in the second figure
as always refutable (because of undistributed middle) (234-7), but
he also describes those in the third figure as refutable because,
though they prove something, they do not prove what they claim
to prove (because of illicit minor) (*3o-4). Ch. 27 in fact draws a
much sharper line between σημεῖα in the first figure (τεκμήρια)
and those in the other two, than it does between those in the
third and those in the second figure. Susemihl seems to be right
in regarding the sentence as the work of a copyist who read
ch. 27 carelessly and overstressed the condemnation of the second
figure σημεῖον in 70434~7. There is no trace of the sentence in P.
38-70%. 'Emwxerréov δὲ ... λαβεῖν. In Rhet. ii. 25 A. recog-
nizes four kinds of ἔνστασις : (1) ἀφ᾽ ἑαυτοῦ. If the opponent's
statement is that love is good, we reply either (a) universally by
saying that all want is bad, or (δὴ particularly by saying that
incestuous love is bad. (2) ἀπὸ τοῦ ἐναντίου. If the opponent's
statement is that a good man does good to all his friends, we reply
II. 26. 69536—7022 497
‘a bad man does not do evil to all his friends’. (3) ἀπο τοῦ ὁμοίου. If
the statement attacked is that people who have been badly
treated always hate those who have so treated them, we reply
that people who have been well treated do not always love those
whohaveso treated them. (4) αἱ κρίσεις ai ἀπὸ τῶν γνωρίμων ἀνδρῶν.
If the statement attacked is that we should always be lenient
to those who are drunk, we reply ‘then Pittacus is not worthy
of praise; for if he were he would not have inflicted greater
penalties on the man who does wrong when drunk’.
Here the first kind agrees exactly with that described in the
present chapter; the other three kinds (which answer to ἐκ τοῦ
ἐναντίου καὶ τοῦ ὁμοίου καὶ τοῦ κατὰ δόξαν here), not being sus-
ceptible of simple syllogistic treatment, are not suitable for dis-
cussion in the Prior Analytics.
The second half of the sentence raises the question whether it
is not possible to prove a particular ‘objecting’ statement in the
first figure, or a negative one in the second. But even to suggest
this is to undermine the whole teaching of the chapter.
From the irrelevance of the first part of the sentence and the
improbability of the second, Cook Wilson (in Gótt. Gel. Anzeiger,
1880, Bd. I, 469-74), followed by Maier (ii a. 460 n. 2), has inferred
that the sentence is a later addition by someone familiar with the
teaching of RAet. ii. 25. This conclusion would be justified if the
Prior Analytics were a work prepared for publication. But
probably none of A.’s extant works was so prepared, and in an
‘acroamatic’ work the sentence is not impossible as a note to
remind the writer himself that the whole chapter needs further
consideration. Similar notes are to be found in 3522, 41631, 4519,
49*9, 67926.
We need not concern ourselves with the wider sense in which
the word ἔνστασις is used in the Topics, covering any attempt to
interfere with an opponent's carrying through his argument. Cf.
for instance 1612r—rs, where four kinds are named, of which the
first (ἀνελόντα παρ᾽ ὃ γίνεται τὸ ψεῦδος, disproving the premiss on
which the false conclusion of our opponent depends) includes
ἔνστασις as described in the: present chapter, but also ἔνστασις
against an inductive argument. But it may be noted that the
great majority of the ἐνστάσεις in the Topics belong to the second
of the two types discussed in this chapter—refutation of a pro-
position by pointing to a negative instance (114820, 11514,
117*18, 123517, 27, 34, 124532, 12581, 12856, 156234, 15762). For the
discussion of ἔνστασις in the wider sense reference may be made
to Maier, ii. a. 462-74.
4985 Kk
498 COMMENTARY
CHAPTER 27
Inference from signs
7o*1a. An enthymeme is a syllogism starting from probabilities
or signs. A probability is a generally approved proposition, some-
thing known to happen, or to be, for the most part thus and thus.
6. A sign is a demonstrative premiss that is necessary or gene-
rally approved; anything such that when it exists another thing
exists, or when it has happened the other has happened before or
after, is a sign of that other thing’s existing or having happened.
II. A sign may be taken in three ways, corresponding to the
position of the middle term in the three figures. First figure, This
woman is pregnant ; for she has milk. Third figure, The wise are
good; for Pittacus is good. Second figure, This woman is preg-
nant; for she is sallow.
24. If we add the missing premiss, each of these is converted
from a sign inito a syllogism. The syllogism in the first figure is
irrefutable if it is true; for it is universal. That in the third figure
is refutable even if the conclusion is true; for it is not universal,
and does not prove the point at issue. That in the second figure is
in any case refutable ; for terms so related never yield a conclusion.
Any sign may lead to a true conclusion; but they have the differ-
ences we have stated.
bx. We may either call all such symptoms signs, and those of
them that are genuine middle terms evidences (for an evidence
is something that gives knowledge), or call the arguments from
extreme ternis signs and those from the middle term evidences;
for that which is proved by the first figure is most generally
accepted and most true.
7. It is possible to infer character from bodily constitution, if
(1) it be granted that natural affections change the body and the
soul together (a man by learning music has presumably undergone
some change in his soul; but that is not a natural affection; we
mean such things as fits of anger and desires) ; if (2) it be granted
that there is a one-one relation between sign and thing signified ;
and if (3) we can discover the affection and the sign proper to each
species.
14. For if there is an affection that belongs specially to some
infima species, e.g. courage to lions, there must be a bodily sign of
it; let this be the possession of large extremities. This may belong
to other species also, though not to them as wholes; for a sign is
proper to a species in the sense that it is characteristic of the
whole of it, not in the sense that it is peculiar to it.
IT. 27 499
22. If then (1) we can collect such signs in the case of animals
which have each one special affection, with its proper sign, we
shall be able to infer character from physical constitution.
26. But if (2) the species has two characteristics, e.g. if the lion
is both brave and generous, how are we to know which sign is the
sign of which characteristic? Perhaps if both characteristics
belong to some other species but not to the whole of it, and if
those other animals in which one of the two characteristics is
found possess one of the signs, then in the lion also that sign will
be the sign of that characteristic.
3z. To infer character from physical constitution is possible
because in the first-figure argument the middle term we use is
convertible with the major, but wider than the minor; e.g. if B
(larger extremities) belongs to C (the lion) and also to other
species, and A (courage) always accompanies B, and accompanies
nothing else (otherwise there would not be a single sign correlative
with each affection).
The subject of this chapter is the enthymeme. The enthymeme
is discussed in many passages of the Rhetoric, and it is impossible
to extract from them a completely consistent theory of its nature.
Its general character is that of being a rhetorical syllogism (Rhet.
135654). This, however, tells us nothing directly about its real
nature ; it only tells us that it is the kind of syllogism that orators
tend to use. But inasmuch as the object of oratory is not know-
ledge but the producing of conviction, to say that enthymeme is
a rhetorical syllogism is to tell us that it lacks something that a
scientific demonstration has. It may fail short of a demonstra-
tion, however, in any one of several ways. It may be syllogisti-
cally invalid (as the second- or third-figure arguments from signs
in fact are, 70*30—7). It may proceed from a premiss that states
not a necessary or invariable fact but only a probability (as the
argument ἐξ εἰκότων does, ib. 3-7). It may be syllogistically
correct and start from premisses that are strictly true, but these
may not give the reason for the fact stated in the conclusion, but
only a symptom from which it can be inferred (as in the first-
figure argument from signs (ib. 13-16).
A.'s fullest list of types of enthymeme (Rhet. 1402513) describes
them as based on four different things—eixós, παράδειγμα,
τεκμήριον, σημεῖον. But elsewhere παράδειγμα is made co-ordinate
with ἐνθύμημα, and is said to be a rhetorical induction, as enthy-
meme is a rhetorical syllogism (135654-6). Thus the list is reduced
to three, and since τεκμήριον is really one species of σημεῖον
500 COMMENTARY
(robr-6), the list is reduced finally to two-—the enthymeme
ἐξ εἰκότων and the enthymeme ἐκ σημείων. εἰκός is described here
as πρότασις ἔνδοξος (70*4) ; in Rhet. 1357334-b1 it is described more
carefully—ro μὲν yap εἰκός ἐστιν ws ἐπὶ τὸ πολὺ γινόμενον, ody
ἁπλῶς δὲ καθάπερ ὁρίζονταί τινες, ἀλλὰ τὸ περὶ τὰ ἐνδεχόμενα ἄλλως
ἔχειν, οὕτως ἔχον πρὸς ἐκεῖνο πρὸς ὃ εἰκὸς ὡς τὸ καθόλου πρὸς τὸ
κατὰ μέρος. l.e., an εἰκός is the major premiss in an argument of
the form ‘B as a rule is 4, C is B, Therefore C is probably A’.
The description of εἰκός in the present chapter (70*3-7) is per-
functory, because the real interest of the chapter is in σημεῖον.
σημεῖον is described as a πρότασις ἀποδεικτικὴ ἢ ἀναγκαία 7) ἔνδοξος
(47). The general nature of the πρότασις is alike in the two cases;
it states a connexion between a relatively easily perceived
characteristic and a less easily perceived one simultaneous,
previous, or subsequent to it (38-10). The distinction expressed
by 7j ἀναγκαία 7 ἔνδοξος is that later pointed out between the
τεκμήριον Or sure symptom and the kind of σημεῖον which is an
unsure symptom. The distinction is:indicated formally by saying
that a τεκμήριον gives rise to a syllogism in the first figure—e g.
(‘All women with milk are pregnant), This woman ‘has milk,
Therefore she is pregnant’, while a σημεῖον of the weaker kind
gives rise to a syllogism in the third figure—e.g. ‘Pittacus is
good, (Pittacus is wise,) Therefore the wise are good'—or in the
second—e.g. (‘Pregnant women are sallow,) This woman is
sallow, Therefore she is pregnant'. The first-figure syllogism is
unassailable, if its premisses are true, for its premisses warrant
the universal conclusion which it draws (229-30). The third-figure
syllogism is assailable even if its conclusion is true; for the
premisses do not warrant the universal conclusion which it draws
(*3o-4). The second-figure syllogism is completely invalid because
two affirmative premisses in that figure warrant no conclusion at
all (434-7).
. In modern books on formal logic the enthymeme is usually
described as a syllogism with one premiss or the conclusion
omitted; A.-notes (319-20) that an obvious premiss is often
omitted in speech, but this forms no part of his definition of the
enthymeme, being a purely superficial characteristic.
On À.'s treatment of the enthymeme in general (taking account
of the passages in the Rhetortc) cf. Maier, ii a. 474—501.
70*10. ᾿Ενθύμημα δὲ... σημείων. These words should stand
at the beginning of the chapter, which in its traditional form
begins with strange abruptness; the variation in the MSS.
between δέ and μὲν οὖν may point to the sentence's having got
II. 27. 7o*10 — 538 501
out of place and to varying attempts having been made to fit
it in. If the words are moved to 2 a, the chapter about ἐνθύμημα
begins just as those about ἐπαγωγή, παράδειγμα, ἀπαγωγή, and
ἔνστασις do, with a summary definition.
7-8. σημεῖον δὲ... ἔνδοξος. Strictly only a necessary premiss
can be suitable for a place in a demonstration, and Maier there-
fore brackets ἀναγκαία as a gloss on ἀποδεικτική. But ἀναγκαία is
well supported, and ἀποδεικτική may once in a way be used in a
wider sense, the sense of συλλογιστική; cf. Soph. El. 16758 ἐν τοῖς
ῥητορικοῖς αἱ κατὰ τὸ σημεῖον ἀποδείξεις ἐκ τῶν ἑπομένων εἰσίν
(which is apparently meant to include all arguments from σημεῖα,
not merely those from τεκμήρια), De Gen. et Corr. 333924 7) ὁρίσασθαι
ἢ ὑποθέσθαι ἢ ἀποδεῖξαι, ἢ ἀκριβῶς ἢ μαλακῶς, Met. 1025>13
ἀποδεικνύουσιν ἢ ἀναγκαιότερον ἢ μαλακώτερον.
by—5. Ἤ δὴ ... σχήματος. τὸ μέσον is the term which occupies
a genuinely intermediate position, i.e. the middie term in the
first figure, which is the subject of the major premiss and the
predicate of the minor. τὰ ἄκρα are the middle terms in the other
two figures, which are either predicated of both the other terms
or subjects to them both.
7-38. Τὸ δὲ φυσιογνωμονεῖν... σημεῖον. τὸ φυσιογνωμονεῖν is
offered by A. as an illustration of the enthymeme ἐκ σημείων.
The passage becomes intelligible only if we realize something that
A. never expressly says, viz. that what he means by τὸ φυσιογνω-
povety is the inferring of mental characteristics in men from the
presence in them of physical characteristics which in some other
kind or kinds of animal go constantly with those mental character-
istics. This is most plainly involved in A.’s statement in 532-8
of the conditions on which the possibility of τὸ φυσιογνωμονεῖν
depends. Our inference that this is what he means by τὸ φυσιο-
γνωμονεῖν is confirmed by certain passages in the Phystognomonica,
which, though not by A., is probably Peripatetic in origin and
serves to throw light on his meaning. The following passages are
significant: 805218 oi μὲν οὖν προγεγενημένοι φυσιογνώμονες κατὰ τρεῖς
τρόπους ἐπεχείρησαν φυσιογνωμονεῖν, ἕκαστος καθ᾽ ἕνα. οἱ μὲν γὰρ ἐκ
τῶν γενῶν τῶν ζῴων φυσιογνωμονοῦσι, τιθέμενοι καθ᾽ ἕκαστον γένος
εἶδός τι ζῴου καὶ διάνοιαν οἷα ἕπεται τῷ τοιούτῳ σώματι, εἶτα τὸν
ὅμοιον τούτῳ τὸ σῶμα ἔχοντα καὶ τὴν ψυχὴν ὁμοίαν ὑπελάμβανον
(so Wachsmuth). 807329 οὐ γὰρ ὅλον τὸ γένος τῶν ἀνθρώπων
φυσιογνωμονοῦμεν, ἀλλά τινα τῶν ἐν τῷ γένει. 810%11 ὅσα δὲ πρὸς τὸ
φυσιογνωμονῆσαι συνιδεῖν ἁρμόττει ἀπὸ τῶν ζῴων, ἐν τῇ τῶν
σημείων ἐκλογῇ ῥηθήσεται.
The preliminary assumptions A. makes are (1) that natural (as
502 COMMENTARY
opposed to acquired) mental phenomena (παθήματα, κινήσεις,
πάθη), such as fits of anger or desire, and the tendencies to them,
such as bravery or generosity, are accompanied by a physical
alteration or characteristic (707-11) ; (2) that there is a one-one
correspondence between each such πάθος and its bodily accompani-
ment (ib. 12); (3) that we can find (by an induction by simple
enumeration) the special πάθος and the special σημεῖον of each
animal species (ib. 12-13). Now, though these have been described
as ἴδια to the species they characterize, this does not prevent
their being found in certain individuals of other species, and in
particular of the human species; and, the correspondence of ση-
μεῖον to πάθος being assumed to be a one-one correspondence,
we shall be entitled to infer the presence of the πάθος in any human
being in whom we find the σημεῖον (ib. 13-26). Let S, be a species
of which all the members (or all but exceptional members) have
the mental characteristic M,, and the physical characteristic P,.
Not only can we, if we are satisfied that P, is the sign of M,,
infer that any individual of another species S, (say the human)
that has P, has M,. We can also reason back from the species
only some of whose members have P, to that all of whose mem-
bers have it. If the members of S, have two mental characteristics
M, and M,, and two physical characteristics P, and P,, how are
we to know which P is the sign of which M? We can do so if we
find that some members of S, have (for instance) M, but not
M,, and P, but not P, (ib. 26-32).
Thus the possibility of inferring the mental characteristics of
men from the presence of physical characteristics which are in
some other species uniformly associated with those character-
istics depends on our having a first-figure syllogism in which the
major premiss is simply convertible and the minor is not, e.g.
All animals with big extremities are brave, All lions have big
extremities, Therefore all lions are brave. The major premiss
must be simply convertible, or else we should not have any
physical symptorn the absence of which would surely indicate
lack of courage ; the minor premiss must not be simply convertible,
or else we should have nothing from whose presence in men we
could infer their courage (ib. 32-8).
19. ὅτι ὅλου... [πάθος]. If weread πάθος, we must suppose that
this word, which in Pro, 13, 15, 24 stands for a mental characteristic
(in contrast with σημεῖον), here stands for a physical one. It would
be pointiess to bring in a reference to the mental characteristic
here, where A. is only trying to explain the sense in which the
σημεῖον can be called ἴδιον. There is no trace of πάθος in P.
POSTERIOR ANALYTICS
BOOK I
CHAPTER 1
The student's need of pre-existent knowledge. Its nature
71*x. All teaching and learning by way of reasoning proceeds
from pre-existing knowledge; this is true both of the mathe-
matical and of all other sciences, of dialectical arguments by way
of syllogism or induction, and of their analogues in rhetorical
proof—enthymeme and example.
ir. With regard to some things we must know beforehand
that they are (e.g. that everything may be either truly affirmed
or truly denied); with regard to others, what the thing referred
to (e.g. triangle) is; with regard to others (e.g. the unit) we must
have both kinds of knowledge.
17. Some of the premisses are known beforehand, others may
come to be known simultaneously with the conclusion—i.e. the
instances falling under the universal of which we have knowledge.
That every triangle has its angles equal to two right angles one
knew beforehand; that this figure in the semicircle is a triangle
one comes to know at the moment one draws the conclusion.
(For some things we learn in this way, i.e. individual things
which are not attributes—the individual thing not coming to
be known through the middle term.)
24. Before one draws the conclusion one knows in one sense,
and in another does not know. For how could one have known
that to have angles equal to two right angles, which one did not
know to exist? One knows in the sense that one knows univer-
sally ; one does not know in the unqualified sense.
29. If we do not draw this distinction, we get the problem of
the Meno; a man will learn either nothing or what he already
knows. We must not solve the problem as some do. If A is
asked 'Do you know that every pair is even?' and says 'Yes',
B may produce a pair which A did not know to exist, let alone
to be even. These thinkers solve the problem by saying that the
claim is not to know that every pair is even, but that every pair
known to be a pair is even.*
34. But we know that of which we have proof, and we have
proof not about 'everything that we know to be a triangle, or a
number', but about every number or triangle.
504 COMMENTARY
bs. There is, however, nothing to prevent one’s knowing
already in one sense, and not knowing in another, what one learns;
what would be odd would be if one knew a thing in the same
sense in which one was learning it.
g1*1. Πᾶσα διδασκαλία... .. διανοητική. διανοητική is used to
indicate the acquisition of knowledge by reasoning as opposed to
its acquisition by the use of the senses.
2-11. φανερὸν δὲ... συλλογισμός. That all reasoning pro-
ceeds from pre-existing knowledge can be seen, says A., by
looking (1) at the various sciences (*3-4), or (2) at the two kinds
of argument used in dialectical reasoning (*5-9), or (3) at the
corresponding kinds used in rhetoric (39-11). The distinction
drawn between ai ἐπιστῆμαι and of λόγοι indicates that by the
latter we are to understand dialectical arguments. For the dis
tinction cf. ἐν rois μαθήμασιν )( xarà τοὺς λόγους, Top. 158b29,
159*1, and the regular use of Aoy:xds in the sense of ‘dialectical’.
λαμβάνοντες ws παρὰ Évriévrow (^7) is an allusion to the dialectical
method of ἐρώτησις, i.e. of getting one's premisses by questioning
the opponent.
3. al τε γὰρ μαθηματικαὶ τῶν ἐπιστημῶν. Throughout the
first book of the Postertor Analytics A.’s examples of scientific
procedure are taken predominantly from mathematics; cf. chs. 7,
9, IO, I2, 13, 27.
3-4 τῶν ἐπιστημῶν... τῶν GÀAov . .. τεχνῶν. While A. does
not here draw a clear distinction between ἐπιστῆμαι and τέχναι,
ἐπιστῆμαι is naturally used of the abstract theoretical sciences,
while τέχναι points to bodies of knowledge that aim at production
of some kind ; cf. IO0*9 ἐὰν μὲν περὶ γένεσιν, τέχνης, ἐὰν δὲ περὶ τὸ
ὄν, ἐπιστήμης, and the fuller treatment of the distinction in ΕΝ.
1139>18—1140%23.
5-6. ὁμοίως δὲ... ἐπαγωγῆς. The grammar is loose. ‘So too
as regards the arguments, both syllogistic and inductive argu-
ments proceed from pre-existing knowledge.’
Q-II. ἢ γὰρ... συλλογισμός. On the relation of παράδειγμα
to ἐπαγωγή cf. An. Pr. ii. 24, and on that of ἐνθύμημα to συλλο-
γισμός cf. ib. 27.
11-17. διχῶς δ᾽... ἡμῖν. A. has before his mind three kinds of
proposition which he thinks to be known without proof, and to be
required as starting-points for proof: (1) nominal definitions of
the meanings of certain words (he tells us in 76232-3 that a science
assumes the nominal definitions of all its special terms); (2)
statements that certain things exist (he tells us in 76433-6 that
I. r. 71*1-21 505
only the primary entities should be assumed to exist, e.g. in
arithmetic units, in geometry spatial figures); (3) general state-
ments such as 'Any proposition may either be truly affirmed or
truly denied’. Of these (1) are properly called ὁρισμοί (72421),
(2) ὑποθέσεις (ib. 20), (3) ἀξιώματα (ib. 17). But here he groups
(2) and (3) together under the general name of statements ὅτι ἔστι,
which by a zeugma includes both statements that so-and-so
exists (2) and statements that so-and-so is the case (3), in dis-
tinction from statements that such-and-such a word means so-
and-so (x).
I4. τὸ Bé τρίγωνον, ὅτι τοδὶ σημαίνει. Elsewhere A. some-
times treats the triangle as one of the fundamental subjects of
geometry, whose existence, as well as the meaning of the word,
is assumed. Here triangularity seems to be treated as a property
whose existence is not assumed but to be proved. In that case
he is probably thinking of points and lines as being the only
fundamental subjects of geometry, and of triangularity as an
attribute of certain groups of lines. This way of speaking of it
occurs again in 92>15~16 and (according to the natural interpreta-
tion) in 76*33-6.
17-19. Ἔστι 86. . . γνῶσιν. A. does not say in so many words,
but what is implied is, that the major premiss of a syllogism
must be known before the conclusion is drawn, but that the
minor premiss and the conclusion may come to be known simul-
taneously.
I7. Ἔστι δὲ... yvopícavra. The sense requires yrwpicarra, and
the corruption is probably due to the eye of the writer of the
ancestor of all our MSS. having travelled on to λαμβάνοντα.
18-19. olov ὅσα τυγχάνει... γνῶσιν. The best that can be
made of this, with the traditional reading τὸ καθόλου, ὧν ἔχει τὴν
γνῶσιν, is to take it to mean ‘knowledge, this latter, of the parti-
culars actually falling under the universal and therein already
virtually known’ (Oxf. trans.). But this interpretation is difficult,
since the whole sentence states an opposition between the major
premiss, which is previously known, and the minor, which comes
to be known simultaneously with the conclusion. This clearly
points to the reading τὸ καθόλου οὗ ἔχει THY γνῶσιν, which alone
appears to be known to P. (12. 23) and to T. (3. 16). The corruption
has probably arisen through an omission of οὗ after καθόλου,
which a copyist then tried to patch up by inserting óv.
I9-21. ὅτι μὲν yàp . . . ἐγνώρισεν. The reference is to the
proof of the proposition that the angle in a semicircle is a right
angle (Euc. iii. 31) by means of the proposition that the angles of
506 COMMENTARY
a triangle equal two right angles (Euc. i. 32). There are fuller
references to the proof in 94328-34 and Met. 1051?26—33.
Heath in Mathematics in Aristotle, 37-9, makes an ingenious
suggestion. He suggests a construction such that it is only in the
course of following a proof that a learner realizes that what he
is dealing with is a triangle (one of the sides having been drawn
not as one line but two as meeting at a point).
21-4. ἅμα ἐπαγόμενος .. . ἐπαχθῆναι. In a note prefixed to
An. Pr. ii. 23 I have examined the usage of ἐπάγειν in A., and have
argued that ἅμα ἐπαγόμενος here means ‘at the very moment one
is led on to the conclusion', and that this is the main usage under-
lying the technical sense of ἐπαγωγή = ‘induction’. Yet the pro-
cess referred to here is not inductive. The fact referred to is the
fact that if one already knows a major premiss of the form All
M is P, knowledge of the minor premiss S is M may come
simultaneously with the drawing of the conclusion S is P; the
reasoning referred to is an ordinary syllogism. ἐπαχθῆναι in *25
has the same meaning; ἐπαχθῆναι and λαβεῖν συλλογισμόν are
different ways of referring to the same thing.
21-4. ἐνίων yàp . . . τινός, i.e. while it is (for instance) through
the middle term 'triangle' that an individual figure is known to
have its angles equal to two right angles, it is not through a
middle term that the individual figure is known to be a triangle;
it is Just seen directly to be one.
24-5. πρὶν δ᾽ érax8rvaL . . . συλλογισμόν, cf. #21 n.
26-98. ὃ γὰρ... ὥς. With this discussion may be compared
that in An. Pr. ii. 21.
29. τὸ ἐν τῷ Μένωνι ἀπόρημα. Cf. Meno 80d καὶ τίνα τρόπον
ζητήσεις, ὦ Σώκρατες, τοῦτο ὃ μὴ οἶσθα τὸ παράπαν ὅ τι ἐστίν; ποῖον
yap ὧν οὐκ οἶσθα προθέμενος ζητήσεις; ἢ εἰ καὶ ὅτι μάλιστα ἐντύχοις
αὐτῷ, πῶς εἴσει ὅτι τοῦτό ἐστιν ὃ σὺ οὐκ ἤδησθα; This problem,
which Plato solved by his doctrine that all learning is reminiscence,
A. solves by pointing out that in knowing the major premiss one
already knows the conclusion potentially.
30-65. οὐ yàp δή... παντός. The question is whether a man
who has not considered every pair of things in the world and
noticed its number to be even can be said to know that every pair
is even. It would seem absurd to deny that one knows this; but
if one claims to know it, one might seem to be refuted by being
confronted with a pair which one did not even know to exist.
A solution which had evidently been offered by certain people
was that what one knows is that every pair that one knows to be
a pair is even; but A. rightly points out that this is a completely
I. r. 71321 —55 507
unnatural limitation to set on the claim to know that every pair
is even. His own solution (55-8) is that we must distinguish two
modes of knowledge and say that one knows beforehand in a
sense (i.e. potentially) that the particular pair is even, but does
not know it in another sense (i.e. actually).
CHAPTER 2
The nature of scientific knowledge and of its premisses
γερο. We think we know a fact without qualification, not
in the sophistical way (i.e. Per accidens), when we think that we
know its cause to be its cause, and that the fact could not be
otherwise; those who think they know think they are in this con-
dition, and those who do know both tnink they are, and actually
are, ir it.
16. We will discuss later whether there is another way of
knowing ; but at any rate there is knowledge by way of proof, i.e.
by way of scientific syllogism.
19. If knowledge is such as we have stated it to be, demonstra-
tive knowledge must proceed from premisses that are (1) true,
(2) primary and immediate, (3) (a) better known than, (δ) prior
to, and (c) causes of, the conclusion. That is what will make
our starting-points appropriate to the fact to be proved. There
can be syllogism without these conditions, but not proof, because
there cannot be scientific knowledge.
25. (ri) The premisses must be true, because it is impossible
to know that which is not.
26. (2) They must be primary, indemonstrable premisses be-
cause otherwise we should not have knowledge unless we had
proof of them (which is impossible» ; for to know (otherwise than
per accidens) that which is provable is to have proof of it.
29. (3) They must be (a) causes, because we have scientific
knowledge only when we know the cause; (2) prior, because they
are causes; (c) known beforehand, not only in the sense that we
understand what is meant, but in the sense that we know them
to be the case.
33. Things are prior and better known in two ways: for the
same thing is not prior by nature and prior to us, or better known
by nature and better known to us. The things nearer to sense are
prior and better known relatively to us, those that are more
remote prior and better known without qualification. The most
universal things are farthest from sense, the individual things
nearest to it; and these are opposed to each other.
508 COMMENTARY
4245. To proceed from what is primary is to proceed from the
appropriate starting-points. A starting-point of proof is an im-
mediate premiss, i.e. one to which no other is prior. A premiss is
a positive or negative proposition predicating a single predicate
of a single subject ; a dialectical premiss assumes either of the pair
indifferently, a demonstrative premiss assumes one definitely to be
true. A proposition is either side of a contradiction. A contra-
diction is an opposition which of itself excludes any intermediate.
A side of a contradiction is, if it asserts something of something,
an affirmation ; it it denies something of something, a negation.
14. Of immediate syllogistic starting-points, I give the name
of thesis to one that cannot be‘ proved, and that is not such that
nolhing can be known without it; that of axiom to one which
a man needs if he is to learn anything. Of theses, that which
assumes a positive or negative proposition, i.e. that so-and-so
exists or that it does not exist, is an hypothesis; that which does
not do this is a definition. For a definition is a thesis, since it
lays it down that a unit is that which is indivisible in quantity ;
but it is not an hypothesis, since it is not the same thing to say
what a unit is and that a unit exists.
28. Since what is required is to believe and know a fact by
having a demonstrative syllogism, and that depends on the truth
of the premisses, we must not only know beforehand the first
principles (all or some of them), but also know them better ; for
to that by reason of which an attribute belongs to something,
the attribute belongs still more—e.g. that for which we love some-
thing is itself more dear. Thus if we know and believe because
of the primary facts, we know and believe /Aem still more. But
if we neither know a thing nor are better placed with regard
to it than if we knew it, we cannot believe it more than the
things we know ; and one who believed as a result of proof would
be in this case if he did not know his premisses beforehand ; for
we must believe our starting-points (all or some) more than our
conclusion.
37. One who is to have demonstrative knowledge must not
only know and believe his premisses more than his conclusion,
but also none of the opposite propositions from which the
opposite and false conclusion would follow must be more credible
to or better known by him, since one who knows must be abso-
lutely incapable of being convinced to the contrary.
7159-10. ἀλλὰ μὴ... συμβεβηκός. The reference is not, as
P. 21. 15-28 supposes, to sophistical arguments employing the
I. 2. 7159-23 509
fallacy of accident. The meaning is made plain by 7425-30,
where A. points out that if one proves by separate proofs that the
equilateral, the isosceles, and the scalene triangle have their angles
equal to two right angles, one does not yet know, except τὸν
σοφιστικὸν τρόπον, that the triangle has that property, since one
does not know the triangle to have it as such, but only the triangle
when conjoined with any of its separable accidents of being equi-
lateral, being isosceles, or being scalene. In such a case, as A. says
here, one does not know the cause of its having the property,
nor know that it could not fail to have it.
16-17. Ei μὲν οὖν... ἐροῦμεν. In 7251922 A. recognizes the
existence of ἐπιστήμη τῶν ἀμέσων ἀναπόδεικτος as well as of
ἐπιστήμη ἀποδεικτική, and in 76216-22 he describes it as the higher
ofthe two kinds. But in ii. 19 he discusses the question at length,
and gives the name of voós to the faculty by which we know the
ἀρχαί, distinguishing this from ἐπιστήμη, which is thus finally
identified with ἐπιστήμη ἀποδεικτική (1005-17).
19-23. εἰ τοίνυν... δεικνυμένου. A. states first the charac-
teristics which the ultimate premisses of demonstration must
have in themselves. They must be (1) true, (2) primary, immedi-
ate, or indemonstrable (b21, 27). πρῶτα here does not mean ‘most
fundamental', for A. could not, after saying that the premisses
must be fundamental in the highest degree, go on to make the
weaker statement that they must be more fundamental (mpo-
τέρων, *22) than the conclusion. To say this would be to confuse
the characteristics of the premisses in themselves (ἀληθῶν xai
πρώτων) with their characteristics in relation to the conclusion
(γνωριμωτέρων καὶ προτέρων καὶ αἰτίων τοῦ συμπεράσματος).
πρώτων, then, means just the same as ἀμέσων or ἀναποδείκτων
(b27)—that the premisses must be such that the predicate at-
taches to the subject directly as such, not through any middle
term.
A. next states the characteristics which the ultimate premisses
must have in relation to the conclusion. He states these as if
they were three in number—yrwpidrepa, πρότερα, αἴτια (P21, 29).
But in fact they seem to be reducible to two. (1) The facts stated
in the premisses must be objectively the grounds (αἴτια) of the
fact stated in the conclusion; it is only another way of saying
this to say that they must be objectively prior to, i.e. more
fundamental than, the fact stated in the conclusion (πρότερα,
εἴπερ αἴτια, >31). (2) It follows from this that they must be more
knowable in themselves; for if C is A only because B is A and
C is B, we can know (so À. maintains) that C is 4 only if we
510 COMMENTARY
understand why it is so, i.e. only if we know that B is A, that
C is B, and that C’s being A is grounded in B’s being A and in
C’s being B. It must be possible to know that B is A and that
C is B without already knowing that C is A, while it will be
impossible to know that C is A without already knowing that
B is A and that C is B. Further, the premisses must be known
beforehand not only in the sense that their meaning must be
grasped, but that they must be known to be true (531-3, cf.
41-17).
The fact that C is A may well be more familiar to us (ἡμῖν
γνωριμώτερον, 721). Le. it may be accepted as true, as being a
probable inference from the data of perception. But it will not
be known in the proper sense of the word, unless it is known on
the basis of the fact on which it is objectively grounded.
If these conditions (especially that indicated by the word
αἴτια) are all satisfied, the premisses that satisfy them will 7250
facto be the principles appropriate to the proof of the fact to be
proved ; no further condition is necessary (71522-3).
28. τὸ yàp ἐπίστασθαι.... μὴ κατὰ συμβεβηκός, cf. Pg—1o n.
72*8—7. ἐκ πρώτων δ᾽... ἀρχήν. This seems to be intended
to narrow down the statement that demonstration must proceed
ἐκ πρώτων (71Pz1). Not any and every immediate proposition
will serve; the premisses must be appropriate to the science.
This does not mean that they must be peculiar to the science
(though οἰκεῖος often implies that) ; for among them are included
premisses which must be known if anything is to be known
(#16-18)—the axioms which lie at the root of all proof, e.g. the
law of contradiction. What is excluded is the use of immediate
propositions not appropriate to the subject-matter in hand, in
other words the μετάβασις ἐξ ἄλλου γένους, the use of arithmetical
propositions, for instance, to prove a geometrical proposition
(cf. chs. 7 and 9).
8-9. πρότασις δ᾽ ἐστὶν. . . μόριον, i.e. a premiss is either an
affirmative or a negative proposition.
9-10. διαλεκτικὴ μὲν... ὁποτερονοῦν. The method of dia-
lectic is to ask the respondent a well-chosen question and, what-
ever answer he gives, to prove your own case with his answer
as a basis; cf. De Int. 20522-3.
14-24. ᾿Αμέσου δ᾽ ἀρχῆς... ταὐτόν. It must be noted that the
definitions here given of θέσις, ἀξίωμα, ὑπόθεσις are definitions of
them as technical terms, and that this does not preclude A. from
often using these words in wider or different senses. The various
kinds of ἀρχή are dealt with more fully in ch. xo. On the partial
I. 2. 71528 —72>3 511
correspondence which exists between A.’s ἀξιώματα (κοινά 76238,
77927, 30, κοιναὶ ἀρχαί 88528, κοιναὶ δόξαι Met. 996528), ὑποθέσεις,
and δρισμοί, and Euclid’s κοιναὶ ἔννοιαι, αἰτήματα, and ὅροι, cf.
H. D. P. Lee in C.Q. xxix. 113-18 and Heath, Mathematics in
Aristotle, 53-7.
17-18. τοῦτο yàp . . . λέγειν, ie. A. here strictly (μάλιστα)
restricts the name ἀξίωμα to propositions like the ‘laws of thought’
which underlie all reasoning, while implicitly admitting that it
is often applied to fundamental propositions relating only to
quantities—what in Met. 1005?20 A. calls τὰ ἐν rots μαθήμασι
καλούμενα ἀξιώματα (implying that the word is borrowed from
mathematics), the «owai ἔννοιαι which are prefixed to Euclid’s
Elemenis, and probably also were prefixed to the books of
Elements that existed in A.’s time. Thus in 77230-1 both the law
of excluded middle and the principle that if equals are taken
from equals, equals remain are quoted as instances of τὰ κοινά.
18-20. θέσεως δ᾽... ὑπόθεσις. The present passage is the only
one in which ὑπόθεσις has this strict sense. In 76535-9, 7723-4 the
distinction of ὑπόθεσις from definition is maintained, but in that
context (76923—31) ὑπόθεσις is said to be, not a self-evident truth,
but something which, though provable, is assumed without
proof. That corresponds better with the ordinary meaning of
the word.
28. ἢ πάντα ἢ ἔνια. The discussion in 71529-72*5 has stated
that the premisses of demonstration must all be known in advance
of the conclusion. But A. remembers that he has pointed out
in 71217-21 that the minor premiss in a scientific proof need not
be known before the conclusion; and the qualification 7 πάντα
ἢ ἔνια is introduced with reference to this.
29-30. αἰεὶ γὰρ... μᾶλλον. What A. is saying is evidently
that if the attribute A belongs to C because it belongs to B and
B to C, it belongs to B more properly than to C. I have therefore
read ἐκείνῳ for the MS. reading ἐκεῖνο. T. evidently read ἐκείνῳ
(8. 6), and so did P. (38. 15).
36. ἢ πάσαις ἢ τισί, cf. 228 n.
51-3. ἀλλὰ pnd’... ἀπάτης. This may mean (1) ‘but also
nothing else, i.e. none of the propositions opposed to the first
principles, from which propositions the opposite and false con-
clusion would follow, must be more credible or better known to
him than the first principles’, or (2) ‘but also nothing must be
more credible or better known to him than the propositions
opposed to the principles from which the opposite and false
conclusion would follow’, i.e. than the true principles. T. 8. 16-20
512 COMMENTARY
and P. 41. 21-42. 2 take the words in the first sense; Zabarella
adopts a third interpretation—'but also nothing must be more
credible or better known to him than the falsity of the propositions
opposed to the principles, from which propositions the opposite
and false conclusion would follow' ; but this is hardly a defensible
interpretation. Between the other two it is difficult to choose.
CHAPTER 3
Two errors—the view that knowledge ts impossible because 1t involves
an infinite regress, and the view that circular demonstration 15
satisfactory
7255. Because the first principles need to be known, (1) some
think knowledge is not possible, (2) some think it is but everything
is provable; neither view is either true or required by the facts.
(1) The former school think we are involved in an infinite regress,
on the ground that we cannot know the later propositions because
of the earlier «nless there are first propositions (and in this they
are right ; for it is impossible to traverse an infinite series) ; while
if there are, they are unknowable because there is no proof of
them, and if they cannot be known, the later propositions cannot
be known simply, but only known to be true if the first .principles
are.
15. (2) The latter school agree that knowledge is possible only
by way of proof, but say there can be proof of all the propositions,
since they can be proved from one another.
18. (Repudiation of the underlying assumption that all know-
ledge is demonstrative.» We maintain that (a) not all knowledge
is demonstrative, that of immediate premisses not being so (this
must be true; for if we need to know the earlier propositions,
and these reach their limit in immediate propositions, the latter
must be indemonstrable) ; and (δ) that there is not only scientific
knowledge but also a starting-point of it, whereby we know the
limiting propositions.
25. (Refutation of second view.» (a) That proof in the proper
sense cannot be circular is clear, if knowledge must proceed from
propositions prior to the conclusion; for the same things cannot
be both prior and posterior to the same things, except in the
sense that some things may be prior for us and others prior with-
out qualification—a distinction with which induction familiarizes
us. If induction be admitted as giving knowledge, our definition
of unqualified knowledge will have been too narrow, there being
I. 3. 7255-6 513
two kinds of it; or rather the second kind is not demonstration
proper, since it proceeds only from what is more familiar to us.
32. (δ) Those who say demonstration is circular make the
further mistake of reducing knowledge to the knowledge that a
thing is so if it is so (and at that rate it is easy to prove anything).
We can show this by taking three propositions; for it makes no
difference whether circular proof is said to take place through
a series of many or few, but it does matter whether it is said to
take place through few but more than two, or through two
(i) When A implies B and B implies C, A implies C. Nowif
(ii) A implies B and B implies A, we may represent this as a
special case of (i) by putting A in the place of C. Then to say (as
in (ii)) ‘B implies A’ is a case of saying (as in (i)) ‘B implies C’,
and this «together with ‘A implies B’> amounts to saying
‘A implies C’; but C is the same as A. Thus all they are saying
is that A implies A; but at that rate it would be easy to prove
anything.
73°6. But indeed (c) even such proof as this is possible only in
the case of coextensive terms, i.e. of attributes peculiar to their
subjects. We have shown that from the assumption of one term
or one premiss nothing follows; we need at least two premisses,
as for syllogism in general. If A is predicable of B and C, and
these of each other and of A, we can prove, in the first figure, all
of these assumptions from one another, but in the other figures
we get either no conclusion or one different from the original
assumptions. When the terms are xot mutually predicable
circular proof is impossible. Thus, since mutually predicable
terms are rare in demonstration, it is a vain claim to say that
proof is circular and that in that way there can be proof of every-
thing.
7255-6. ᾿Ενίοις μὲν οὖν... εἶναι. There are allusions to this
view in Met. 101133-13 (εἰσὶ δέ τινες ot ἀποροῦσι kai τῶν ταῦτα
πεπεισμένων καί τῶν τοὺς λόγους τούτους μόνον λεγόντων' ζητοῦσι
γὰρ τίς ὃ κρινῶν τὸν ὑγιαίνοντα καὶ ὅλως τὸν περὶ ἕκαστα κρινοῦντα
ὀρθῶς. τὰ δὲ τοιαῦτα ἀπορήματα ὅμοιά ἐστι τῷ ἀπορεῖν πότερον καθεύ-
δομεν νῦν ἢ ἐγρηγόραμεν, δύνανται δ᾽ αἱ ἀπορίαι αἱ τοιαῦται πᾶσαι τὸ
αὐτό: πάντων γὰρ λόγον ἀξιοῦσιν εἶναι οὗτοι: ἀρχὴν γὰρ ζητοῦσι, καὶ
ταύτην δι’ ἀποδείξεως λαμβάνειν, ἐπεὶ ὅτι γε πεπεισμένοι οὐκ εἰσί,
φανεροί εἰσιν ἐν ταῖς πράξεσιν. ἀλλ᾽ ὅπερ εἴπομεν, τοῦτο αὐτῶν τὸ
πάθος ἐστίν: λόγον γὰρ ζητοῦσιν ὧν οὐκ ἔστι λόγος" ἀποδείξεως γὰρ
ἀρχὴ οὐκ ἀπόδειξίς ἐστιν), 100625—9 (ἀξιοῦσι δὴ καὶ τοῦτο ἀποδεικνύναι
τινὲς δι’ ἀπαιδευσίαν: ἔστι γὰρ ἀπαιδευσία τὸ μὴ γιγνώσκειν τίνων
4085 Ll
514 COMMENTARY
Set ζητεῖν ἀπόδειξιν καὶ τίνων οὐ δεῖ" ὅλως μὲν yap ἁπάντων ἀδύνατον
ἀπόδειξιν εἶναι (εἰς ἄπειρον γὰρ ἂν βαδίζοι, ὥστε μηδ᾽ οὕτως εἶναι
ἀπόδειξιν), 1012420-1 (o£ m οὖν διὰ τοιαύτην αἰτίαν λέγουσιν, οἱ δὲ
διὰ τὸ πάντων ζητεῖν λόγον). It is not improbable that the school
of Antisthenes is referred to (cf. 1006*s—g quoted above with
of ᾿ἀντισθένειοι kal of οὕτως ἀπαίδευτοι (1043524), Ἀντισθένης ero
εὐήθως (1024532). The arguments for supposing Antisthenes to be
referred to are stated by Maier (2 b. 15 n. 2); he follows Dümmler
too readily in scenting allusions to Antisthenes in Plato, but he
is probably right in saying that A.'s allusions are to Antisthenes.
Cf. my note on Met. 1oosb2-5.
We cannot certainly identity the second school, referred to (in
b6—7) as having held that knowledge is possible because there
is no objection to circular proof. P. offers no conjecture on the
subject. Cherniss (A.’s Criticism of Plato and the Academy,
i. 68) argues that 'it is probable that the thesis which A. here
criticizes was that of certain followers of Xenocrates who had
abandoned the last vestiges of the theory of ideas and therewith
the objects of direct knowledge that served as the principles of
demonstrative reason' ; and he may well be right.
6. πάντων μέντοι ἀπόδειξις εἶναι. ἀπόδειξις is more idiomatic
than ἀποδείξεις (cf. P2, 17, 73220), which is easily accounted for
by itacism.
7-15. oi μὲν yàp ὑποθέμενοι. . . ἔστιν. The argument is a
dilemma: (1) If there are not primary propositions needing no
proof, the attempt to prove any proposition involves an infinite
regress, which necessarily cannot be completed ; (2) if it is claimed
that there ave such propositions, this must be denied, since the
only knowledge is by way of proof.
7-8. of μὲν yap ὑποθεμένοι.... ἐπίστασθαι. Bekker and Waitz
are right in reading ὅλως with n, against the evidence of most of
the MSS.; for these words answer to ἐνίοις μέν (05) and refer to
those who believe knowledge to be impossible, while of δέ (>r5)
answers to τοῖς δ᾽ (6) and refers to those who hold that circular
reasoning gives knowledge. That knowledge is not possible other-
wise than by proof is common ground to both schools (b15-16),
so that ἄλλως would not serve to distinguish the first school from
the second. P. read ὅλως (42.11, 45. 17).
22. ἵσταται δέ ποτε τὰ ἄμεσα. This is a rather careless account
of the situation more accurately expressed in 95522 by the words
στήσεταί που eis ἄμεσον. What A. means is that in the attempt
to prove what we want to prove, we must sooner or later come
to immediate premisses, not admitting of proof.
I. 3. 7256— 7336 515
23-4. kai οὐ μόνον . . . γνωρίζομεν. A.’s fullest account of the
faculty by which ἀρχαί come to be known is to be found in An.
Post. ii. 19.
29. ὅνπερ τρόπον... γνώριμον is rather loosely tacked on—
‘a distinction of senses of "prior" with which induction familiar-
izes us', since in it what is prior in itself is established by means of
what is prior to us.
30-2. εἴ δ᾽ οὕτως... γνωριμωτέρων. If the establishment of
what is prior in itself by what is prior to us be admitted, (a)
knowledge in the strict sense will not have been correctly defined
by us in ch. 2 as proof from what is prior in itself, since there is
another kind of it, or rather (b) the other is not strictly proof
(nor strictly knowledge).
31. γινομένη γ᾽. Neither Bekker's reading γινομένη, Waitz's
reading γινομένη ἡ, nor P.'s reading ἡ γινομένη is really satisfac-
tory; a more idiomatic text is produced by reading γινομένη y'—
*or should we say that one of the two processes is not demonstra-
tion in the strict sense, since it arises from what is more familiar
to us?', not from what is more intelligible in itself.
32773'6. συμβαίνει δὲ. . . padiov. The passage is difficult
because it is so tersely expressed. The sense is as follows: 'The
advocates of circular reasoning cannot show that by it any pro-
position can be known to be true, but only that it can be known
to be true if it is true—which is clearly worthless, since if this
were proof of the proposition, any and every proposition could
be proved. This becomes clear if we take three ὅροι; it does not
matter whether we take many or few, but it does matter whether
we take few or two’ ('few' being evidently taken to mean ‘three
or more’). One's first instinct is to suppose that A. is asserting
the point, fundamental to his theory of reasoning, that there
must be three terms—two to be connected and one to connect
them. But it is clear that in 72537-7336 A, B, and C are pro-
positions, not terms; and in fact A. very often uses ópos loosely in
this sense. What he goes on to say is this: The advocates of
circular proof claim that if they can show that if A is the case
B is the case, and that if B is the case A is the case, they have
shown that A is the case. But, says A., the situation they en-
visage is simply a particular case of a wider situation—that in
which if A is the case B is the case, and if B is the case C is the
case; and just as there what is proved is not that C is the case,
but that C is the case if A is the case, so here what is proved
is not that A is the case, but only that A is the case if A is the
case.
516 COMMENTARY
τοῦτο δ᾽ ὅτι τοῦ A ὄντος τὸ Γ ἔστι (7343) is difficult, and may be
corrupt. If it is genuine, it must be supposed to mean ‘and (since
if A is true B is true» this implies that if A is true C is true’.
73*6-20. Οὐ μὴν GAA’... ἀπόδειξιν. A. comes now to his
third argument against the attempt to treat all proof as being
circular. He has considered circular proof in An. Pr. ii. 5-7. He
has shown that if we have a syllogism All B is A, All C is B,
Therefore all C is A, we can prove the major premiss from the
conclusion and the converse of the minor premiss (All C is A,
Ali B is C, Therefore all B is A), and the minor premiss from the
conclusion and the converse of the major premiss (All A is B,
All C is A, Therefore all C is B) (57b21-9). But these proofs
are valid only if the original minor and major premiss, respec-
tively, are convertible. And that can be proved only if we add
to the original data (All B is A, All C is B) the datum that the
original conclusion is convertible. Then we can say All 4 is C,
All B is A, Therefore all B is C, and All C is B, All A is C, There-
fore all A is B. Thus, he maintains, we can prove each of the
original premisses by a circular proof in the first figure, only if
we know all three terms to be convertible (73211—14, 57^35-58*15).
The words δέδεικται δὲ καὶ ὅτι ἐν rois ἄλλοις σχήμασιν ἢ οὐ
γίνεται συλλογισμὸς ἢ οὐ περὶ τῶν ληφθέντων (73*15-16) rather over-
state the results reached in An. Pr. ii. 6, 7. What A. has shown
there is that there cannot be in those figures a perfect circular
proof, ie. a pair of arguments proving each premiss from the
conclusion + the converse of the other premiss, because (1) in
the second figure, the original conclusion being always negative,
it is impossible to use it to prove the affirmative original premiss,
and (2) in the third figure, the original conclusion being always
particular, it is impossible to use it to prove the untversal original
premiss (or either premiss if both were universal). The discrepancy
is, however, unimportant ; for A.’s main point is that, even where
the form of a syllogism does not make circular proof impossible,
the matter usually does, since most propositions are not in fact
convertible. A proposition will assert of a subject either its
essence, or part of its essence, or some other attribute of it. Now
if it states any part of the essence other than the lowest differ-
entia, the proposition will not be convertible ; and of non-essential
attributes the great majority are not coextensive with their
subjects; thus only propositions stating the whole essence, or
the last differentia, or one of a comparatively small number out
of the non-essential attributes, are convertible (7376-7, 16-18).
7-11. ἑνὸς μὲν οὖν... συλλογίσασθαι, cf. An. Pr. 34216-21,
I. 3. 736-14 517
40°30-7. Two premisses and three terms are necessary for demon-
strative syllogism, since they are necessary for any syllogism
(εἴπερ καὶ συλλογίσασθαι, *11).
4. ὥσπερ τὰ ἴδια. ἴδια may be used as in Top. 102418 of
attributes convertible with the subject and non-essential, or, as
it is sometimes used (e.g. in 9238), as including also the whole
definition and the lowest differentia, both of which are convertible
with the subject.
II-14. ἐὰν μὲν οὖν... συλλογισμοῦ. A. has shown in An.
Pr. ii. 5 that if we have the syllogism All B is A, All C is B,
Therefore all C is A, then by assuming B and C convertible we
can say All C is A, All B is C, Therefore All B is A, and by
assuming A and B convertible we can say All A is B, All C is A,
Therefore all C is B. Thus the assumptions All C is A, All B is
C, All A is B are all that is needed to prove the two original
assumptions. In the present passage A. names six assumptions—
All B is A, AUC is A, All B is C, AIL C is B, All A is B, All A is
C—and speaks of proving all the airg8évra. What he means, then,
must be that we can prove any of these six propositions by taking
a suitable pair out of the other five; which is obviously true.
CHAPTER 4
The premisses of demonstration must be such that the predicate ts
true of every instance of the subject, true of the subject per se, and
and true of it precisely qua ttself
493221. Since that which is known in the strict sense is in-
capable of being otherwise, that which is known demonstratively
must be necessary. But demonstrative knowledge is that which
we possess by having demonstration; therefore demonstration
must proceed from what is necessary. So we must examine the
nature of its premisses ; but first we must define certain terms.
28. I call that 'true of every instance' which is not true of one
instance and not of another, nor at one time and not at another.
This is supported by the fact that, when we are asked to admit
something as true of every instance, we object that in some
instance or at some time it is not.
34. I describe a thing as ‘belonging fer se’ to something else
if (x) it belongs to it as an element in its essence (as line to
triangle, or point to line; for the being of triangles and lines con-
sists of lines and points, and the latter are included in the defini-
tion of the former); or (2) it belongs to the other, and the other
is included in its definition (as straight and curved belong to line,
518 COMMENTARY
or odd and even, prime and composite, square and oblong, to
number). Things that belong to another but in neither of these
ways are accidents of it.
bg. (3) I describe as ‘existing per se’ that which is not predicated
of something else; e.g. that which is walking or is white must
first be something else, but a substance—an individual thing—is
what it is without needing to be something else. Things that are
predicated of something else I call accidents.
ro. (4) That which happens to something else because of that
thing’s own nature I describe as per se to it, and that which
happens to it not because of its own nature, as accidental; e.g. if
while a man is walking there is a flash of lightning, that is an
accident; but if an animal whose throat is being cut dies, that
happens to the animal fer se.
16. Things that are per se, in the region of what is strictly
knowable, i.e. in sense (1) or (2), belong to their subjects by the
very nature of their subjects and necessarily. For it is impossible
that such an attribute, or one of two such opposite attributes
(e.g. straight or curved), should not belong to its subject. For
what is contrary to another is either its privation or its contra-
dictory in the same genus; e.g., that which is not odd, among
numbers, is even, in the sense that the one follows on the other.
Thus if it is necessary either to affirm or to deny a given attribute
of a given subject, per se attributes must be necessary.
28. I call that ‘universally true’ of its subject which is true of
every case, and belongs to the subject per se, and as being itself.
Therefore what is universally true of its subject belongs to it
of necessity. That which belongs to it per se and that which
belongs to it as being itself are the same. Point and straight belong
to the line per se, for they belong to it as being itself; having
angles equal to two right angles belongs to triangle as being
itself, for they belong to it per se.
32. A universal connexion of subject and attribute is found
when (1) an attribute is proved true of any chance instance of the
subject and (2) the subject is the first (or widest) of which it is
proved true. E.g. (1) possession of angles equal to two right
angles is not a universal attribute of figure (it can be proved true
of a figure, but not of any chance figure); (2) it ss true of any
chance ‘sosceles triangle, but triangle is the first thing of which
it is true.
73°34-°16. Ka8' aórà ... ἀποθανεῖν. Having in *28—34 dealt
with the first characteristic of the premisses of demonstration,
I. 4..73°34—?16 519
that they must be true of every instance of their subject without
exception, A. now turns to the second characteristic, that they
must be true of it καθ᾽ αὑτό, in virtue of its own nature. He pro-
ceeds to define four types of case in which the phrase is applicable,
but of these only the first two are relevant to his theme, the
nature of the premisses of demonstration (cf. b16—:8 n.); the
others are introduced for the sake of completeness. (1) The first
case (*34-7) is this: that which ὑπάρχει to a thing as included in
its essence is καθ᾽ αὑτό to it. ὑπάρχειν is a word constantly used
by A. in describing an attribute as belonging to a subject, and
the type of proposition he has mainly in mind is a proposition
stating one or more attributes essential to the subject and in-
cluded in its definition. But ὑπάρχειν is a non-technical word. Not
only can an attribute be said ὑπάρχειν to its subject, but a con-
stituent can be said ὑπάρχειν to that of which it is a constituent,
and the instances actually given of καθ᾽ αὑτὰ ὑπάρχοντα are limits
involved in the being of complex wholes—lines in the triangle,
points in the line (*35). These two types of καθ᾽ αὑτὰ ὑπάρχοντα
can be included under one formula by saying that καθ᾽ αὑτὰ
ὑπάρχοντα in this sense are things that are mentioned in the
definition of the subject (whether as necessary attributes or as
necessary elements in its nature).
(2) The second case (23755) is that of attributes which while
belonging to certain subjects cannot be defined without mention-
ing these subjects. In all the instances A. gives of this sort of
situation (*38-51, b19—21) these attributes occur in pairs such that
every instance of the subject must have one or other of the
attributes; but there is no reason why they should not occur in
groups of three (e.g. equilateral, isosceles, scalene as attributes
of the triangle) or of some larger number.
For the sake of completeness A. mentions two other cases
in which the expression καθ᾽ αὑτό is used. (3) (Ps-10) From pro-
positions in which an attribute belonging καθ᾽ αὑτό to a subject
is asserted of it, he turns to propositions in which a thing is said
to exist καθ᾽ αὑτό. It is only individual substances (57) that exist
καθ᾽ αὑτά, not in virtue of some implied substratum. When on
the other hand we refer to something by an adjectival or partici-
pial phrase such as τὸ λευκόν or τὸ βαδίζον, we do not mean that
the quality or the activity referred to exists in its own right; it
can exist only by belonging to something that has or does it;
what is white must be a body (or a surface), what.is walking an
animal.
Finally (4) (10-16) we use the phrase to describe a necessary
§20 COMMENTARY
connexion not between an attribute and a subject, but between
two events, viz. the causal relation, as when we say that a thing
to which one event happened became καθ᾽ αὑτό involved in an-
other event, xara standing for διά, which more definitely refers
to the causal relation. This fourth type of καθ᾽ αὑτό is akin to
the first two in that it points to a necessary relation between
that which is καθ᾽ αὑτό and that to which it is καθ᾽ αὐτό, but the
relation here involves temporal sequence, as distinguished from
the timeless connexions between attribute and subject that are
found in the first two types.
34. ὅσα ὑπάρχει τε ἐν τῷ τί ἐστιν. If the position of re be
stressed, A. should be here giving the first characteristic of a
certain kind of καθ᾽ αὐτό, to be followed by another character-
istic introduced by καί; and this we can actually get if we ter-
minate the parenthesis at ἐστί, 5426. But then the second clause,
καὶ ἐν τῷ λόγῳ τῷ λέγοντι τί ἐστιν ἐνυπάρχει, would be practically
a repetition of the first. It is better therefore to suppose that τε
is, as often, slightly misplaced, and that what answers to the
present clause is xai ὅσοις... δηλοῦντι, 437-8.
Zarabella (In Duos Artist. Libb. Post. Anal. Comm.? 23 R-V)
points out that ὅσα ὑπάρχει ἐν τῷ τί ἐστιν does not mean, strictly,
‘those that are present in the τί ἐστιν. The construction of
ὑπάρχειν is not with ἐν (as is that of ἐνυπάρχειν) but with a simple
dative, and the proper translation is 'those things which belong
to a given subject, as elements in its essence'. The full construc-
tion, with both the dative and ἐν, is found in 7458 τοῖς δ᾽ αὐτὰ ἐν
τῷ τί ἐστιν ὑπάρχει κατηγορουμένοις αὐτῶν.
37-8. καὶ ὅσοις τῶν ὑπαρχόντων... δηλοῦντι. ὑπάρχειν, in
A.’s logic, has a rather general significance, including the ‘be-
longing’ of a predicate to its subject, as straight and curved
belong to a line, and the ‘belonging’ to a thing of an element in
its nature, as a line belongs to a triangle. ἐνυπάρχειν on the other
hand is a technical word used to denote the presence of something
as an element in the essence (and therefore in the definition) of
another thing. In certain passages the distinction is very clearly
marked: 838-2 οἷον τὸ εὐθὺ ὑπάρχει γραμμῇ . . . kai πᾶσι
τούτοις ἐνυπάρχουσιν ἐν τῷ λόγῳ τῷ Ti ἐστι λέγοντι ἔνθα μὲν
γραμμή κτλ., 84512 καθ᾽ αὑτὰ δὲ διττῶς" ὅσα τε γὰρ ἐν ἐκείνοις
ἐνυπάρχει ἐν τῷ τί ἐστι, καὶ οἷς αὐτὰ ἐν τῷ τί ἐστιν (Sc. ἐνυπάρχει)
ὑπάρχουσιν (participle agreeing with οἷς) αὐτοῖς" οἷον τῷ ἀριθμῷ
τὸ περιττόν, ὃ ὑπάρχει μεν ἀριθμῷ, ἐνυπάρχει δ᾽ αὐτὸς ὁ ἀριθμὸς
ἐν τῷ λόγῳ αὐτοῦ, ib. 20 πρῶτον ὁ ἀριθμὸς ἐνυπάρξει ὑπάρχουσιν
αὐτῷ. For other instances of ἐνυπάρχειν cf. 73Ρ17, 18, 84*25.. Any-
T..4..73*34 —P18 521
thing that ἐνυπάρχει ἐν something may be said ὑπάρχειν to it,
but not vice versa. In view of these passages I concluded that
ὑπαρχόντων should be read here, and afterwards found that I had
been anticipated by Bonitz (Arist. Stud. iv. 21). The emendation
derives some support from T. 10. 3o ὅσων δὴ συμβεβηκότων
τισὶ τὸν λόγον ἀποδιδόντες τὰ ὑποκείμενα αὐτοῖς συνεφελκόμεθα ἐν TH
λόγῳ, ταῦτα καθ᾽ αὑτὰ ὑπάρχειν τούτοις λέγεται τοῖς ὑποκειμένοις.
The MSS. are similarly confused in 338, 84512, 19, 20, and in
Án. Pr. 65°15.
39-'1. kai τὸ περιττὸν... ἑτερόμηκες. Not only odd and
even, but prime and composite, square and oblong (i.e. non-square
composite), are καθ᾽ αὑτό to number in the second sense of καθ᾽
αὑτό.
b7. καὶ τὸ λευκὸν (Aeuxóv». The editions have καὶ λευκόν.
But this does not give a good sense, and n’s καὶ τὸ λευκόν points
the way to the true reading.
16-18. rà ἄρα λεγόμενα... ἀνάγκης. A. seems here to be
picking out the first two senses of καθ᾽ αὑτό as those most per-
tinent to his purpose (the other two having been mentioned in
order to give an exhaustive account of the senses of the phrase).
Similarly it is they alone that are mentioned in 84211-28. They
are specially pertinent to the subject of the Postertor Analytics
(demonstrative science). Propositions predicating of their subject
what is καθ᾽ αὑτό to it in the first sense (viz. its definition or some
element in its definition) occur among the premisses of demon-
stration. With regard to propositions predicating of their subject
something that is καθ᾽ αὑτό to it in the second sense, A. seems not
to have made up his mind whether their place is among the
premisses or among the conclusions of scientific reasoning. In
7455-12 they are clearly placed among the premisses. In 7528-31
propositions asserting of their subjects something that is καθ᾽ αὑτό
to them are said to occur both as premisses and as conclusions,
but A. does not there distinguish between the two kinds of καθ᾽
αὑτό proposition. In 76#32-6 τὸ εὐθύ (a καθ᾽ αὑτό attribute of the
second kind) appears to be treated, in contrast to μονάς and
μέγεθος, as something whose existence has to be proved, not to
be assumed; and περιττόν and ἄρτιον are clearly so treated in
7696-11. In 75*4o-i and in 84311-17 propositions involving καθ᾽
αὑτό attributes are said to be objects of proof, and this must refer
to those which involve καθ᾽ αὑτό attributes of the second kind,
since A. says consistently that both the essence and the existence
of καθ᾽ αὐτό attributes of the first kind are assumed, not proved.
The truth is that A. has not distinguished between two types
522 COMMENTARY
of proposition involving καθ᾽ αὑτό attributes of the second kind.
That every line is either straight, crooked, or curved, or that
every number is either odd or even, must be assumed; that a
particular line is straight (ie. that three particular points are
collinear), or that a number reached by a particular arithmetical
operation is odd, must be proved. Thus to the two types of
ἴδιαι ἀρχαί recognized by A. in 72718-24 he ought to have added
a third type, disjunctive propositions such as ‘every number must
be either odd or even’.
17. οὕτως ὡς ἐνυπάρχειν rots κατηγορουμένοις ἢ ἐνυπάρχεσθαι,
‘as inhering in (i.e. being included in the essence of) the subjects
that are accused of possessing them’ (mode (1) of the καθ᾽ αὑτό
(334—7)), ‘or being inhered in by them (ie. having the subjects
included in their essence),’ (mode (2) of the καθ᾽ αὑτό (337—53)).
κατηγορούμενον, generally used of the predicate, is occasionally,
as here, used of the subject ‘accused’, i.e. predicated about (cf.
An. Pr. 4791).
For ὡς ἐνυπάρχειν = ὡς ἐνυπάρχοντα, cf. 75225.
I9. fj ἁπλῶς ἢ rà ἀντικείμενα. ἁπλῶς applies to the attributes
that are καθ᾽ αὐτό in the first sense, τὰ ἀντικείμενα to those that
are καθ᾽ αὑτό in the second sense.
21-2. ἔστι yàp . . . ἕπεται. Of two contrary terms, i.e. two
terms both positive in form but essentially opposed, either one
stands for a characteristic and the other stands for the complete
absence of that characteristic, while intermediate terms standing
for partial absences of it are possible (as there are colours between
white and black), or one term is 'identical with the contradictory
of the other, within the same genus'. In the latter case, while
the one term is not the bare negation of the other (if it were,
they would be contradictories, not contraries), yet within the
only genus of which either is an appropriate predicate, every term
must be characterized either by the one or by the other. Not
every entity must be either odd or even; but the only entities
that can be odd or even (i.e. numbers) must be one or the other.
The not-odd 2» number is even, not in the sense that ‘even’ means
nothing more than ‘not odd’, but inasmuch as every number that
is not odd must in consequence be even (f ἕπεται).
25-32. Τὸ μὲν ov... ἴσον. A. has in 428-24 stated the first
two conditions for a predicate's belonging καθόλου to its subject—
that it must be true of every instance (κατὰ παντός) and true in
virtue of the subject's nature (καθ᾽ αὑτό). He now adds a third
condition, that it must be true of the subject 7j αὐτό, precisely
as being itself, not as being a species of a certain genus. It is
I. 4. 73°17 —74%2 523
puzzling, then, to find A. saying τὸ καθ᾽ αὑτὸ καὶ fj αὐτὸ ταὐτόν
(028). It must be remembered, however, that he is making his
terminology as he goes. Having first used καθ᾽ αὐτό and # αὐτό as
standing for different conditions, he now intimates that καθ᾽ αὐτό
in a stricter sense means the same as ἦ αὐτό; that which belongs
to a subject strictly καθ᾽ αὑτό is precisely that which belongs to
it gua itself, not in virtue of a generic nature which it shares
with other things; cf. 74?2 n.
This strict sense of καθόλου is, perhaps, found nowhere else
in A. ; usually the word is used in the sense of κατὰ παντός simply ;
e.g. in 99*33-4.
32-74'3. τὸ καθόλου δὲ... πλέον. Universality is present
when (r) the given predicate is true of every chance instance of
the subject, and (2) the given subject is the first, i.e. widest, class,
such that the predicate is true of every chance instance of it.
As a subject of ‘having angles equal to two right angles’, figure
violates the first condition, isosceles triangle the second; only
triangle satisfies both.
34. οὔτε τῷ σχήματί ἐστι καθόλου is answered irregularly by
τὸ δ᾽ ἰσοσκελὲς xrA., 538.
452. τῶν δ᾽ ἄλλων... .. αὑτό,.1.6. not καθ᾽ αὑτό in the stricter
sense of καθ᾽ αὐτό in which it is identified with # αὐτό (73528-9).
CHAPTER 5
How we fall into, and how we can avoid, the error of thinking our
conclusion a true universal proposition when it ts not
7434. We may wrongly suppose a conclusion to be universal,
when (1) it is impossible to find a class higher than the sub-class
of which the predicate is proved, (2) there is such a class but it
has no name, or (3) the subject of which we prove an attribute
is taken only in part of its extent (then the attribute proved will
belong to every instance of the part taken, but the proof will not
apply to this part primarily and universally, i.e. qua itself).
13. (3) If we prove that lines perpendicular to the same line
do not meet, this is not a universal proof, since the property
belongs to them not because they make angles equal in this
particular way, but because they make equal angles, with the
single line.
16. (1) If there were no triangle except the isosceles triangle,
some property of the triangle as such might have been thought
to be a property of the isosceles triangle.
524 COMMENTARY
17. (2) That proportionals alternate might be proved separ-
ately in the case of numbers, lines, solids, and times. It can be
proved of all by a single proof, but separate proofs used to be
given because there was no common name for all the species.
Now the property is proved of all of these in virtue of what they
have in common.
25. Therefore if one proves separately of the three kinds of
triangle that the angles equal two right angles, one does not yet
know (except in the sophistical sense) that the triangle has this
property—even if there is no other species of triangle. One knows
it of every triangle numerically, but not of every triangle in
respect of the common nature of all triangles.
32. When, then, does one know universally? If the essence of
triangle had been the same as the essence of equilateral triangle,
or of each of the three species, or of all together, we should have
been knowing, strictly. But if the essence is not the same, and
the property is a property of the triangle, we were not knowing.
To find whether it is a property of the genus or of the species, we
must find the subject to which it belongs directly, as qualifica-
tions are stripped away. The brazen isosceles triangle has the
property, but the property remains when ‘brazen’ and ‘isosceles’
are stripped away. True, it does not remain when ‘figure’ or
‘closed figure’ is stripped away, but these are not the first quali-
fication whose removal removes the property. If triangle is the
first, it is of triangle that the property is proved universally.
7496-13. ἀπατώμεθα 86 . . . καθόλου. The three causes of
error (i.e. of supposing that we have a universal proof when we
have not) are (1) that in which a class is notionally a specification
of a genus, but it is impossible for us to detect the genus because
no examples of its other possible species exist (27-8, illustrated
916-17); (2) that in which various species of a genus exist, but
because they have no common name we do not recognize the
common nature on whicli a property common to them all depends,
and therefore offer separate proofs that they possess the property
(28-9, illustrated 217—32); (3) that in which various species exist
but a property common to all is proved only of one (?9-13,
illustrated 413-16).
Most of the commentators take the first case to be that in
which a class contains in fact only one individual (like the class
('earth', ‘world’, or ‘sun’), and we prove a property of the
individual without recognizing that it possesses the property not
qua this individual but qua individual of this species. But (a)
I. 5. 7426-32 525
the only instance given (16-17) is that in which we prove some-
thing of a spectes without recognizing that it is a property of the
genus, and (5) in the whole of the context the only sort of proof
A. contemplates is the proof that a class possesses a property.
The reference, therefore, cannot be to unique individuals.
ἢ τὰ καθ᾽ ἕκαστα (#8) can hardly be right. In the illustration
(216-17) A. contemplates only the case in which there is no more
than one species of a genus; and if more than one were referred
to here, the case would be identical with the second, in which
several species are considered but the attribute is not detected
as depending on their generic character, or else with the third,
in which only one out of several species is considered. The words
are omitted by C, and apparently by T. (13. 12-29) and by P.
(72. 23-73. 9); they are a mistaken gloss.
What is common to all three errors is that an attribute which
belongs strictly to a genus is proved to belong only to one, or
more than one, or all, of the species of the genus. In such a case
the attribute is true of the species κατὰ παντός and καθ᾽ αὑτό, but
not 5 αὐτό (as this is defined in ch. 4).
13-16. εἰ οὖν... ἴσαι. The reference is to the proposition
established in Euc. El. i. 28, ‘if a straight line intersecting two
straight lines makes the exterior angle equal to the interior and
opposite angle falling on the same side of it . . . the two straight
lines will be parallel’. The error lies in supposing that the par-
allelness of the lines follows from the fact that the exterior angle
and the interior and opposite angle are equal by being both of
them right angles, instead of following merely from their equality.
17-25. kai τὸ áváAoyov ... ὑπάρχειν. A. refers here to a pro-
position in the general theory of proportion established by
Eudoxus and embodied in Euc. El. v, viz. the proposition that if
A: B —C: D, A:C — B: D, and points out the superiority of
Eudoxus' proof to the earlier proofs which established this pro-
position separately for different kinds of quantity; cf. 85*36-Pr.
and Heath, Mathematics in Aristotle, 43-6.
25-32. διὰ τοῦτο... οἶδεν. Geminus (apud Eutocium im
Apollonium (Apollonius Pergaeus, ed. Heiberg, ii. 170)) says that
οἱ ἀρχαῖοι actually did prove this proposition separately for the
three kinds of triangle. But Eudemus (apud Proclum, in Euclidem,
379), while he credits the Pythagoreans with discovering the
proposition, gives no hint of an earlier stage in which distinct
proofs were given. Geminus' statement may rest on a misunder-
standing of the present passage. This example does not precisely
illustrate the second cause of error (58-9); for the genus triangle
526 COMMENTARY
was not ἀνώνυμον. But it illustrates the same general principle,
that to prove separately that an attribute belongs to several
species, when it really rests upon their common nature, is not
universal proof.
28. εἰ μὴ τὸν σοφιστικὸν τρόπον. A sophist might well say
‘You know that all triangles are either equilateral, isosceles, or
scalene. You have proved separately that each of them has its
angles equal to two right angles. Therefore you know that all
triangles have the property.' A. would reply.'Yes, but you do
not know that all triangles as such have this property ; and only
knowledge that B as such is A is real scientific knowledge that
all B is A’.
29. οὐδὲ καθ᾽ ὅλου τριγώνου, ‘nor does he know it of triangle
universally', should clearly be read instead of the vulgate reading
οὐδὲ καθόλου τρίγωνον. Cf. 75>25 n.
33-4. δῆλον 57... πᾶσιν. It is possible to translate 7j ἑκάστῳ
ἢ πᾶσιν ‘either for each or for all’ but there is no obvious point
in this. A better sense seems to be got if we translate the whole
sentence ‘we should have had true knowledge if it had been the
same thing to be a triangle and (a) to be equilateral, or (b) to
be each of the three severally (equilateral, isosceles, scalene), or
(c) to be all three taken together' (i.e. if to be a triangle were the
same thing as to be equilateral, isosceles, or scalene).
CHAPTER 6
The premisses of demonstration must state necessary connexions
74>5. (x) If, then, demonstrative knowledge proceeds from
necessary premisses, and essential attributes are necessary to
their subjects (some belonging to them as part of their essence,
while to others the subjects belong as part of their essence, viz.
to the pairs of attributes of which one or other necessarily belongs
to a given subject), the demonstrative syllogism must proceed
from such premisses; for every attribute belongs to its subject
either thus or per accidens, and accidents are nof necessary to
their subjects.
13. (2) Alternatively we may argue thus: Since demonstration
is of necessary propositions, its premisses must be necessary.
For we may reason from true premisses without demonstrating,
but not from necessary premisses, necessity being the charac-
teristic of demonstration.
18. (3) That demonstration proceeds from necessary premisses
is shown by the fact that we object to those who think they are
I. 5. 7428-34 527
demonstrating, by saying of their premisses 'that is not neces-
sary'—whether we think that this is so or that it may be so,
as far as the argument goes.
21. Plainly, then, it is folly to be satisfied with premisses that
are plausible and true, like the sophistical premiss 'to know is to
possess knowledge’. It is not plausibility that makes a premiss;
it must be true directly of the subject genus, and not anything
and everything that is true is peculiar to the subject of which
it is asserted.
26. (4) That the premisses must be necessary may also be
proved as follows: If one who cannot show why a thing is so,
though demonstration is possible, has no scientific knowledge of
the fact, then if A is necessarily true of C, but B, his middle term,
is not necessarily connected with the other terms, he does not
know the reason; for the conclusion is not true because of his
middle term, since his premisses are contingent but the conclusion
is necessary.
32. (5) Again, if someone does not know a certain fact now,
though he has his explanation of it and is still alive, and the fact
still exists and he has not forgotten it, then he did not know the
fact before. But if his premiss is not necessary, it might cease
to be true. Then he will retain his explanation, he will still exist,
and the fact will still exist, but he does not know it. Therefore
he did not know it before. If the premiss has not ceased to be
true but is capable of ceasing to be so, the conclusion will be
contingent ; but it is impossible to know, if that is one's state of
mind.
75*1. (When the conclusion is necessary, the middle term used
need not be necessary; for we can infer the necessary from the
non-necessary, as we can infer what is true from false premisses.
But when the middle term is necessary, the conclusion is so, just
as true premisses can yield only a true conclusion ; when the con-
clusion is not necessary, the premisses cannot be so.)
I2. Therefore since, if one knows demonstratively, the facts
known must be necessary, the demonstration must use a neces-
sary middle term—else one will not know either why or that the
fact is necessary ; he will either think he knows when he does not
(if he takes what is not necessary to be necessary), or he will not
even think he knows—whether he knows the fact through middle.
terms or knows the reason, and does so through immediate
premisses.
18. Of non-essential attributes there is no demonstrative
knowledge. For we cannot prove the conclusion necessary, since
528 COMMENTARY
such an attribute need not belong to the subject. One might
ask why such premisses should be sought, for such a conclusion,
if the conclusion cannot be necessary ; one might as well take any
chance premisses and then state the conclusion. The answer is
that one must seek such premisses not as giving the ground on
which a necessary conclusion really rests but as forcing anyone
who admits them to admit the conclusion, and to be saying what
is true in doing so, if the premisses are true.
28. Since the attributes that belong to a genus fer se, and as
such, belong to it necessarily, scientific demonstration must pro-
ceed to and from propositions stating such attributes. For
accidents are not necessary, so that by knowing them it is not
possible to know why the conclusion is true—not even if the
attributes belong always to their subjects, as in syllogisms
through signs. For with such premisses one will not know the
necessary attribute to be a necessary attribute, or know why it
belongs to its subject. Therefore the middle term must belong
to the minor, and the major to the middle, by the nature of the
minor and the middle term respectively.
74^7-10. τὰ μὲν yap... ὑπάρχειν. Cf. the fuller statement in
735343.
13. ὅτι ἡ ἀπόδειξις ἀναγκαίων ἐστί. The sense is much im-
proved by reading dvayxaiwy or dvayxaiov. P.’s paraphrase
(84. 18) εἰ yap ἡ ἀπόδειξις τῶν ἐξ ἀνάγκης ἐστὶν ὑπαρχόντων points to
ἀναγκαίων. A. is arguing that demonstration, which is of necessary
truths, must be from necessary premisses.
21. ἕνεκά ye τοῦ λόγου, not ‘for the sake of the argument’
(which would be inappropriate with οἰώμεθα), but ‘so far as the
argument goes’ (sense 2 of ἕνεκα in L. and 5.)
23-4. olov oi codiorai . . . ἔχειν. The reference must be to
Pl. Euthyd. 277 b, where this is used as a premiss by the sophist
Dionysodorus.
44. φθαρείη δ᾽ ἂν τὸ μέσον, i.e. the connexion of the middle
term with the major or with the mir.or might cease to exist.
7571-17. Ὅταν μὲν οὖν... ἀμέσων. This is usually printed as
a single paragraph, but really falls into two somewhat uncon-
nected parts. The first part (*1-11) points out that the conclusion
of a syllogism may state something that is in fact necessarily
true, even when the premisses do not state such facts, while,
on the other hand, if the premisses state necessary facts, so will
the conclusion. This obviously does not aid A.’s main thesis,
that since the object of demonstration is to infer necessary facts,
Ι. 6. γ407 = 75°17 529
it must use necessary premisses. It is rather a parenthetical com-
ment, and the conclusion drawn in #12 (ἐπεὶ τοίνυν κτλ.) does not
follow from it, but sums up the result of the arguments adduced
in 7455-39, and especially of that in 74>26-32 (cf. οὔτε διότι
75314 with οὐκ οἶδε διότι 74>30). 7521-11 points out the com-
patibility of non-necessary premisses with a necessary conclusion ;
but the fact remains that though you may reach a necessary
conclusion from non-necessary premisses, you will not in that
case know either why or even that the conclusion is necessary.
3-4. ὥσπερ καὶ ἀληθὲς... ἀληθῶν, cf. An. Pr. ii. 2-4.
12-17. ᾿Επεὶ τοίνυν ... ἀμέσων. The conclusion of the sentence
is difficult. The usual punctuation is ἢ οὐδ᾽ οἰήσεται ὁμοίως, ἐάν
τε κτλ. One alteration is obvious ; ὁμοίως must be connected with
what follows, not with what precedes. But the main difficulty
remains. A. says that ‘if one is to know a fact demonstratively,
it must be a necessary fact, and therefore he must know it by
means of premisses that are necessary. If he does not do this,
he will not know either why or even that the fact is necessary, but
will either think he knows this (if he thinks the premisses to be
necessary) without doing so, or will not even think this (sc. if
he does not think the premisses necessary)—alike whether he
knows the fact through middle terms, or knows the reason, and
does so through immediate premisses. There is an apparent
contradiction in representing one who is using non-necessary pre-
misses, and not thinking them to be necessary, as knowing the
conclusion and even as knowing the reason for it. Two attempts
have been made to avoid the difficulty. (r) Zabarella takes A.
to mean 'that you may construct a formally perfect syllogism,
inferring the fact, or even the reasoned fact, from what are
actually true and necessary premisses; yet because you do not
realize their necessity, you have not knowledge’ (Mure ad loc.).
But (a), as Mure observes, in that case we should expect cvàÀ-
λογίσηται for εἴδῃ. This might be a pardonable carelessness ; what
is more serious is (6) that any reference to a man whose premisses
are necessary, but not known by him to be such, has no relevance
to the rest of the sentence, since the words beginning ἢ οὐκ
ἐπιστήσεται deal with a person whose premisses are non-necessary.
(2) Maier (2 b. 250) takes ἐάν re τὸ ὅτι... ἀμέσων to mean ‘when
through other middle terms he knows the fact, or even knows the
reason of the necessity, and knows it by means of other premisses
that are immediate’. But there is no hint in the Greek of refer-
ence to a second syllogism also in the possession of the same
thinker.
4985 Mm
530 COMMENTARY
The solution lies in stressing ἀνάγκη in *14. A. is saying that
if someone uses premisses that are not apodeictic (e.g. All B ts
A, All C is B), and does not think he knows that all B must be
A and all C must be B, he will not know why or even that all
B must be A—alike whether he knows by means of premisses
simply that all C is A, or knows why all C ts A, and does so by
means of immediate premisses—since his premisses are in either
case ex hypothesi assertoric, not apodeictic.
18-19. Sv τρόπον... αὑτά, cf. 7337-53, 7458-10.
21. περὶ τοῦ τοιούτου yap λέγω συμβεβηκότος, in distinction
from ἃ συμβεβηκὸς καθ᾽ αὑτό (i.e. a property).
22-3. καίτοι ἀπορήσειεν .. . εἶναι. The word ἐρωτᾶν, as well as
the substance of what A. says, shows that the reference is to
dialectical arguments.
25-7. δεῖ δ᾽... ὑπάρχοντα. A. points here to the distinction
between the formal necessity which belongs to the conclusion
of any valid syllogism, and the material necessity which belongs
only to the conclusion of a demonstrative syllogism based on
materially necessary premisses.
For ὡς... εἶναι = ὡς... ov cf. 7317.
33. olov of διὰ σημείων συλλογισμοί. For these cf. An. Pr.
70*7—6. These are, broadly speaking, arguments that are neither
from ground to consequent nor from cause to effect, but from
effect to cause or from one to another of two attributes inci-
dentally connected.
CHAPTER 7
The premisses of a demonstration must state essential attributes of
the same genus of which a property ts to be proved
75°38. Therefore it is impossible to prove a fact by transition
from another genus, e.g. a geometrical fact by arithmetic. For
there are three elements in demonstration—(1) the conclusion
proved, i.e. an attribute’s belonging to a genus per se, (2) the
axioms from which we proceed, (3) the underlying genus, whose
per se attributes are proved.
b2. The axioms may be the same; but where the genus is
different, as of arithmetic and geometry, the arithmetical proof
cannot be applied to prove the attributes of spatial magnitudes,
unless spatial magnitudes are numbers; we shall show later that
such application may happen in some cases. Arithmetical proof,
and every proof, has its own subject-genus. Therefore the genus
must be either the same, or the same in some respect, if proof
I. 6. 75818 —7. 75242 531
is to be transferable ; otherwise it is impossible; for the extremes
and the middle term must be drawn from the same genus, since
if they are not connected per se, they are accidental to each other.
12. Therefore geometry cannot prove that the knowledge of
contraries is single, or that the product of two cubic numbers is a
cubic number, nor can one science prove the propositions of
another, unless the subjects of the one fall under those of the
other, as is the case with optics and geometry, or with harmonics
and arithmetic. Nor does geometry prove any attribute that
belongs to lines not gua lines but in virtue of something common
to them with other things.
75*41-2. ἕν δὲ... dv. The ἀξιώματα are the κοιναὶ ἀρχαΐ, the
things one must know if one is to be able to infer anything
(72*16-17). It is rather misleading of A. to describe them as
the ἐξ dv; any science needs also ultimate premisses peculiar to
itself (θέσεις), viz. ὁρισμοί, definitions of all its terms, and ὑπο-
θέσεις, assumptions of the existence in reality of things answering
to its fundamental terms (7214-24). But the axioms are in a
peculiar sense the ἐξ ὧν, the most fundamental starting-points
of all. The ὁρισμοί and ὑποθέσεις, being concerned with the
members of the yévos, are here included under the term yévos.
A.’s view here seems to be that axioms can be used as actual
premisses of demonstration (which is what ἐξ ὧν naturally sug-
gests); and such axioms as 'the sums of equals are equal' are
frequently used as premisses in Euclid (and no doubt were used
in the pre-Euclidean geometry A. knew). But the proper function
of the more general (non-quantitative) axioms, such as the laws
of contradiction and excluded middle, is to serve as that not
from which, but according to which, argument proceeds; even
if we insert the law of contradiction as a premiss, we shall still
have to use it as a principle in order to justify our advance from
that and any other premiss to a conclusion. This point of view
is hinted at in 8836-3 (ἀλλ᾽ οὐδὲ τῶν κοινῶν ἀρχῶν οἷόν τ᾽ εἶναί
τινας ἐξ ὧν ἅπαντα δειχθήσεται: λέγω δὲ κοινὰς οἷον τὸ πᾶν φάναι
ἢ ἀποφάναι' τὰ γὰρ γένη τῶν ὄντων ἕτερα, καὶ τὰ μὲν τοῖς ποσοῖς
τὰ δὲ τοῖς ποιοῖς ὑπάρχει μόνοις, μεθ᾽ ὧν δείκνυται διὰ τῶν κοινῶν).
The conclusion is arrived at by means of (διὰ) the axioms with the
help of (werd) the ἴδιαι ἀρχαί. 76510 puts it still better—Seuavovar
διά τε τῶν κοινῶν καὶ ἐκ τῶν ἀποδεδειγμένων. In accordance with
this, A. points out that the law of contradiction is not expressly
assumed as a premiss unless we desire a conclusion of the form
‘C is A and not also not A’ (7710-21). He points out further that
532 COMMENTARY
the most universal axioms are not needed in their whole breadth
for proof in any particular science, but only ὅσον ἱκανόν, ἱκανὸν
δ᾽ ἐπὶ τοῦ γένους (ib. 23-4, cf. 76942-b2).
bg-6. εἰ μὴ . . . λεχθήσεται. μεγέθη are not ἀριθμοΐ, μεγέθη
being ποσὰ συνεχῆ, ἀριθμοὶ ποσὰ διωρισμένα (Cat. 4522-4). τοῦτο δ᾽
. . . λεχϑήσεται does not, then, mean that in some cases spatial
magnitudes are numbers, but that in some cases the subjects
of one science are at the same time subjects of another, or, as
A. puts it later, fall under those of another, are complexes formed
by the union of fresh attributes with the subjects of the other
(614-17).
6. ὕστερον λεχθήσεται, 7629-15, 23-5, 78534—79*16.
9. ἢ πῇ, Le. in the case of the subaltern sciences referred to
in 56.
13. ὅτι οἱ δύο κύβοι κύβος. This refers not, as P. supposes, to
the famous problem of doubling the cube (i.e. of finding a cube
whose volume is twice that of a given cube), but to the proposition
that the product of two cube numbers is a cube number, a purely
arithmetical proposition, proved as such in Euc. El. ix. 4.
CHAPTER 8
Only eternal connexions can be demonstrated
75°21. If the premisses are universal, the conclusion must be
an eternal truth. Therefore of non-eternal facts we have demon-
stration and knowledge not strictly, but only in an accidental way,
because it is not knowledge about a universal itself, but is limited
to a particular time and is knowledge only in a qualified sense.
26. When a non-eternal fact is demonstrated, the minor pre-
miss must be non-universal and non-eternal—non-eternal because
a conclusion must be true whenever its premiss is so, non-universal
because the predicate will at any time belong only to some
instances of the subject; so the conclusion will not be universal,
but only that something is the case at a certain time. So too with
definition, since a definition is either a starting-point of demon-
stration, or something differing from a demonstration only in
arrangement, or a conclusion of demonstration.
33. Demonstrations of things that happen often, in so far as
they relate to a certain type of subject, are eternal, and in so far
as they are not eternal they are particular.
In chapter 7 A. has shown that propositions proper to one
science cannot be proved by premisses drawn from another; in
L 7. 7555-13 533
ch. 9 he shows that they cannot be proved by premisses applying
more widely than to the subject-matter of the science. There is
a close connexion between the two chapters, which is broken by
ch. 8. Zabarella therefore wished to place this chapter immedi-
ately after ch. το. Further, he inserts the passage 77*5-9, which
is clearly out of place in its traditional position, after ἀλλ᾽ ὅτι
νῦν in 75530. In the absence, however, of any external evidence
it would be rash to effect the larger of these two transferences ;
and as regards the smaller, I suggest ad loc. a transference of
7755-9 which seems more probable than that adopted by Zabarella.
The order of the work as a whole is not so carefully thought
out that we need be surprised at the presence of the present
chapter where we find it. A. is stating a number of corollaries
which follow from the account of the premisses of scientific
inference given in chs. 1-6. The present passage states one of
these corollaries, that there cannot strictly speaking be demon-
stration of non-eternal facts. And, carefully considered, what he
says here has a close connexion with what he has said in ch. 7.
In the present chapter A. turns from the universal and eternal
connexions of subject and attribute which mathematics discovers
and proves, to the kind of proof that occurs in such a science as
astronomy (οἷον σελήνης ἐκλείψεως, 75533). Astronomy differs in
two respects from mathematics; the subjects it studies are in
large part not universals like the triangle, but individual heavenly
bodies like the sun and the moon, and the attributes it studies
are in large part attributes, like being eclipsed, which these sub-
jects have only at certain times. A. does not clearly distinguish
the two points; it seems that only the second point caught his
attention (cf. ποτέ 75526, viv ib. 3o, πολλάκις ib. 33). The gist
of what he says is that in explaining why the moon is eclipsed,
or in defining eclipse, we are not offering a strictly scientific
demonstration or definition, but one which is a demonstration
or definition only κατὰ συμβεβηκός (ib. 25). There is an eternal
and necessary connexion involved; it is eternally true that that
which has an opaque body interposed between it and its source
of light is eclipsed; when we say the moon is eclipsed when (and
then because) it has the earth interposed between it and the sun,
we are making a particular application of this eternal connexion.
In so far as we are grasping a recurrent type of connexion, we
are grasping an eternal fact; in so far as our subject the moon
does not always have the eternally connected attributes, we are
grasping a merely particular fact (ib. 33-6).
75>25. ἀλλ᾽ οὕτως... συμβεβηκός. We do not strictly speaking
534 COMMENTARY
prove that or explain why the moon is eclipsed, because it
is not an eternal fact that the moon is eclipsed, but only that
that which has an opaque body interposed between it and its
source of light is eclipsed; the moon sometimes incidentally
has the latter attribute because it sometimes incidentally has
the former.
25. ὅτι οὐ καθ᾽ ὅλου αὐτοῦ ἐστιν. Bekker's reading od καθόλου
is preferable to τοῦ καθόλου, which P. 107. 18 describes as occurring
in most of the MSS. known to him. (T. apparently read καθόλου
simply (21. 18).) But, with Bekker's reading, αὐτοῦ is surprising,
since we should expect αὐτῶν. I have therefore read καθ᾽ ὅλου
αὐτοῦ, ‘not about a whole species itself’; cf. 74*29 n. What A.
means is that strict demonstration yields a conclusion asserting
a species to have an attribute, but that if we know a particular
thing to belong to such a species, we have an accidental sort of
knowledge that it has that attribute.
27. τὴν érépav . . . πρότασιν, the minor premiss, which has for
its subject an individual thing.
27-8. φθαρτὴν μὲν... οὔσης. Bonitz (Arist. Stud. iv. 23-4)
argues that the received text ὅτι καὶ τὸ συμπέρασμα οὔσης makes
A. reason falsely ‘The premiss must be non-eternal if the con-
clusion is so, because the conclusion must be non-eternal if the
premiss is so.’ He therefore conjectures τοιοῦτον for ovens. This
gives a good sense, and is compatible with T.'s εἴπερ τὸ συμπέρασμα
φθαρτὸν ἔσται (21. 22) and P.’s διότι καὶ τὸ συμπέρασμα φθαρτόν
(108. 17). But it is hard to see how τοιοῦτον could have been
corrupted into ovens, and the true reading seems to be provided
by n—ért ἔσται καὶ τὸ συμπέρασμα οὔσης, ‘because the conclusion
will exist when the premiss does', so that if the premiss were
eternal, the conclusion would be so too, while in fact it is ex hy-
pothest not so. For the genitive absolute without a noun, when
the noun can easily be supplied, cf. Kühner, Gr. Gramm. ii. 2.
81, Ànm. 2.
28-9. μὴ καθόλου... ἐφ᾽ Sv. With the reading adopted by
Bekker and Waitz and printed in our text, the meaning will be
that the minor premiss must be particular because the middle
term is at any time true only of some instances of the subject-
genus; with the well-supported reading μὴ καθόλου δὲ ὅτι τὸ μὲν
ἔσται τὸ δὲ οὐκ ἔσται ἐφ᾽ ὧν, the meaning will be that the minor
premiss must be particular because at any time only some
instances of the subject term are in existence. The former sense
is the better, and it is confirmed by the example of eclipse of the
moon (534); for the point there is not that there is a class of
I. 8. 7525-32 535
moons of which not all exist at once, but that the moon has not
always the attribute which, when the moon has it, causes eclipse.
30-2. ὁμοίως δ᾽... ἀποδείξεως. The three kinds of definition
are: (r) a verbal definition of a subject-of-attributes, which needs
no proof but simply states the meaning that everyone attaches
to the name; (2) a causal definition of an attribute, which states
in a concise form the substance of a demonstration showing why
the subject has the attribute; (3) a verbal definition of an attri-
bute, restating the conclusion of such a demonstration without
the premisses (94211-14). An instance of (1) would be ‘a triangle
is a three-sided rectilinear figure’ (9353o-2). An instance of (2)
would be 'thunder is a noise in clouds due to the quenching of
fire’, which is a recasting of the demonstration ‘Where fire is
quenched there is noise, Fire is quenched in clouds, Therefore
there is noise in clouds (93538-94*7). An instance of (3) would be
"thunder is noise in clouds’ (947-9).
Since a definition is either a premiss (ie. a minor premiss
defining one of the subjects of the science in question), or a
demonstration recast, or a conclusion of demonstration, it must
be a universal proposition defining not an individual thing but
a species.
CHAPTER 9
The premisses of demonstration must be peculiar to the science in
question, except in the case of subaltern sciences
75°37. Since any fact can be demonstrated only from its own
proper first principles, i.e. if the attribute proved belongs to the
subject as such, proof from true and immediate premisses does
not in itself constitute scientific knowledge. You may prove
something in virtue of something that is common to other sub-
jects as well, and then the proof will be applicable to things
belonging to other genera. So one is not knowing the subject to
have an attribute qua itself, but per accidens ; otherwise the proof
could not have been applicable to another genus.
7674. We know a fact not per accidens when we know an
attribute to belong to a subject in virtue of that in virtue of which
it does belong, from the principles proper to that thing, e.g. when
we know a figure to have angles equal to two right angles, from
the principles proper to the subject to which the attribute belongs
per se. Therefore if that subject also belongs per se to its subject,
the middle term must belong to the same genus as the extremes.
g. When this condition is not fulfilled, we can still demonstrate
536 COMMENTARY
as we demonstrate propositions in harmonics by means of arith-
metic. Such conclusions are proved similarly, but with a differ-
ence; the fact belongs to a different science (the subject genus
being different), but the reason belongs to the superior science,
to which the attributes are per se objects of study. So that from
this too it is clear that a fact cannot be demonstrated, strictly,
except from its own proper principles; in this case the principles
of the two sciences have something in common.
16. Hence the special principles of each subject cannot be
demonstrated; for then the principles from which we demon-
strated them would be principles of all things, and the knowledge
of them would be the supreme knowledge. For one who knows
a thing from higher principles, as he does who knows it to follow
from uncaused causes, knows it better ; and such knowledge would
be knowledge more truly—indeed most truly. But in fact
demonstration is not applicable to a different genus, except in
the way in which geometrical demonstrations are applicable to
the proof of mechanical or optical propositions, and arithmetical
demonstrations to that of propositions in harmonics.
26. It is hard to be sure whether one knows or not; for it is
hard to be sure that one is knowing a fact from the appropriate
principles. We think we know, when we can prove a thing from
true and immediate premisses; but in addition the conclusions
ought to be akin to the immediate premisses.
75540. ὥσπερ Βρύσων τὸν τετραγωνισμόν. A. refers twice
elsewhere to Bryson's attempt to square the circle—Soph. Εἰ.
171>12-18 rà yap ψευδογραφήματα οὐκ ἐριστικά (κατὰ yàp rà ὑπὸ
τὴν τέχνην oi παραλογισμοῦ, οὐδέ γ᾽ εἴ τί ἐστι ψευδογράφημα περὶ
ἀληθές, οἷον τὸ “Ἱπποκράτους [ἢ ὁ τετραγωνισμὸς ὁ διὰ τῶν μηνίσκων).
ἀλλ’ ὡς Βρύσων ἐτετραγώνιζε τὸν κύκλον, εἰ καὶ τετραγωνίζεται 6
κύκλος, ἀλλ᾽ ὅτι οὐ κατὰ τὸ πρᾶγμα, διὰ τοῦτο σοφιστικός, 172*2-7
οἷον ὁ rerpaywviopos 6 μὲν διὰ τῶν μηνίσκων οὐκ ἐριστικός, ὁ δὲ
Βρύσωνος ἐριστικός- καὶ τὸν μὲν οὐκ ἔστι μετενεγκεῖν ἀλλ᾽ ἣ πρὸς
γεωμετρίαν μόνον διὰ τὸ ἐκ τῶν ἰδίων εἶναι ἀρχῶν, τὸν δὲ πρὸς
πολλούς, ὅσοι μὴ ἴσασι τὸ δυνατὸν ἐν ἑκάστῳ καὶ τὸ ἀδύνατον' ἁρμόσει
γάρ. The point made in all three passages is the same, that
Bryson’s attempt is not scientific but sophistical, or eristic,
because it does not start from genuinely geometrical assumptions,
but from one that is much more general. This was in fact the
assumption that two things that are greater than the same thing,
and less than the same thing, are equal to one another (T. x9. 8,
P. 111. 27). Bryson's attempt is discussed in T. 19. 6—2o, P. 111.
I. 9. 75540— 7623 537
17-114, 17, ps.-Al. in Soph. El. go. 10-21, and in Heath's Hist.
of Gk. Math. i. 223-5, and in his Mathematics in Aristotle, 48-50.
4634-9. Ἕκαστον δ᾽... εἶναι. This difficult passage may be
expanded as follows: ‘We know a proposition strictly, not fer
accidens, when we know an attribute A to belong to a subject C
in virtue of the middle term B in virtue of which A really belongs
to C, as a result of more primary propositions true of B precisely
as B; e.g. we know a certain kind of figure C to have angles equal
to two right angles (A) when we know it as a result of more
primary propositions true precisely of that (B) to which A belongs
per se. And if, as we have seen, A must belong to B simply as B,
it is equally true that B (κἀκεῖνο) must belong to its subject C
(ᾧ ὑπάρχει) precisely as C. Thus the middle term must belong
to the same family as both the extreme terms; i.e. both premisses
must be propositions of which the predicate belongs to the
subject not for any general reason but just because of the specific
nature of the subject.’ A. has in mind such a proof as ‘The angles
made by a line when it meets another line (not at either end of
the second line) equal two right angles, The angles of a triangle
equal the angles made by such a line, Therefore the angles of a
triangle equal two right angles’, where the predicate of each
premiss belongs to that subject precisely as that subject.
16-18. Ei δὲ... πάντων. Zabarella supposes A. not to be
denying that metaphysics can prove the ἀρχαί of the sciences,
but only that the sciences can prove their own ἀρχαί. But it is
impossible to reconcile this interpretation with what A. says.
What he says amounts to denying that there can be a master-
knowledge (#18) which, like Plato's dialectic, proves the principles
of the special sciences. There is, so far as I know, no trace in A.
of the doctrine Zabarella suggests as his; in the Metaphysics no
attempt is made to prove the dpyai of the sciences.
22-4. ἡ δ᾽ ἀπόδειξις... ápyovikág. The connexion of thought
is: If it were possible to prove the first principles of the sciences,
the science that did so would be the supreme science (16-22);
but in fact no such use of the conclusions of one science as first
principles for another is possible, except where there is something
common to the subject-matters of the two sciences (cf. 415).
23. ὡς εἴρηται, 75>14-17, 7679-15.
538 COMMENTARY
CHAPTER 10
The different kinds of ultimate premiss required by a science
76°31. The first principles in each genus are the propositions
that cannot be proved. We assume the meaning both of the
primary and of the secondary terms; we assume the existence
of the primary and prove that of the secondary terms.
37- Of the first principles some are special to each science,
others common, but common in virtue of an analogy, since they
are useful just in so far as they fall within the genus studied.
Special principles are such as the definition of line or straight,
common principles such as that if equals are taken from equals,
equals remain. It is sufficient to assume the truth of such a
principle within the genus 1n question.
b3. There are also special principles which are assumptions
of the existence of the subjects whose attributes the science
studies; of the attributes we assume the meaning but prove the
existence, through the common principles and from propositions
already proved.
II. For every demonstrative science is concerned with three
things—the subjects assumed to exist (i.e. the genus), the common
axioms, and the attributes.
16. Some sciences may omit some of these; e.g., we need not
expressly assume the existence of the genus, or the meaning of
the attributes, or the truth of the axioms, if these things are
obvious. Yet by the nature of things there are these three
elements.
23. That which must be so by its own nature, and must be
thought to be so, is not an hypothesis nor a postulate. There are
things which must be thought to be so; for demonstration does
not address itself to the spoken word but to the discourse in the
soul ; one can always object to the former, but not always to the
latter.
27. Things which, though they are provable, one assumes
without proving are hypotheses (i.e. hypotheses ad hominem) if
they commend themselves to the pupil, postulates if he has no
opinion or a contrary opinion about them (though 'postulate'
may be used more generally of any unproved assumption of what
can be proved).
35. Definitions are not hypotheses (not being assumptions of
existence or non-existence). The hypotheses occur among the
expressed premisses, but the definitions need only be understood ;
I. το. 76834 — ^9 539
and this is not hypothesis, unless one is prepared to call listening
hypothesis.
39. (Nor does the geometer make false hypotheses, as he has
been charged with doing, when he says the line he draws is a foot
long, or straight, when it is not. He infers nothing from this; his
conclusions are only made obvious by this.)
773. Again, postulates and hypotheses are always expressed
as universal or particular, but definitions are not.
76°34-5. olov τί μονὰς . . . Tolywvov. μονάς is an example of
τὰ πρῶτα (ἴῃ subjects whose definition and existence are assumed
by arithmetic). εὐθύ is put forward as an example of rà ἐκ τούτων
(whose definition but not their existence is assumed by geometry) ;
this is implied by its occurrence as an instance of rà καθ᾽ αὑτά
in the second sense of καθ᾽ αὑτά (i.e. essential attributes) in 73*38.
τρίγωνον might have been put forward as an example of rà πρῶτα
assumed by geometry; for in 73235 it occurs among the subjects
possessing καθ᾽ αὑτά in the first sense (i.e. necessary elements in
their being). But here it is treated as one of rà ἐκ τούτων (i.e.
attributes), as being a particular arrangement of lines. This way
of thinking of it occurs clearly in 71*14 and gz?rs. The genus
whose existence arithmetic presupposes is that of μονάδες
(76435, ^4) or of ἀριθμοί (75b5, 7652, 18, 88528) ; that whose existence
geometry presupposes is that of μεγέθη (7555, 76236, Pr, 88bz9),
or of points and lines (765s, cf. 7517).
bg. ἢ τὸ κεκλάσθαι ἢ νεύειν. κλᾶσθαι is used of a straight line
deflected at a line or surface; cf. Phys. 228524, Pr. 912529, Euc.
El. ii. 2o, Data 89, Apollon. Perg. Con. ii. 52, 3. 52, etc. A. dis-
cusses the problem of ἀνάκλασις in Mete. 372534-373'19, 375>16-
377228. νεύειν is used of a straight line tending to pass through
a given point when produced; cf. Apollon. Perg. Com. i. 2. ai
veces was the title of a work by Apollonius, consisting of pro-
blems in which a straight line of given length has to be placed
between two lines (e.g. between two straight lines, or between
a straight line and a circle) in such a direction that it 'verges
towards' (ie. if produced, would pass through) a given point
(Papp. 67o. 4). It is remarkable that A. should refer to 'verging'
as one of the terms whose definitions must be presupposed in
mathematics; for it played no part in elementary Greek mathe-
matics as it is known to us. Oppermann and Zeuthen (Die Lehre
v. d. Kegelschnitten im Alterthum, 261 ff.) conjecture that νεύσεις
were in earlier times produced by mechanical means and thus
played a part in elementary mathematics.
540 COMMENTARY
X0. διά re τῶν κοινῶν. .. ἀποδεδειγμένων, cf. 75241—2 n.
I4. τὰ κοινὰ λεγόμενα ἀξιώματα, the axioms which the mathe-
maticians call common (cf. Met. 1005820 rà ἐν τοῖς μαθήμασι
καλούμενα ἀξιώματα), though in truth they are common only
κατ᾽ ἀναλογίαν, as explained in 238-52.
23-7. Οὐκ ἔστι δ᾽... dei. A. here distinguishes ἀξιώματα
from ὑποθέσεις and αἰτήματα. The former are propositions that
are necessarily and immediately (8 αὐτό) true, and are neces-
sarily thought to be true. They may indeed be denied in words;
but demonstration addresses itself not to winning the verbal
assent of the learner, but to winning his internal assent. He may
always verbally object to our verbal discussion, but he cannot
always internally object to our process of thought.
The phrase 6 ἔσω λόγος was suggested by Plato's λόγον ὃν αὐτὴ
πρὸς αὑτὴν ἡ ψυχὴ διεξέρχεται περὶ ὧν ἂν σκοπῇ (Theaet. 189 e).
The distinction between αἴτημα and ἀξίωμα corresponds (as
B. Einarson points out in A.J.P. lvii (1936), 48) with that between
αἰτῶ, ‘request’, and ἀξιῶ, ‘request as fair and reasonable’. .
On the terms ὑπόθεσις and αἴτημα cf. Heath, Mathematics in
Aristotle, 54-7.
27-9. Soa μὲν οὖν... ὑποτίθεται. This sense of ὑπόθεσις, as
the assumption of something that is provable (which is scienti-
fically improper), is to be distinguished from the other sense of
the word in the Posterior Analytics, in which it means the assump-
tion of something that cannot and need not be proved, viz. of
the existence of the primary objects of a science; cf. 72*18-20,
where it is one kind of ἄμεσος ἀρχή, i.e. of unprovable first prin-
ciple. A.’s logical terminology was still in process of making.
It is probably to distinguish the kind of ὑπόθεσις here referred
to from the other that A. adds xai ἔστιν οὐχ ἁπλῶς ὑπόθεσις ἀλλὰ
πρὸς ἐκεῖνον μόνον. Such an hypothesis is not something to be
assumed without qualification, since it is provable (presumably
by a superior science (cf. 75>14-17); but it is a legitimate hypo-
thesis in face of a student of the inferior science who is prepared
to take the results of the superior science for granted.
32-4. ἔστι γὰρ. . . δείξας. The fact that two definitions of
αἴτημα are offered indicates that it, like ὑπόθεσις, has not yet
hardened into a technical term.
M. Hayduck (Obs. Crit. in aliquot locos Arist. 14), thinking that
a reference to the state of mind of the learner is a necessary part
of the definition of an αἴτημα, and pointing out that the second
definition given of αἴτημα is equivalent to that given in 27-8
of the genus which includes ὑπόθεσις as well, omits ἢ in 533. But
I. ro. 76610 — 7752 541
it is read by P. (129. 8-17) as well as by all the MSS., and 6 ἂν
... λαμβάνῃ suggests that a wider sense than that indicated in
b30—3 is being introduced.
The sense given by A. to αἴτημα is quite different from that
given by Euclid to it. Euclid's first three postulates are practical
claims—claims to be able to do certain things—to draw a straight
line from any point to any other, to produce a finite straight line,
to draw a circle with any centre and any radius. The other two,
which Euclid illogically groups with these, are theoretical assump-
tions—the assumptions that all right angles are equal, and that
if a straight line falling on two other straight lines makes interior
angles on the same side of it less than two right angles, the two
straight lines if produced indefinitely will meet—the famous
postulate of parallels.
35-6. οὐδὲν yàp . Ls λέγεται. Neither οὐδὲ. . . λέγονται
(Bekker) nor οὐδὲν... λέγονται (Waitz) gives a good sense; it
seems necessary to read οὐδὲν... λέγεται. When οὐδέν had once
been corrupted into οὐδέ, the corruption of λέγεται naturally
followed.
36-9. ἀλλ᾽ ἐν ταῖς mporáoeow . . . συμπέρασμα. Hypotheses
must be definitely stated in the premisses (536), and the conclu-
sions follow from them (38-9). Definitions have only to be under-
stood by both parties, and they should not be called hypotheses
unless we are prepared to call intelligent listening a form of
hypothesis or assufnption.
39-7722. οὐδ᾽ ὁ γεωμέτρης . . . δηλούμενα. The statement that
definitions are not hypotheses, because they do not occur among
the premisses on which proof depends, leads A. to point out
parenthetically that the same is true of the geometer’s ‘let AB be
a straight line’. It does not matter if what he draws is not a
straight line, for what he draws serves for illustration, not for
proof. In 773 A. returns to his main theme.
7731-2. τῷ tHVvde . . . ἔφθεγκται, ‘from the line’s being the kind
of line he has called it’. The omission of the article between τήνδε
and γραμμήν is made possible by the fact that a relative clause
follows; cf. Kühner, Gr. Gramm. ii. 1. 628, Anm. 6 (a), which
quotes Thuc. ii. 74 ἐπὶ γῆν τήνδε ἤλθομεν ἐν ἧ xrÀ., and other
passages. But it may be conjectured that we should read οἵαν
for ἥν and translate ‘The geometer infers nothing from this
particular line's being a line such as he has described it as being’.
542 COMMENTARY
CHAPTER 11
The function of the most general axioms in demonstration
77'5. Proof does not require the existence of Forms—i.e. of
a one apart from the many—but of one predicable of many, i.e.
of a universal (not a mere ambiguous term) to serve as middle
term.
10. No proof asserts the law of contradiction unless it is
desired to draw a conclusion in the form ‘C is A and not not-A’;
such a proof does require a major premiss 'B is A and not not-A’.
It would make no difference if the middle term were both true
and untrue of the mihor, or the minor both true and untrue of
itself.
18. The reason is that the major term is assertible not only
of the middle term but also of other things, because it is wider,
so that if both the middle and its opposite were true of the minor,
it would not affect the conclusion.
22. The law of excluded middle is assumed by the reductio ad
impossibile, and that not always in a universal form, but in the
form that is sufficient, i.e. as applying to the genus in question.
26. All the sciences are on common ground in respect of the
common principles (ie. the starting-points, in distinction from
the subjects and the attributes proved). Dialectic too has com-
mon ground with all the sciences, and so would any attempt to
prove the common principles. Dialectic is not, like the sciences,
concerned with a single genus; if it were, it would not have
proceeded by asking questions ; you cannot do that in demonstra-
tion because you cannot know the same thing indifferently from
either of two opposite premisses.
775-9. Εἴδη piv οὖν... ὁμώνυμον. T. (21. 7-15) apparently
found this passage, in the text he used, between 75524 ἀποδείξεως
and ib. 25 οὐκ ἔστιν, and Zabarella transfers it to 7553o. But at
both these points it would somewhat break the connexion. On
the other hand, it would fit in thoroughly well after 83%32-5.
It is clearly out of place in its present position.
12-18. δείκνυται δὲ... οὔ. A. points out (1) that in order to
get the explicit conclusion ‘C is A and not non-A’, the major
premiss must have the explicit form ‘B is A and not non-A’
(*12-13). (2) As regards the minor premiss it would make no
difference if we defied the law of contradiction and said 'C is
both B and non-B’ (213-14), since if B is A and not non-A, then
I. τι. 7735-35 543
if C is B (even if it is also non-B), it follows that C is A and not
non-A. To this A. adds (ὡς δ᾽ αὔτως xai τὸ τρίτον, *14-15) the
further point (3) that it would make no difference if the opposite
of the minor term were predicable of the minor term, since it
would still follow that C is A and not non-A.
εἰ yap... οὔ (415-18), ‘if it was given that that of which ‘man’
can truly be asserted—even if not-man could also be truly
asserted of it (point (2) above)—if it was merely given, I say, that
man is an animal, and not a not-animal (point (1) above), it
will be correct to infer that Callias—even if it is true to say that
he is also not-Callias (point (3) above)—is an animal and not a
not-animal'.
20-1. οὐδ᾽ εἰ... μὴ αὐτό, ‘not even if the middle term were
both itself and not itself’—so that both it and its opposite could
be predicated of the minor term.
25. ὥσπερ εἴρηται kai πρότερον, cf. 76242->2.
27. κοινὰ δὲ... ἀποδεικνύντες, cf. 75241—2 n.
29. «ai ἡ διαλεκτικὴ πάσαις. It is characteristic of dialectic
to reason not from the principles peculiar to a particular genus
(as the sciences do) but from general principles. These include
both the axioms, which are here in question, and the vaguer
general maxims called τόποι, with the use of which the Topics
are concerned.
29-31. kai εἴ τις... ἄττα. Such an attempt would be a meta-
physical attempt, conceived after the manner of Plato's dialectic,
to deduce hypotheses from an unhypothetical first principle.
A. calls it an attempt, for there can be no proof, in the strict
sense, of the axioms, since they are ἄμεσα. What A. tries to do
in Met. I is rather to remove difficulties in the way of acceptance
of them than to prove them, strictly. It is obvious that no proof
of the law of contradiction, for example, is possible, since all
proof assumes this law.
32. οὕτως, like a science, or even like metaphysics.
34-5. δέδεικται δὲ... συλλογισμοῦ. The reference is not, as
Waitz and Bonitz's Index say, to An. Pr. 6457-13, which deals
with quite a different point, but to Am. Pr. 57*36-b17.
544 COMMENTARY
CHAPTER 12
Error due to assuming answers to questions inappropriate to the
science distinguished from that due to assuming wrong answers to
appropriate questions or to reasoning wrongly from true and appro-
priate assumptions. How a science grows
77°36. If that which an opponent is asked to admit as a basis
for syllogism is the same thing as a premiss stating one of two
contradictory propositions, and the premisses appropriate to a
science are those from which a conclusion proper to the science
follows, there must be a scientific type of question from which
the conclusions proper to each science follow. Only that is a
geometrical question from which follows either a geometrical
proposition or one proved from the same premisses, e.g. an optical
proposition.
b3. Of such propositions the geometer must render account, on
the basis of geometrical principles and conclusions, but of his
principles the geometer as such must not render account. There-
fore a man who knows a particular science should not be asked,
and should not answer, any and every kind of question, but only
those appropriate to his science. If one reasons with a geometer,
qua geometer, in this way, one will be reasoning well—viz. if one
reasons from geometrical premisses.
11. If not, one will not be reasoning well, and will not be
refuting the geometer, except fer accidens; so that geometry
should not be discussed among ungeometrical people, since among
such people bad reasoning will not be detected.
16. Are there ungeometrical as well geometrical assumptions?
Are there, corresponding to each bit of knowledge, assumptions due
to a certain kind of ignorance which are nevertheless geometrical
assumptions ? Is the syllogism of ignorance that which starts from
premisses opposite to the true premisses, or that which is formally
invalid but appropriate to geometry, or that which is borrowed from
another science? A musical assumption applied to geometry is
ungeometrical, but the assumption that parallels meet is in one
sense geometrical and in another not. ‘Ungeometrical’ is am-
biguous, like 'unrhythmical'; one assumption is ungeometrical
because it has not geomeirical quality, another because it is
bad geometry; it is the latter ignorance that is contrary to
geometrical knowledge.
27. In mathematics formal invalidity does not occur so often,
because it is the middle term that lets in ambiguity (having the
I. 12 545
major predicated of all of it, and being predicated of all of the
minor—we do not add ‘all’ to the predicate in either premiss),
and geometrical middle terms can be seen, as it were, by in-
tuition, whereas in dialectical argument ainbiguity may escape
notice. Is every circle a figure? You have only to draw it to
see that it is. Are the epic poems a circle in the same sense?
Clearly not. ‘
34. We should not meet our opponent’s assumption with an
objection whose premiss is inductive. For as that which is not
true of more things than one is not a premiss (for it would not be
true of ‘all so-and-so’, and it is from universals that syllogism
proceeds), neither can it be an objection. For anything that is
brought as an objection can become a premiss, demonstrative
or dialectical.
40. People sometimes reason invalidly because they assume
the attributes of both the extreme terms, as Caeneus does when
he reasons that fire spreads in geometrical progression, since both
fire and this progression increase rapidly. That is not a syllogism ;
but it would be one if we could say ‘the most rapid progression
is geometrical, and fire spreads with the most rapid progression
possible to movement’. Sometimes it is impossible to reason
from the assumptions ; sometimes it is possible but the possibility
is not evident from the form of the premisses.
786. If it were impossible to prove what is true from what is
false, it would be easy to resolve problems; for conclusions would
necessarily reciprocate with the premisses. If this were so, then
if A (the proposition to be proved) entails a pair of propositions
B, which I know to be true, I could infer the truth of A from
that of B. Reciprocity occurs more in mathematics, because
mathematics assumes no accidental connexions (differing in this
also from dialectic) but only definitions.
I4. A science is extended not by inserting new middle terms,
but (1) by adding terms at the extremes (e.g. by saying ‘A is
true of B, B of C, C of D', and so ad infinitum) ; or (2) by lateral
extension, e.g. if A is finite number (or number finite or infinite),
B finite odd number, C a particular odd number, then A is true
of C, and our knowledge can be extended by making a similar
inference about a particular even number.
The structure of this chapter is a very loose one. There is a
main theme—the importance of reasoning from assumptions
appropriate to the science one is engaged in and not borrowing
assumptions from another sphere; but in addition to that source
4485 Nn
546 COMMENTARY
of error A. mentions two others—the use of assumptions appro-
priate to the science but false, and invalid reasoning (77518-21)—
and devotes some space to the latter of these two (627-33, 40-
7896). Finally, there are three sections which are jottings having
little connexion with the rest of the chapter (77534-9, 78°6-13,
14-21).
727538-9. εἴη ἄν. . . ἐπιστημονικόν. A. has just said (433)
ἀποδεικνύντα οὐκ ἔστιν ἐρωτᾶν; there must therefore be some
change in the meaning of ἐρωτᾶν. When he says the scientist
does not ask questions, he means that the scientist does not, like
the dialectician, ask questions with the intention of arguing from
either answer indifferently (233-4). The only kind of question
he should ask is one to which he can count on a certain answer
being given, and ἐρώτημα in this connexion therefore = ‘as-
sumption'.
br. ἢ ἃ ἐκ τῶν αὐτῶν. The received text omits d, and Waitz
tries to defend the ellipse by such passages as An. Pr. 25635
καλῶ δὲ μέσον μὲν ὃ kai αὐτὸ ἐν ἄλλῳ καὶ ἄλλο ἐν τούτῳ ἐστίν (cf.
An. Post. 81539, 8241, P1, 3). περὶ ὧν stands for τούτων περὶ ὧν,
and he takes 7 to stand for 7 rovrov d. But Bonitz truly remarks
(Ar. Stud. iv. 33) that where a second relative pronoun is irregu-
larly omitted or replaced by a demonstrative, the relative pronoun
omitted would have had the same antecedent as the earlier
relative pronoun—a typical instance being 81539 ὃ μηδενὶ ὑπάρχει
ἑτέρῳ ἀλλ᾽ ἄλλο ἐκείνῳ (= ἀλλ᾽ ᾧ ἄλλο). d is necessary; it stands
for τούτων d, as περὶ ὧν stands for τούτων περὶ ὧν.
3-6. καὶ περὶ μὲν τούτων... γεωμέτρης, Le. when it is possible
to prove our assumptions from the first principles of geometry and
from propositions already proved, we must so prove them; but
we must not as geometers try to prove the first principles of
geometry ; that is the business, 2f of anyone, of the metaphysician
(cf. #29-31).
18-21. καὶ πότερον. . . τέχνης. P. (following in part 79523)
aptly characterizes the three kinds of ἄγνοια as follows: (1) ἡ κατὰ
διάθεσιν, involving a positive state of opinion about geometrical
questions but erroneous (4) materially or (b) formally, according
as it (a) reasons from untrue though geometrical premisses, or
(b) reasons invalidly from true geometrical premisses, (2) ἡ κατὰ
ἀπόφασιν, a complete absence of opinion about geometrical
questions, with a consequent borrowing of premisses ἐξ ἄλλης
τέχνης.
The sense requires the insertion of 6 before ἐξ ἄλλης τέχνης.
25. ὥσπερ τὸ ἄρρυθμον. It is difficult to suppose that A. can
I. 12. 77°38 —*39 547
have written these words here as well as in the previous line; the
repetition is probably due to the similarity of what follows—xat
TO μὲν ἕτερον... τὸ δ᾽ ἕτερον.
26—7. καὶ ἡ ἄγνοια. . . ἐναντία, ‘and this ignorance, i.e. that
which proceeds from geometrical’ (though untrue) ‘premisses, is
that which is contrary to scientific knowledge’.
32-3. τί δέ... ἔστιν. The Epic poems later than Homer were
designated by the word κύκλος, but if you draw a circle you see
they are not a circle in that sense, and therefore you will be in
no danger of inferring that they are a geometrical figure.
34-9. Οὐ Set δ᾽... διαλεκτική. The meaning of this passage
and its connexion with the context have greatly puzzled com-
mentators, and Zabarella has dealt with the latter difficulty
by transferring the passage to 17. 81237, basing himselt on T.,
who has no reference to the passage at this point but alludes
rather vaguely to it at the end of his commentary on chs. 16 and
17 (31. 17-24). There is, however, no clear evidence that T. had
the passage before him as part of ch. 17, and nothing is gained by
transferring it to that chapter; all the MSS. and P. have it here.
If we keep the MS. reading in 534, dv ἦ ἡ πρότασις ἐπακτική, the
connexion must be supposed to be as follows: À. has just pointed
out (616-33) three criticisms that may be made of an attempted
syllogistic argument—that the premisses, though mathematical
in form, are false, that the reasoning is invalid, that the premisses
are not mathematical at all. He now turns to consider arguments
that are not ordinary syllogisms (with at least one universal
premiss) but are inductive, reasoning to a general conclusion
from premisses singular in form, and says that in such a case
we must not bring an ἔνστασις to our opponent's ἐρώτημα (eis
αὐτό, ^34). This is because a proposition used in an ἔνστασις must
be capable of being a premiss in a positive argument (537-8; cf.
An. Pr. 6903), and any premiss in a scientific argument must be
universal (636-7), while a proposition contradicting a singular
proposition must be singular.
A difficulty remains. In ^34 a singular statement used in induc-
tion is called a πρότασις, but in 535-7 it is insisted that a πρότασις
must be universal. The explanation is that a singular proposition,
which may loosely be called a premiss as being the starting-point
of an induction, is incapable of being a premiss of a syllogism
whether demonstrative or dialectical.
The relevance of the passage to what precedes will be the
greater if we suppose the kind of induction A. has in mind to be
that used in mathematics, where a proposition proved to be true
548 COMMENTARY
of the figure on the blackboard is thereupon seen to be true of all
figures of the same kind.
I have stated the interpretation which must be put on the
passage if the traditional reading be accepted. But the text
is highly doubtful. The reference of αὐτό is obscure, and we should
expect πρός rather than eis (cf. 74>19, 76526). Further, the meaning
is considerably simplified if we read ἐν ἦ ἡ πρότασις ἐπακτική and
suppose the πρότασις in question to be not the original premiss but
that of the objector. This seems to have been the reading which
both T. and P. had before them: T. 31. 18 τὰς ἐνστάσεις ποιητέον
οὐκ ἐπὶ μέρους οὐδ᾽ ἀντιφατικῶς ἀντικειμένας ἀλλ᾽ ἐναντίας xai
καθόλου, P. 157. 22 δεῖ... ἐνισταμένους τὰς ἐνστάσεις μὴ δι᾽ ἐπαγωγῆς
φέρειν... ἀλλὰ καθολικῶς ἐνίστασθαι.
If this reading be accepted the paragraph has much more
connexion with what precedes. There will be no reference to
inductive arguments by the opponent; the point will be that
Syllogistic arguments by him must be met not by inductive
arguments, which cannot justify a universal conclusion, but by
syllogistic arguments of our own.
40-1. Συμβαίνει & . . . ἑπόμενα, ie. by trying to form a
syllogism in the second figure with two affirmative premisses,
they commit the fallacy of undistributed middle (of which one
variety, ambiguous middle, has already been referred to in
527-33).
41. οἷον καὶ ὁ Καινεὺς ποιεῖ. P. describes Caeneus as a sophist,
but no sophist of the name is known and P. is no doubt merely
guessing. The present tense implies that Caeneus was either a
writer or a character in literature, and according to Fitzgerald's
canon à Kawevs should be the latter. The reference must be to
the Καινεύς of A.’s contemporary the comic poet Antiphanes;
A. quotes from the play (fr. 112 Kock) in Rhet. 1407917, 1413*1,
and in Poet. 1457521. The remark quoted in the present passage
is a strange one for a Lapith, but in burlesque all things are
possible.
78*5-6. ἐνίοτε μὲν οὖν... ὁρᾶται. Though a syllogism with
two affirmative premisses in the second figure is always, so far
as can be seen from the form (ὁρᾶται), fallacious, yet if the pre-
misses are true and the major premiss is convertible, the con-
clusion will be true.
6-13. Ei δ᾽... ὁρισμούς. Pacius and Waitz think the move-
ment of thought from A to B here represents an original syllogism,
and that from B to A the proof (Pacius) or the discovery (Waitz)
of the premisses of the original syllogism from its conclusion.
I. 12. 77540 — 78*13 549
This interpretation is, however, negated by the fact that A is
represented as standing for one fact (τούτου) and B for more than
one (ταδί). Two premisses might no doubt be thought of as a
single complex datum, but since from two premisses only one
conclusion follows, it is impossible that the conclusion of an
ordinary syllogism should be expressed by the plural ταδί, There
must be some motive for the use of the singular and the plural
respectively ; and the motive must be (as P. and Zabarella recog-
nize) that the movement from A to B is a movement from a
proposition to premisses—from which, in turn, it may be
established.
When this has been grasped, the meaning of the passage be-
comes clear. ἀναλύειν means not the analysis or reversal of a
given syllogism but the analysis of a problem, i.e. the discovery
of the premisses which will establish the truth of a conclusion
which it is desired to prove. This is just the sense which ἀνάλυσις
bears in a famous passage of the Ethics, 1112620. A. says there
ὁ yàp βουλευόμενος ἔοικε ζητεῖν καὶ ἀναλύειν τὸν εἰρημένον τρόπον
ὥσπερ διάγραμμα (φαίνεται δ᾽ ἡ μὲν ζήτησις οὐ πᾶσα εἶναι βούλευσις,
οἷον af μαθηματικαί, ἡ δὲ βούλευσις πᾶσα ζήτησις), καὶ τὸ ἔσχατον ἐν
τῇ ἀναλύσει πρῶτον εἶναι ἐν τῇ γενέσει. In deliberation we desire
an end ; we ask what means would produce that end, what means
would produce those means, and so on, till we find that certain
means we can take forthwith would produce the desired end.
This is compared to the search, in mathematics, for simpler
propositions which wil enable us to prove what we desire to
prove—which is in fact the method of mathematical discovery,
as opposed to that of mathematical proof.
This gives the clue to what A. is saying here, viz. If true con-
clusions could only follow from true premisses, the task of
analysing a problem would be easy, since premisses and con-
clusion could be seen to follow from each other (46-8). We should
proceed as follows. We should suppose the truth of A, which
we want to prove. We should reason ‘if this is true, certain
other propositions are true', and if we found among these a pair
B, which we knew to be true, we could at once infer that A is
true (48-10). But since in fact true conclusions can be derived
from false premisses (An. Pr. ii. 2-4), if A entails B and B is true
it does not follow that A is true, and so the analysis of problems
is not easy, except in mathematics, where it more often happens
that a proposition which entails others is in turn entailed by
them. This is because the typical propositions of mathematics
are reciprocal, the predicates being necessary to the subjects and
550 COMMENTARY
the subjects to the predicates (as in definitions) (210-13). Thus, for
instance, since it is because of attributes peculiar to the equilateral
triangle that it is proved to be equiangular, the equiangular
triangle can equally well be proved to be equilateral. This con-
stitutes a second characteristic in which mathematics differs from
dialectical argument (#12; the first was mentioned in 77527-33).
The passage may usefully be compared with another dealing
with the method of mathematical discovery, Met. 1051321—-33,
where A. emphasizes the importance of the figure in helping the
discovery of the propositions which will serve to prove the
demonstrandum.
For a clear discussion of analysis in Greek geometry, see
R. Robinson in Mind, xlv (1936), 464-73.
14-21. Αὔξεται δ᾽... τοῦ E. The advancement of a science,
says A., is not achieved by interpolating new middle terms. This
is because the existing body of scientific knowledge must already
have based all its results on a knowledge of the immediate pre-
misses from which they spring ; otherwise it would not be science.
Advancement takes place in two ways: (1) vertically, by extra-
polating new terms, e.g. terms lower than the lowest minor term
hitherto used (214-16), and (2) laterally, by linking a major term,
already known to be linked with one minor through one middle
term, to another minor through another middle; e.g. if we
already know that ‘finite number’ (or ‘number finite or infinite’)
is predicable of a particular odd number, through the middle
term ‘finite odd number’, we can extend our knowledge by making
the corresponding inference about a particular even number,
through the middle term ‘finite even number’. What A. is
speaking of here is the extension of a science by the taking up of
new problems which have a common major term with a problem
already solved; when he speaks of science as coming into being
(not as being extended) by interpolation of premisses, he is think-
ing of the solution of a single problem of the form ‘why is B A?’
(cf. 84519—85212).
CHAPTER 13
Knowledge of fact and knowledge of reasoned fact
78422. Knowledge of a fact and knowledge of the reason for
it differ within a single science, (1) if the syllogism does not pro-
ceed by immediate premisses (for then we do not grasp the
proximate reason for the truth of the conclusion); (2) (a) if it
proceeds by immediate premisses, but infers not the consequent
I. 12. 78*14-21 551
from the ground but the less familiar from the more familiar of
two convertible terms.
28. For sometimes the term which is not the ground of the
other is the more familiar, e.g. when we infer the nearness of the
planets from their not twinkling (having grasped by perception
or induction that that which does not twinkle is near). We have
then proved that the planets are near, but have proved this not
from its cause but from its effect.
39. (b) If the inference were reversed —if we inferred that the
planets do not twinkle from their being near—we should have
a syllogism of the reason.
b4. So too we may either infer the spherical shape of the moon
from its phases, or vice versa.
rr. (3) Where the middle terms are sot convertible and the
non-causal term is the more familiar, the fact is proved but not
the reason.
13. (4) (a) So too when the middle term taken is placed outside
the other two. Why does a wall not breathe? 'Because it is not
an animal.' If this were the cause, being an animal should be the
cause of breathing. So too if the presence of a condition is the
cause of an attribute, its absence is the cause of the absence of
the attribute.
21. But the reason given is not the reason for the wall's not
breathing; for not every animal breathes. Such a syllogism is
in the second figure—Everything that breathes is an animal, No
wall is an animal, Therefore no wall breathes.
28. Such reasonings are like (b) far-fetched explanations, which
consist in taking too remote a middle term—like Anacharsis’ ‘there
are no female flute-players in Scythia because there are no vines'.
32. These are distinctions between knowledge of a fact and
knowledge of the reason within one science, depending on the
choice of middle term; the reason is marked off from the fact
in another way when they are studied by different sciences—
when one science is subaltern to another, as optics to plane
geometry, mechanics to solid geometry, harmonics to arithmetic,
observational astronomy to mathematical.
39. Some such sciences are virtually ‘synonymous’, e.g. mathe-
matical and nautical astronomy, mathematical harmonics and
that which depends on listening to notes. Observers know the
fact, mathematicians the reason, and often do not know the fact,
as people who know universal laws often through lack of observa-
tion do not know the particular facts.
79*6. This is the case with things which manifest forms but
552 COMMENTARY
have a distinct nature of their own. For mathematics is concerned
with forms not characteristic of any particular subject-matter ;
or if geometrical attributes do characterize a particular subject-
matter, it is not as doing so that mathematics studies them.
IO. There is a science related to optics as optics is to geometry,
e.g. the theory of the rainbow; the fact is the business of the
physicist, the reason that of the student of optics, or rather of
the mathematical student of optics. Many even of the sciences
that are not subaltern are so related, e.g. medicine to geometry ;
the physician knows that round wounds heal more slowly, the
geometer knows why they do so.
7822-531. To δ᾽ ὅτι... ἄμπελοι. The distinction between
knowledge of a fact and knowledge of the reason for it, where
both fall within the same science, is illustrated by A. with refer-
ence to the following cases:
(x) (423-6) ‘if the syllogism is not conducted by way of im-
mediate premisses'. Le. if D is A because B is A, C is B, and
D is C, and one says 'D is A because B is A and D is B' or
“because C is A and D is C', one is stating premisses which entail
the conclusion but do not fully explain it because one of them
(D is B', or 'C is A’) itself needs explanation.
(z) Where ‘B is A’ stands for an immediate connexion and is
convertible and being A is in fact the cause of being B, then (a)
(226-39) if you reason 'C is A because B is A and C is B’ (e.g. ‘the
planets are near because stars that do not twinkle are near and
the planets do not twinkle’), you are grasping the fact that C is A
but not the reason for it, since in fact C is B because it is Á, not
A because it is B. But (b) (3539-511), since ‘stars that do not
twinkle are near' is (ex vi materiae, not, of course, ex vi formae)
convertible, you can equally well say 'the planets do not twinkle,
because stars that are near us do not twinkle and the planets
are near us', and then you are grasping both the fact that the
planets do not twinkle and the reason for the fact.
A. describes this as reasoning δι᾽ ἀμέσων (and in this respect
correctly), but only means that the major premiss is ἄμεσος.
(3) (11-13) The case is plainly not improved if, of two non-
convertible terms which might be chosen alternatively as middle
term, we choose that which is not the cause but the effect of the
other. Here not only does our proof merely prove a fact without
giving the ground of it, but we cannot by rearranging our terms
get a proof that does this. Pacius illustrates the case by the
syllogism What is capable of laughing is an animal, Man is
I. 13. 78222 — P31 553
capable of laughing, Therefore man is an animal. Such terms
will not lend themselves to a syllogism τοῦ διότι, i.e. one in which
the cause appears as middle term; for we cannot truly say All
animals are capable of laughing, Man is an animal, Therefore
man is capable of laughing.
(4) (a) (513-28) ‘When the middle term is placed outside.’ In
An. Pr. 26559, 28414 A. says that in the second and third figures
τίθεται τὸ μέσον ἔξω τῶν ἄκρων, and this means that it does not
occur as subject of one premiss and predicate of the other, but
as predicate of both or subject of both. But the third figure is
not here in question, since the Posterior Analytics is concerned
only with universal conclusions; what A. has in mind is the second
figure (>23-4). And the detail of the passage (P15-16, 24-8)
(‘Things that breathe are animals, Walls are not animals, There-
fore walls do not breathe’) shows that the case A. has in mind
is that in which the middle term is asserted of the major and
denied of the minor (Camestres)—the middle, further, not being
coextensive with the major but wider in extension than it. Then
the fact that the middle term is untrue of the minor entails
that the major term is untrue of the minor, but is not the precise
ground of its being so. For if C's non-possession of attribute
A were the cause of its non-possession of attribute B, its pos-
session of A would entail its possession of B; but obviously the
possession of a wider attribute does not entail the possession of
a narrower one.
(b) (528-31) A. says that another situation is akin to this, viz.
that in which people, speaking καθ᾽ ὑπερβολήν, in an extravagant
and epideictic way, explain an effect by reference to a distant
and far-fetched cause. So Anacharsis the Scythian puzzled his
hearers by his riddle *why are there no female flute-players in
Scythia?’ and his answer ‘because there are no vines there’. The
complete answer would be: ‘Where there is no drunkenness there
are no female flute-players, Where there is no wine there is no
drunkenness, Where there are no vines there is no wine, In
Scythia there are no vines, Therefore in Scythia there are no
female flute-players.' The resemblance of this to case (4) is
that in each case a super-adequate cause is assigned; a thing
might be an animal, and yet not breathe, and similarly there
might be drunkenness and yet no female flute-players, wine and
yet no drunkenness, or vines and yet no wine.
Thus the whole series of cases may be summed up as follows:
(1) explanation of effect by insufficiently analysed cause; (2 a)
inference to causal fact from coextensive effect ; (2 b) explanation
554 COMMENTARY
of effect by adequate (coextensive) cause (sctentific explanation) ;
(3) inference to causal fact from an effect narrower than the
cause; (4 à) explanation of effect by super-adequate cause, (4 δ)
explanation of effect by super-adequate and remote cause.
34-5. τοῦτο δ᾽... αἰσθήσεως. Sometimes a single observation
is enough to establish, or at least to suggest, a generalization like
this (cf. 9026-30); more often induction from a number of
examples is required.
38. διὰ τὸ ἐγγὺς εἶναι οὐ στίλβουσιν. A. gives his explanation
more completely in De Caelo 290*17-24.
bz. καὶ τὸ A... στίλβειν. The sense requires the adoption of
n's reading; the MSS. have gone astray through xai ro A τῷ B
having been first omitted and then inserted in the wrong place.
30. olov τὸ τοῦ ᾿Αναχάρσιος. Anacharsis was a Scythian who
according to Hdt. iv. 76-7 visited many countries in the sixth
century to study their customs. Later tradition credits him with
freely criticizing Greek customs (Cic. Tusc. v. 32. 9o; Dio, Or.
32. 44; Luc. Anach., Scyth.). See also Plut. Solon 5.
32-4. κατὰ τὴν τῶν μέσων θέσιν. . . συλλογισμόν, ie. the
different cases differ in respect of the treating of the causal or
the non-causal term as the middle term, and of the placing of the
middle term as predicate of both premisses (as in case (4 a)) or
as subject of the major and predicate of the minor (as in the
other cases).
34~79°16. ἄλλον Bé τρόπον... yewpéerpou. A. recurs here to
a subject he has touched briefly upon in 7553-17, that of the
relation between pure and applied science. He speaks at first as
if there were only pairs of sciences to be considered, a higher
science which knows the reasons for certain facts and a lower
science which knows the facts. Plane geometry is so related to
optics, solid geometry to mechanics, and arithmetic to harmonics.
Further, he speaks at first as if astronomy were in the same rela-
tion to rà φαινόμενα, i.e. to the study of the observed facts about
the heavenly bodies. But clearly astronomy is not pure mathe-
matics, as plane geometry, solid geometry, and arithmetic are.
It is itself a form of applied mathematics. And further, A. goes
on to point out a distinction within astronomy, a distinction
between mathematical astronomy and the application of astro-
nomy to navigation ; and a similar distinction within harmonics,
a distinction between mathematical harmonics and ἡ κατὰ τὴν
ἀκοήν, the application of mathematical harmonics to facts which
are only given us by hearing. The same distinctions are pointed
out elsewhere. In An. Pr. 46?19-21 A. distinguishes astronomical
I. 13. 78834 — 79716 555
experience of rà φαινόμενα from the astronomical science which
discovers the reasons for them. Thus in certain cases A. recog-
nizes a threefold hierarchy, a pure mathematical science, an
applied mathematical science, and an empirical science—e.g.
arithmetic, the mathematical science of music, and an empirical
description of the facts of music; or solid geometry, the mathe-
matical science of astronomy, and an empirical description of
the facts about the heavenly bodies (which is probably what he
means by ναυτικὴ ἀστρολογική) ; or plane geometry, the geometrical
science of optics, and the study of the rainbow (79*10-13). Within
süch a set of three sciences, the third is to the second as the
second is to the first (ib. 10-11); in each case the higher science
knows the reason and the lower knows the fact (78534-9, 7922-6,
11-13). Probably the way in which A. conceives the position is
this: The first science discovers certain very general laws about
numbers, plane figures, or solids. The third, which is only by
courtesy called a science, collects certain empirical facts. The
second, borrowing its major premisses from the first and its minor
premisses from the third, explains facts which the third discovers
without explaining them. Cf. Heath, Mathematics in Aristotle,
58—61.
35. τῷ δι᾽ ἄλλης... θεωρεῖν. τῷ (read by n and p) is obviously
to be read for the vulgate τό.
39-40. σχεδὸν δὲ... ἐπιστημῶν. συνώνυμα are things that
have the same name and the same definition (Cat. 1*6), and T.
rightly remarks that in the case of the pure and applied sciences
mentioned by A. τὸ ὄνομα τὸ αὐτὸ kai ὁ λόγος οὐ πάντῃ ἕτερος.
79°4-6. καθάπερ οἱ τὸ καθόλου θεωροῦντες . . . ἀνεπισκεψίαν.
The possibility of this has been examined in An. Pr. 6748-511.
8-9. οὐ yàp . . . ὑποκειμένου, ‘for mathematics is not about
forms attaching to particular subjects; for even if geometrical
figures attach to a particular subject, mathematics does not study
them qua so doing'.
II. τὸ περὶ τῆς ἴριδος, not, as Waitz supposes, the study of the
iris of the eye, but the study of the rainbow (so T. and P.).
12-13. τὸ δὲ διότι... μάθημα, ‘while the reason is studied by
the student of optics—we may say "by the student of optics"
simply, or (taking account of the distinction between mathe-
matical and observational optics, cf. 78540—79?2) "by one who
is a student of optics in respect of the mathematical theory of
the subject" '.
14-16. ὅτι μὲν yàp . . . γεωμέτρου. P. gives two conjectural
explanations: (1) ‘because circular wounds have the greatest
556 COMMENTARY
area relatively to their perimeter’ ; (2) (which he prefers) "because
ina circular wound the parts that are healing are further separated
and nature has difficulty in joining them up' (sc. by first or second
intention as opposed to granulation) (182. 21-3). He adds that
doctors divide up round wounds and make angles in them, to
overcome this difficulty.
CHAPTER 14
The first figure 1s the figure of scientific reasoning
79°17. The first figure is the most scientific; for (1) both the
mathematical sciences and all those that study the why of things
couch their proofs in this figure.
24. (2) The essence of things can only be demonstrated in this
figure. The second figure does not prove affirmatives, nor the
third figure universals; but the essence of a thing is what it ts,
universally.
29. (3) The first figure does not need the others, but the inter-
stices of a proof in one of the other figures can only be filled up
by means of the first figure.
7925-6. ἐν μὲν γὰρ τῷ μέσῳ . . . συλλογισμός, proved in An.
Pr. i. 5.
27-8. ἐν δὲ τῷ ἐσχάτῳ ... οὐ καθόλου, proved in An. Pr. i. 6.
29-31. ἔτι τοῦτο... ἔλθῃ. With two exceptions, every valid
mood in the second or third figure has at least one universal
affirmative premiss, which can itself be proved only in the first
figure. The two exceptions, Festino and Ferison, have a major
premiss which can be proved only by premisses of the form AE
or EA, and a minor premiss which can be proved only by pre-
misses of the form AA, IA, or AI, and an A proposition can itself
be proved only in the first figure.
30. καταπυκνοῦται. B. Einarson in Á.J.P. lvii (1936), 158, gives
reasons for supposing that this usage of the term was derived
from the use of it to denote the filling up of a musical interval
with new notes.
CHAPTER 15
There are negative as well as affirmative propositions that are
immediate and indemonstrable
79°33- As it was possible for A to belong to B atomically, i.e.
immediately, so it is possible for A to be atomically deniable of
B. (1) When A or B is included in a genus, or both are, A cannot
I. 14. 79*25— 15. 7920 557
be atomically deniable of B. For if A is included in Γ and B is
not, you can prove that A does not belong to B: ‘All A is I’, No
B is I’, Therefore no Bis A.’ Similarly if B is included in a genus,
or if both are.
bs. That B may not be in a genus in which A is, or that A
may not be in a genus in which B is, is evident from the existence
of mutually exclusive chains of genera and species. For if no
term in the chain ATA is predicable of any term in the chain BEZ,
and A is in a genus @ which is a member of its chain, B will
not be in 8; else the chains would not be mutually exclusive.
So too if B is in a genus.
12. But (2) if neither is in any genus, and A is deniable of B,
it must be atomically deniable of it ; for if there were a middle term
one of the two would have to be in a genus. For the syllogism
would have to be in the first or second figure. If in the first, B
will be in a genus (for the minor premiss must be affirmative) ;
if in the second, either 4 or B must (for if both premisses are
negative, there cannot be a syllogism).
79°33. Ὥσπερ δὲ... ἀτόμως. This was proved in ch. 3.
36-7. ὅταν μὲν οὖν... ἄμφω. The reasoning in *38-br2 shows
that by these words A. means ‘when either A is included in a
genus in which B is not, or B in a genus in which 4 is not, or
A and B in different genera’. He omits to consider the case in
which both are in the same genus. The only varieties of this
that need separate consideration are the case in which A and B
are infimae species of the same genus, and that in which they are
members of the same infima species; for in all other cases they
will be members of different species, and the reasoning A. offers
in *38-hi2 will apply. If they are $xfimae species of the same
genus, they will have different differentiae E and F, and we can
infer No B is A from All A is E, No B is E, or from No A is F,
All B is F. A. would have, however, to admit that alternative
differentiae, no less than summa genera or categories, exclude
each other immediately. The case in which A and B are members
of the same infima species would not interest him, since through-
out the Posterior Analytics he is concerned only with relations
between universals.
br-2. ὁμοίως 86 .. . A, sc. καὶ τὸ A μὴ ἔστιν ἐν ὅλῳ τῷ 4.
7. ἐκ τῶν συστοιχιῶν. συστοιχία is a word of variable meaning
in A., but stands here, and often, for a chain consisting of a genus
and its species and sub-species.
15-20. ἢ yap... ἔσται. Only the first and second figure can
558 COMMENTARY
prove a universal negative, and in these only Celarent and Cesare,
in which the minor premiss includes the minor term in the
middle term, and Camestres, in which the major premiss includes
the major term in the middle term.
CHAPTER 16
Error as inference of conclusions whose opposites are
immediately true
79°23. Of ignorance, not in the negative sense but in that in
which it stands for a positive state, one kind is false belief formed
without reasoning, of which there are no determinable varieties ;
another is false belief arrived at by reasoning, of which there are
many varieties. Of the latter, take first cases in which the terms
of the false belief are in fact directly connected or directly dis-
connected.
29. (A) A directly deniable of B
Both premisses may be false, or only one.
33. If we reason All C is A, All B is C, Therefore all B is A,
(a) both premisses will be false if in fact no C is A and no B is C.
The facts may be so; since A is directly deniable of B, B cannot
(as we have seen) be included in C, and since A need not be true
of everything, in fact no C may be A.
40. (b) The major premiss cannot be false and the minor true;
for the minor must be false, because B is included in no genus.
80:2. (c) The major may be true and the minor false, if A is
in fact an átomic predicate of C as well as of B; for when the
same term is an atomic predicate of two terms, neither of these
wil be included in the other. It makes no difference if A is
not an atomic predicate of C as well as of B.
6. (B) A directly assertible of B
While a false conclusion All B is A can only be reached, as
above, in the first figure, a false conclusion No B is A may be
reached in the first or second figure.
9. (x) First figure. If we reason NoC is A, All B is C, Therefore
no B is A, (a) if in fact A belongs directly both to C and to B,
both premisses will be false.
14. (b) The major premiss may be true (because A is not true
of everything), and the minor false, because (all B being A)
all B cannot be C if no C is A; besides, if both premisses were
true, the conclusion would be so.
I. 15. 7915-20 559
21. (c) If B is in fact included in C as well as in A, one of the
two (C and A) must be under the other, so that the major premiss
will be false and the minor true.
27. (2) Second figure. (a) The premisses must be All A is C,
No B is C, or No A is C, All B is C. Both premisses cannot be
wholly false; for if they were, the truth would be that no A is C
and all B is C, or that all A is C and no B is C, but neither of
these is compatible with the fact that all B is A.
33- (b) Both the premisses All A is C, No B is C may be partly
false ; some A may not be C, and some B be C.
37. So too if the premisses are No A is C, All B is C ; some A
may be C, and some B not C.
38. (c) Either premiss may be wholly false. All B being A,
(a) what belongs to all A will belong to B, so that if we reason
All A is C, No B is C, Therefore no B is A, if the major premiss
is true the minor will be false.
bz. (8) What belongs to no B cannot belong to all A, so that
(with the same premisses) if the minor premiss is true the major
will be false.
6. (y) What belongs to no A will belong to no B, so that if we
reason No A is C, All B is C, if the major is true the minor must
be false.
10. (8) What belongs to all B cannot belong to no A, so that
(with the same premisses) if the minor is true the major must be
false.
14. Thus where the major and minor terms are in fact directly
connected or disconnected, a false conclusion can be reached from
two false premisses or from one true and one false premiss.
A. begins with a distinction between ἄγνοια as the negation of
knowledge, i.e. as nescience, and ἄγνοια as a positive state, i.e.
as wrong opinion—a distinction already drawn in 77524 τὸ μὲν
ἕτερον ἀγεωμέτρητον τῷ μὴ ἔχειν... τὸ δ᾽ ἕτερον τῷ φαύλως ἔχειν"
καὶ ἡ ἄγνοια αὕτη... ἐναντία. He first (79524) identifies the latter
with wrong opinion reached by reasoning, but later (625-8) cor-
rects himself by dividing it into wrong opinion so reached and
that formed without reasoning. Wrong opinion of the former
kind admits of different varieties; that of the latter kind is
ἁπλῆ, i.e. does not admit of varieties of which theory can take
account (?28) ; and A. says nothing more about it. Finally, wrong
opinion based on reasoning is divided according as the term
which forms the predicate of our conclusion is in fact directly,
or only indirectly, assertible or deniable of the term which forms
560 COMMENTARY
our subject. The case of terms directly related is discussed in
this chapter, that of terms indirectly related in the next, ἄγνοια
in the sense of nescience in ch. 18.
79537-8. τὸ μὲν yap B . . . ὑπάρχειν. That the subject of an
unmediable negative proposition cannot be included in a whole,
ie. must be a category, was argued in 51-4.
8072-5. τὴν δὲ ΑΓ... ὑπάρχει, ‘but the premiss All C is A
may be true, i.e. if A is an atomic predicate both of C and of B
(for when the same term is an atomic predicate of more than one
term, neither of these will be included in the other). But it makes
no difference if A is not an atomic predicate of both C and B.'
The case in question is that in which in fact AZ C is A, no B is C,
and no B is A; therefore ὑπάρχει in 33 and 5 and κατηγορῆται in
33 must be taken to include the case of deniability as well as that
of assertibility ; and this usage of the words is not uncommon in
the Analytics ; cf. 82214 n. And in fact, whether A is immediately
assertible of both C and B, immediately deniable of both, or
immediately assertible of one and deniable of the other, C cannot
be included in B, or B inC ; in the first case they will be coordinate
classes immediately under 4, in the second case genera outside
it and one another; in the third case one will be a class under A
and one a class outside A.
In *2-4 A. assumes that A is directly assertible of C and directly
deniable of B. But, he adds in *4—5, it makes no difference if it
is not directly related to both. That it is directly deniable of B
is the assumption throughout 79529-8o*5; what A. must mean is
that it makes no difference if it is not directly assertible of C (i.e.
if C is a species of a genus under A, instead of a genus directly
under A). And in fact it does not; the facts will still be that all
C is A, no B isC, and no B is A.
In 34 ἐν should be read before οὐδετέρῳ, as it is by one of the
best MSS. and by P. (196. 28).
7-8. οὐ γὰρ. . . συλλογισμός. ὑπάρχειν stands for καθόλου
ὑπάρχειν; for it is with syllogisms yielding the false conclusion
All B is A that A. has been concerned. He has shown in An. Pr.
i. 5 that the second figure cannot prove an affirmative, and
ib. 6 that the third cannot prove a universal.
15-20. ἐγχωρεῖ γὰρ... ἀληθές. The situation that is being
examined in 36-516 is that in which A is directly true of all B,
and we try to prove that no B is A. If we say No C is A, All
B is C, Therefore no B is A, the major premiss may be true
because A is not true of everything and there is no reason why
it need be true of C ; and if the major is true, the minor not only
I. 16. 79537 — 809 561
may but must be false, because, all B being A, if all B were C
it could not be true that no C is A. Or, to put it otherwise, if
both No C is A and All B is C were (εἰ καί, 419) true, it would
follow that No B is A is true, which it is not.
23. ἀνάγκη yàp . . . εἶναι. A. must mean that A is included
in C; for (1) A cannot fall outside C, since ex hypothesi B is in-
cluded in both, and (2) A cannot include C, since if all C were A,
then, all B being C, All B is A would be a mediable and not (as
it is throughout *8-^16 assumed to be) an immediate proposition.
A. ignores the possibility that 4 and C should be overlapping
classes, with B included in the overlap.
27-33. ὅλας μὲν εἶναι τὰς προτάσεις ἀμφοτέρας ψευδεῖς...
ἐπί τι δ᾽ ἑκατέραν οὐδὲν κωλύει ψευδῆ εἶναι. ‘All B is A’ is wholly
false when in fact no B is A; ‘No B is A’ wholly false when in
fact all B is A; ‘All Bis A’ and ‘No B is A’ are partly false when
in fact some B is A and some is not (cf. An.Pr. 5328-30 n.).
32-3. εἰ odv . . . ἀδύνατον, ‘if, then, taken thus (ie. being
supposed to be All A is C, No BisC, or No A is C, All B is C), the
premisses were both wholly false, the truth would be that no A
is C and all B is C, or that all A is C and no B is C ; but this is
impossible, because in fact all B is A (#28).
bg. ἡ μὲν ΓΑ πρότασις. ΓΑ͂ must be read, as in 51 and 14;
for A. always puts the predicate first, L'A standing for ὅτι τὸ Γ
τῷ A οὐχ ὑπάρχει. Cf. 81411 n., 19 n.
CHAPTER 17
Error as inference of conclusions whose opposites can be
proved to be true
8017, (A) A assertible of B through middle term C
(1) First figure. (a) When the syllogism leading to a false
conclusion uses the middle term which really connects the terms,
both premisses cannot be false. To yield a conclusion, the minor
premiss must be affirmative, and therefore must be the true
proposition All B is C. The major premiss will be the false
proposition No C is A.
26. (5) If the middle term be taken from another chain of
predication, being a term D such that all D is in fact A and all
B is D, the false reasoning must be No D is A, All B is D, There-
fore no B is A; major premiss false.
32. (c) If an improper middle term be used, to give the false
conclusion No B is A the premisses used must be No D is A,
4985 oo
562 COMMENTARY
All B is D. Then (a) if in fact all D is A and no B is D, both
premisses will be false.
40. (B) If in fact no D is A and no B is D, the major will be
true, the minor false (for if it had been true the conclusion No
B is A would have been true).
8145. (2) Second figure. (2) Both premisses (All A is C, No
B is C, or No A isC, All B is C) cannot be wholly false (for when
B in fact falls under A, no predicate can belong to the whole
of one and to no part of the other).
9. (b) If all A is C and all B is C, then (a) if we reason All
A is C, No B is C, Therefore no B is A, the major will be true
and the minor false.
12. (8) If we reason No A is C, All B is C, Therefore no B is
A, the minor will be true and the major false.
15. (B) A dentable of B through C
(a) If the proper middle term be used, the two false premisses
all C is A, No B is C, would yield no conclusion. The premisses
leading to the false conclusion must be All C is A, All B is C;
major false.
20. (b) If the middle term be taken from another chain of
predication, to yield the false conclusion All B is A the premisses
must be All D is A, All B is D, when in fact no D is A and all
B is D ; major false.
24. (c) If an improper middle term be used, to yield the false
conclusion All B is A the premisses must be All D is A, All B is
D. Then in fact (a) all D may be A, and no B be D ; minor false;
29 or (8) no D may be A, and all B be D ; major false;
31 or (y) no D may be A, and no B be D; both premisses
false.
35. Thus it is now clear in how many ways a false conclusion
may be reached by syllogism, whether the extreme terms be
in fact immediately or mediately related.
80b^17-81*4. Ἐν δὲ τοῖς μὴ ἀτόμως . . . ψεῦδος. A. considers
here the case in which All B is in fact A because it is C. The
possible ways in which we may then reach a false negative con-
clusion, in the first figure, are the following:
(1) (8018-26) We may misuse the οἰκεῖον μέσον C by reasoning
thus: No C is A, All B is C, Therefore no B is A. We use a major
premiss which is the opposite of the truth, but there is no dis-
torting of the minor premiss (οὐ yàp ἀντιστρέφεται, 924; for this
use of ἀντιστρέφειν cf. An. Pr. 4596 and ii. 8-10 passim) ; for in the
I. 17. 8017 — 81334 563
first figure the minor premiss must be affirmative and the affirma-
tion All B is C is true.
(2) (626-32) We may use a middle term ἐξ ἄλλης συστοιχίας, i.e.
one which is not the actual ground of the major term's being true
of the minor, but yet entails the major and is true of the minor.
The facts being that all D is A, all B is D, and therefore all B
must be A, we reason No D is A, All B is D, Therefore no B is
A; as before, our major is false and our minor true (b31-2).
(3) (b32-8:1*4) We may reason μὴ διὰ τοῦ οἰκείου μέσου, use a
middle term which is not in fact true of the minor term. Our
reasoning is again No D is A, All B is D, Therefore no B is A
(the only form of reasoning which gives a universal negative
conclusion in the first figure), while the facts may be either that
all D is A and no B is D, in which case both our premisses are
false (33-40), or that no D is A and no B is D, in which case our
major is true and our minor false (540-8124).
35-7. ληπτέαι γὰρ... ψευδεῖς. D in fact entails A, and B
in fact does not possess the attribute D. But to get the conclusion
No B is A we must (to fall in with the rules of the first figure,
as stated in An. Pr. i. 4) have as premisses No D is A and All
B is D—both false.
8135-8. Διὰ δὲ τοῦ μέσου σχήματος ... πρότερον. The situa-
tion is this: In fact all B is A. To reach the false conclusion
No B is A in the second figure, we must use the premisses All
AisC,No BisC, or No AisC, All BisC. If in either case both
premisses were wholly false (i.e. contrary, not contradictory, to
true propositions), in fact no A would be C and all B would be
C, or all A would be C and no B would be C. But, all B being in
fact A, neither of these alternatives can be the case. καθάπερ
ἐλέχθη kai πρότερον refers to 8027-33, where the same point was
made about the case in which A is immediately true of B.
rr. ἡ μὲν ΓΑ. DA must be read; cf. 8059 n., 81219 n.
19. καθάπερ ἐλέχθη kai πρότερον, i.e. in 8022-5.
19-20. ὥστε ἡ AL... ἀντιστρεφομένη. ΑΓ must be read; cf.
8obg n., 81211 n. For the meaning of ἡ ἀντιστρεφομένη cf. 8ob17-
8124 n.
20-4. ὁμοίως 56 . . . πρότερον. For the meaning of ‘taking the
middle term from another chain of predication', cf. 8017-8144 n.
21-2. ὥσπερ ἐλέχθη . . . ἀπάτης cf. 80526-32.
24. τῇ πρότερον, i.e. that described in *19-20.
24-34. ὅταν δὲ... ἔτυχεν. A. here recognizes three cases of
reasoning μὴ διὰ τοῦ οἰκείου. The reasoning in all three is All D
is A, All B is D, Therefore all B is A. The facts are (1) that all
564 COMMENTARY
D is A, no B is D, and no B is A (224-7), (2) that no D is A, all
B is D, and no B is A (229-31), (3) that no D is A, no B is D,
and no B is A (231-2). The second of these cases, however, is
identical with that described in *2o-4 as reasoning with a middle
ἐξ ἄλλης συστοιχίας, but there ought to be this difference between
reasoning μὴ διὰ τοῦ οἰκείου and reasoning with a middle term
ἐξ ἄλλης συστοιχίας, that in the latter by correcting the false
premiss we should get a correct (though unscientific) syllogism
giving a true conclusion, whereas in the former if we correct the
false premiss or premisses we do not get a conclusion at all (cf.
the distinction between the two types of error in 8026-32, 32-
8124). It will be seen that the first and third cases cited as cases
of reasoning μὴ διὰ τοῦ oiketov are really cases of it (answering
to the two cited in 80532-8144), while the second is really a case
of reasoning with a middle term ἐξ ἄλλης συστοιχίας.
The final sentence betrays still greater confusion. It says that
if the middle term does not in fact fall under the major term,
both premisses or ether may be false. But if the middle term does
not in fact fall under the major, the major premiss is inevitably
false, since (the conclusion being All B is A) the major premiss
must be All D is A. So great a confusion within a single sentence
can hardly be ascribed to À., and there is no trace of this sentence
in P.s commentary (xai rà ἑξῆς in P. 213. 12 is omitted by one
of the two best MSS.).
26-7. ἐγχωρεῖ yàp ... ἄλληλα, i.e. A may be truly-assertible-
or-deniable of two terms (in this case assertible of D, deniable
of B) without either of them falling under the other. ὑπάρχειν
has the same significance as in 8033 and 5.
CHAPTER 18
Lack of a sense must involve ignorance of certain wniversal pro-
positions which can only be reached by induction from particular
facts
81:38. If a man lacks any of the senses, he must lack some
knowledge, which he cannot get, since we learn either by induc-
tion or by demonstration. Demonstration is from universals,
induction from particulars ; but it is impossible to grasp universals
except through induction (for even abstract truths can be made
known through induction, viz. that certain attributes belong to
the given class as such—even if their subjects cannot exist
separately in fact), and it is impossible to be led on inductively to
I. 17. 81226-7 565
the universals if one has not perception. For it is perception
that grasps individual facts; you cannot get scientific knowledge
of them; you can neither deduce them from universal facts
without previous induction, nor learn them by induction without
perception.
The teaching of this chapter is that sensuous perception is the
foundation of science. The reason is that science proceeds by
demonstration from general propositions, themselves indemon-
strable, stating the fundamental attributes of a genus, and that
these propositions can be made known only by intuitive induction
from observation of particular facts by which they are seen to
be implied. The induction must be intuitive induction, not
induction by simple enumeration nor even 'scientific' induction,
since neither of these could establish propositions having the
universality and necessity which the first principles of science
have and must have.
The induction in question is said to be ἐκ τῶν κατὰ μέρος (P1),
and this leaves it in doubt whether A. is thinking of induction
from species to the genus, or from individuals to the species. But
since induction is described as starting from perception, it is clear
that the first stage of it would be from individual instances, and
that induction from species to genus is only a later stage of the
same process.
Even abstract general truths, says A. (53), can be made known
by induction. He treats it as obvious that general truths about
classes of sensible objects must be grasped by induction from
perceived facts, but points out that even truths about things (like
geometrical figures) which have no existence independent of
sensible things (καὶ εἰ μὴ χωριστά ἐστιν, ^4) are grasped by means of
an induction from perceived facts, which enables us to grasp,
e.g. that a triangle, whatever material it is embodied in, must
have certain attributes. By these he means primarily, perhaps,
the attributes included in its definition. But the ἀρχαί referred
to include also the ἀξιώματα or κοιναὶ ἀρχαί which state the
fundamental common attributes of all quantities (e.g. that the
sums of equals are equal), and even those of all existing things
(like the law of contradiction or that of excluded middle); and
also the ὑποθέσεις in which the existence of certain simple
entities like the point or the unit is assumed. For since no ἀρχή of
demonstration can be grasped by demonstration, all the kinds
of ἀρχή of science (72114-24) must be grasped by induction from
sense-perception.
566 COMMENTARY
The passage contains the thought of a teacher instructing
pupils—that at least is the most natural interpretation of γνωριμὰ
ποιεῖν (63); and the same thought is carried on in the word
ἐπαχθῆναι (bs). ‘It is impossible for learners to be carried on to
the universal unless they have sense- perception. ' The passage
is one of those that indicate that the main idea underlying A.'s
usage of the word ἐπαγωγή is that of this process of carrying on,
not that of adducing instances. Other passages which have the
same implication are 71421, 24, Met. 989233; cf. Pl. Polit. 278a s,
and ἐπαναγωγή in Rep. 5325; cf. also my introductory note on
An. Pr. ii. 23. The process of abstracting mathematical entities
from their sensuous embodiment (which is what A. has at least
chiefly in mind when he speaks of τὰ ἐξ ἀφαιρέσεως) is most fully
described in Met. 1061428-53.
The sum of the whole matter is that sense-perception is the
necessary starting-point for science, since ‘we can neither get
knowledge of particular facts from universal truths without
previous induction to establish the general truths, nor through
induction without sense-perception for it to start from’ (57-9).
CHAPTER 19
Can there be an infinite chain of premisses in a demonstration,
(1) of the primary attribute 1s fixed, (2) 1f the ultimate subject 15 fixed,
(3) af both terms are fixed ?
81*ro. Every syllogism uses three terms; an affirmative
syllogism proves that 'is A because Bis A and l'is B; a negative
syllogism has one affirmative and one negative premiss. These
premisses are the starting-points; it is by assuming these that
one must conduct one’s proof, proving that A belongs to I'
through the mediation of B, again that A belongs to B through
another middle term, and B to Γ΄ similarly.
18. If we are reasoning dialectically we have only to consider
whether the inference is drawn from the most plausible premisses
possible, so that if there is a middle term between A and B but
it is not obvious, one who uses the premiss ‘B is A’ has reasoned
dialectically ; but if we are aiming at the truth we must start from
the real facts.
23. There are things that are predicated of something else
not per accidens; by per accidens 1 mean that we can say ‘that
white thing is a man’, which is not like saying ‘the man is white;’
for the man is white without needing to be anything besides being
I. 19. 8120-2 567
a man, but the white is a man because it is an accident of the
man to be white.
30. (1) Let I" be something that belongs to nothing else, while
B belongs to it directly, Z to B, and E to Z ; must this come to
an end, or may it go on indefinitely? (2) Again, if nothing is
assertible of A per se, and A belongs to @ directly, and 0 to H,
and H to B, must this come to an end, or not?
37. The two questions differ in that (1) is the question whether
there is a limit in the upper direction, (2) the question whether
there is a limit in the lower.
8222. (3) If the ends are fixed, can the middle terms be indeter-
minate in number? The problem is whether demonstration pro-
ceeds indefinitely, and everything can be proved, or whether
there are terms in immediate contact.
9. So too with negative syllogisms. If A does not belong to
any B, either B is that of which A is immediately untrue or there
intervenes a prior term H, to which A does not belong and which
belongs to all B, and beyond that a term 6 to which A does not
belong and which belongs to all H.
15. The case of mutually predicable terms is different. Here
there is no first or last subject; all are in this respect alike, no
matter if our subject has an indefinite number of attributes,
or even if there is an infinity in both directions; except where
there is per accidens assertion on one side and true predication
on the other.
Chs. 19-23 form a continuous discussion of the question whether
there can be an infinite chain of premisses in a demonstration.
In ch. 19 this is analysed into the three questions: (1) Can there
be an infinite chain of attributes ascending from a given subject?
(2) Can there be an infinite chain of subjects descending from a
given attribute? (3) Can there be an infinite number of middle
terms between a given subject and a given attribute? Ch. 2o
proves that if (1) and (2) are answered negatively, (3) also must
be so answered. Ch. 21 proves that if an affirmative conclusion
always depends on a finite chain of premisses, so must a negative
conclusion. Ch. 22 proves that the answers to (1) and (2) must be
negative. Ch. 23 deduces certain corollaries from this.
81>20-2. Gor’ εἰ... διαλεκτικῶς. There is here a disputed
question of reading. A? B? Cdn? and P. (218. 14) have ἔστι,
A! B! n! μὴ ἔστι. B? dn have δὲ μή, A? C? (apparently) δὲ μὴ
εἶναι, B! δὲ, A! ( δὲ εἶναι. The presence or absence of εἶναι does
not matter; what matters is, where μή belongs. The reading
568 COMMENTARY
with μή in the earlier position has the stronger MS. support, but
the clear testimony of P. may be set against this. διὰ τούτου,
however, is decisive in favour of the reading μὴ ἔστι... δοκεῖ
δὲ εἶναι.
24-9. ἐπειδὴ ἔστιν... κατηγορεῖσθαι. A. is going to assume
in 630-7 that there are subjects that are not attributes of any-
thing, and attributes that are not subjects of anything. But he
first clears out of the way the fact that we sometimes speak as if
each of two things could be predicated of the other, as when we
say ‘that man is white’ and ‘that white thing is a man’. These,
he says, are very different sorts of assertion. The man does not
need to be anything-other than a man, in order to be white; the
white thing is a man (τὸ λευκόν in 628 is no doubt short for this)
in the sense that whiteness inheres in the man. A. is hampered
by the Greek idiom by which τὸ λευκόν may mean either ‘white
colour’ or ‘the white thing’. What he is saying is in effect that
‘man’ is the name of a particular substance which exists in its
own right, ‘white’ the name of something that can exist only by
inhering in a substance. At the end of the chapter {τὸ δ᾽ ὡς
κατηγορίαν, 82220) he implies that ‘the white thing is a man’ is
not a genuine predication, and he definitely says so in 83114-17.
8236-8. ἔστι δὲ... περαίνεται. This seems to refer to the last
of the three questions stated in 81530-82%6. εἰ af ἀποδείξεις εἰς
ἄπειρον ἔρχονται might refer to any of the three; but εἰ ἔστιν
ἀπόδειξις ἅπαντος refers to the third, for the absence of an ultimate
subject or of an ultimate predicate would not imply that all
propositions are provable; there might still be immediate con-
nexions between pairs of terms within the series. πρὸς ἄλληλα
περαίνεται means that some terms are bounded at each other,
‘touch’ each other; in other words that there are terms with no
term between them. Finally, it 1s the third question that is
carried on into the next paragraph.
9-14. Ὁμοίως δὲ... ἵσταται. Take the proposition No Bis A.
Either this is unmediable, or there is a term H such that no H is
A, and all Bis H. Again either No H is A is unmediable, or there
is a term © such that no @ is A, and all H is O. The question
is whether an indefinite number of terms can always be inter-
polated between B and A, or there are immediate negative
propositions.
I4. f| ἄπειρα ols ὑπάρχει προτέροις. The question is whether
there is an infinite number of terms higher than B to which A
cannot belong. We must therefore either read οἷς οὐχ ὑπάρχει
with n, or more probably take ὑπάρχει to be used in the sense in
I. το. 81524 — 82*20 569
which it means 'occurs as predicate' whether in an affirmative
or a negative statement ; cf. 8032-5 n.
15-20. 'Emi δὲ τῶν ἀντιστρεφόντων . . . κατηγορίαν. A. now
recurs to the first two questions, and points out that the situation
with regard to these is different if we consider not terms related
in linear fashion so that one is properly predicated of the other
but not vice versa, but terms which are properly predicated of
each other. Here there is no first or last subject. Such terms
form a shuttle service, if there are but two, or a circle if there are
more, of endless predication, whether you say that each term is
subject to an infinite chain of attributes, or is that and also
attribute to an infinite chain of subjects (εἴτ᾽ ἀμφότερά ἐστι τὰ
ἀπορηθέντα ἄπειρα, *18—19).
The best examples of ἀντικατηγορούμενα are not, as Zabarella
suggests, correlative terms, or things generated in circular
fashion from each other (for neither of these are predicable of
each other), but (to take some of P.’s examples) terms related as
τὸ γελαστικόν, τὸ νοῦ Kal ἐπιστήμης δεκτικόν, τὸ ὀρθοπεριπατητικόν,
τὸ πλατύωνυχον, τὸ ἐν λογικοῖς θνητόν (all of them descriptions
of man) are to one another.
Finally, A. points out (519-20) that what he has just said does
not apply to pairs of terms that are only in different ways assert-
ible of each other (cf. 81525-9), the one assertion (like ‘the man
is white') being a genuine predication, the other (like 'that white
thing is a man’) being an assertion only per accidens. For this
way of expressing the distinction cf. 83214—18.
CHAPTER 20
There cannot be an infinite chain of premisses if both extremes
are fixed
82:21. The intermediate terms cannot be infinite in number,
if predication is limited in the upward and downward directions.
For if between an attribute A and a subject Z there were an
infinite number of terms B,, B,, .. . , By, there would be an
infinite number of predications from A downwards before Z is
reached, and from Z upwards before A is reached.
30. It makes no difference if it is suggested that some of the
terms A, B,, B,,..., B,, Z are contiguous and others not. For
whichever B I take, either there will be, between it and A or Z,
an infinite number of terms, or there will not. At what term the
infinite number starts, be it immediately from A or Z or not,
makes no difference; there is an infinity of terms after it.
570 COMMENTARY
82°30-2. οὐδὲ γὰρ. . . διαφέρει. Waitz’s reading ABZ is
justified ; for in #25 and 32 all the middle terms are designated B,
and there is no place for a term I’. ABZ stands for AB, B,...
B,Z. Waitz may be right in supposing the reading ABI to have
sprung from the habit of the Latin versions of translating Z by
C (which they do in 225, 27, 28, 29, 33).
34. εἴτ᾽ εὐθὺς εἴτε μὴ εὐθύς, ie. whether we suppose the
premiss which admits of infinite mediation to have A for its
predicate or Z for its subject, or to have one of the B’s for its
predicate and another for its subject.
CHAPTER 21
If there cannot be an infinite chain of premisses in affirmative
demonstration, there cannot in negative
82236. If a series of affirmations is necessarily limited in both
directions, so is a series of negations.
bg. For a negative conclusion is proved in one of three ways.
(1) The syllogism may be No B is A, All C is B, Therefore no
C is A. The minor premiss, being affirmative, ex hypothest
depends, in the end, on immediate premisses. If the major
premiss has as zfs major premiss No D is A, it must have as its
minor All B is D; and if No D is A itself depends on a negative
major premiss, it must equally depend on an affirmative minor.
Thus since the series of ascending affirmative premisses is limited,
the series of ascending negative premisses will be limited; there
will be a highest term to which A does not belong.
13. (2) The syllogism may be All A is B, No C is B, Therefore
no C is A. If NoC is B is to be proved, it must be either by the
first figure (as No B is A was proved in (1)), by the second, or by
the third. If by the second, the premisses will be All B is D,
No C is D; and if No C is D is to be proved, there will have to
be something else that belongs to D and not to C. Therefore
since the ascending series of affirmative premisses is limited, so
will be the ascending series of negative premisses.
21. (3) The syllogism may be Some B is not C, All B is A,
Therefore some A is not C. Then Some B is not C will have to be
proved either (a) as the negative premiss was in (1) or in (2), or (0)
as we have now proved that some A is not C. In case (a), as we
have seen, there is a limit; in case (b) we shall have to assume
Some E is not C, All E is B; and soon. But since we have assumed
that the series has a downward limit, there must be a limit to
the number of negative premisses with C as predicate.
I. 20. 82330-4 571
29. Further, if we use all three figures in turn, there will still
be a limit; for the routes are limited, and the product of a finite
number and a finite number is finite.
34. Thus if the affirmative series is limited, so is the negative.
That the affirmative series is so, we shall now proceed to show by
a dialectical proof.
A.’s object in this chapter is to prove that if there is a limit to
the number of premisses needed for the proof of an affirmative
proposition, there is a limit to the number of those needed for the
proof of a negative (82436-7). He assumes, then, that if we start
from an ultimate subject, which is not an attribute of anything,
there is a limit to the chain of predicates assertible of it, and that
if we start from a first attribute, which has no further attribute,
there is a limit to the chain of subjects of which it is an attribute
(238-53). Now the proof of a negative may be carried out in any
of the three figures; A. takes as examples a proof in Celarent
(55-13), one in Camestres (P13-21), and one in Bocardo (21-8).
The point he makes is that in each case, if we try to insert a
middle term between the terms of the negative premiss, we shall
need an affirmative premiss as well as a negative one, so that if
the number of possible affirmative premisses is limited, so must
be the number of negative premisses.
First figure Second figure Third figure
No Bis A All Ais B Some B is not C
AllCis B NoCisB All B is A
J.No C is A -.NoC is A ..Some A is not C
No Dis A All Bis D Some E is not C
All Bis D No Cis D All Eis B
“No Bis A .NoCis B Some B is not C
If we try to carry the process of mediation further, it will take
the following three forms, respectively (610-11, 19-20, 26-7).
No Eis A All DisE Some F is not C
All Dis E NoCisE All Fis E
“No Dis A “.NoC is D ..Some E is not C
In the second figure the regress from the original syllogism to
the prosyllogism is said to be in the upward direction (920-1);
and this is right, because the new middle term D is wider than
the original middle term B. In the third figure the movement is
said to be in the downward direction (527); and this is right,
because the new middle term E is narrower than the original
middle term B. In the first figure the new middle term D is
572 COMMENTARY
wider than the original middle term B, so that here too the move-
ment is upward, and ἄνω, not κάτω, must be read in >11. But in
bra neither Bekker's ἄνω nor Waitz's κάτω will do; obviously not
ἄνω, because that stands or falls with the reading κάτω in *rr;
not κάτω, for three reasons: (1) The regress of negative premisses,
as well as of affirmative, is in the first figure upwards; for we
pass from No B is A in the original syllogism to No D is A in
the prosyllogism, and the latter proposition is the wider (B being
included in D, as stated in the minor premiss of the prosyllogism).
(2) The last words of the sentence, xai ἔσται τι πρῶτον d οὐκ
ὑπάρχει, are clearly meant to elucidate the previous clause; but
what they mean is not that there is a lowest term of which A
is deniable (for it is assumed that C is that term), but that there
is a highest term, of which A is immediately deniable. Thus what
the sense requires in hi2 is ‘the search for higher negative pre-
misses also must come to an end’. (3) A comparison of b11-12
with the corresponding words in the case of the other two figures
(οὐκοῦν ἐπεὶ τὸ ὑπάρχειν ἀεὶ TH ἀνωτέρω ἵσταται, στήσεται Kai TO
μὴ ὑπάρχειν b20-1, ἐπεὶ δ᾽ ὑπόκειται ἵστασθαι καὶ ἐπὶ τὸ κάτω,
δῆλον ὅτι στήσεται καὶ τὸ I' οὐκ ὑπάρχον 527-8) would lead us to
expect in the present sentence not a contrast between an upward
and a downward movement, but a comparison between the
search for affirmative premisses and the search for negative.
The right sense is given by n’s reading, καὶ ἡ ἐπὶ τὸ A στήσεται.
These words mean ‘the attempt to mediate the negative premiss
No B is A will come to an end, no less than the attempt to mediate
the affirmative premiss All C is B' (dealt with in 6-8). The
passage from the original major premiss No B is A to the new
major premiss No D is A is a movement ‘towards A’; for if in
fact no D is A and all B is D, in passing from No B is A to No
Dis A we have got nearer Yo finding a subject of which not being
A is true jj αὐτό, not merely καθ᾽ αὑτό.
At an early stage some scribe, having before him dvo in Pr1,
must have yielded to the temptation to write κάτω in 512, and
a later (though still early) scribe, seeing that this would not
work, must have reversed the two words; for P. clearly read
KQTW .. . GVW.
8256-7. τοῦ μὲν... διαστήματος. For the use of the genitive
at the beginning of a sentence in the sense of ‘with regard to...’
cf. Kühner, Gr. Gramm. ii. 1. 363 n. 11.
I4. τοῦτο, i.e. that no C is B.
18-19. «i ἀνάγκη... B, ‘if in fact there is any particular term
D that necessarily belongs to B'.
I. 21. 8256-36 573
20. τὸ ὑπάρχειν ἀεὶ τῷ ἀνωτέρω, ‘the belonging to higher and
higher terms’, i.e. the movement from All A is B to All B is D,
and so on. τὸ μὴ ὑπάρχειν, ‘the movement from No C is B to No
C is D, and so on’.
24. τοῦτο, i.e. that some B is not C.
35-6. λογικῶς pev . . . φανερόν. A. describes his first two
arguments (that drawn from the possibility of definition, 537—
83531, and that drawn from the possibility of knowledge by
inference, 83532-8436) as being conducted λογικῶς (cf. 8457) be-
cause they are based on principles that apply to all reasoning,
not only to demonstrative science. His third argument is called
analytical (8438) because it takes account of the special nature of
demonstrative science, which is concerned solely with proposi-
tions predicating attributes of subjects to which they belong
per se (ib. 11-12).
CHAPTER 22
There cannot be an infinite chain of premisses in affirmative
demonstration, if either extreme is fixed
82537. (A) (First dialectical proof.) That the affirmative series
of predicates is limited is clear in the case of predicates included
in the essence of the subject; for otherwise definition would be
impossible. But let us state the matter more generally.
831. (First preliminary observation. You can say truly (1)
(a) ‘the white thing is walking’ or (5) ‘that big thing is a log’ or
(2) ‘the log is big’ or ‘the man is walking’. (1 ὁ) ‘That white thing
is a log’ means that that which has the attribute of being white
is a log, not that the substratum of the log is white colour; for
it is not the case that it was white or a species of white and
became a log, and therefore it is only per accidens that ‘the white
thing is a log’. But (2) ‘the log is white’ means not that there is
something else that is white, and that that has the accidental
attribute of being a log, as in (1 a); the log is the subject, being
essentially a log or a kind of log.
14. If we are to legislate, we must say that (2) is predication,
and (1) either not predication, or predication per accidens; a term
like ‘white’ is a genuine predicate, a term like ‘log’ a genuine
subject. Let us lay it down that the predications we are con-
sidering are genuine predications; for it is such that the sciences
use. Whenever one thing is genuinely predicated of one thing, the
predicate will always be either included in the essence of the
574 COMMENTARY
subject, or assign a quality, quantity, relation, action, passivity,
place, or time to the subject.
24. (Second preliminary observation.) Predicates indicating
essence express just what the subject is, or what it is a species of;
those that do not indicate substance, but are predicated of a sub-
ject which is not identical with the predicate or with a specifica-
tion of it, are accidents (e.g. man is not identical with white,
or with a species of it, but presumably with animal). Predicates
that do not indicate substance must be predicated of a distinct
subject; there is nothing white, which is white without being
anything else. For we must say good-bye to the Platonic Forms;
they are meaningless noises, and if they exist, they are nothing
to the point; science is about things such as we have described.
36. (Third preliminary observation.) Since A cannot be a
quality of B and B of A, terms cannot be strictly counter-
predicated of each other. We can make such assertions, but they
will not be genuine counter-predications. For a term counter-
predicated of its own predicate must be asserted either (1) as
essence, i.e. as genus or differentia, of its own predicate; and
such a chain is not infinite in either the downward or the upward
direction; there must be a widest genus at the top, and an
individual thing at the bottom. For we can always define the
essence of a thing, but it is impossible to traverse in thought an
infinity of terms. Thus terms cannot be predicated as genera
of each other ; for so one would be saying that a thing is identical
with a species of itself.
byo. Nor (2) can a thing be predicated of its own quality, or
of one of its determinations in any category other than substance,
except per accidens; for all such things are concomitants, ter-
minating, in the downward direction, in substances. But there
cannot be an infinite series of such terms in the upward direction
either—what is predicated of anything must be either a quality,
quantity, etc., or an element in its essence; but these are limited,
and the categories are limited in number.
17. I assume, then, that one thing is predicated of one other
thing, not things of themselves, unless the predicate expresses
just what the subject is. All other predicates are attributes, some
per se, some in another way; and all of these are predicates of a
subject, but an attribute is not a subject; we do not class as an
attribute anything that without being anything else is said to be
what it is said to be (while other things are what they are by being
it); and the attributes of different subjects are themselves different.
24. Therefore there is neither an infinite series of predicates nor
I. 22 575
an infinite series of subjects. To serve as subjects of attributes
there are only the elements in the substance of a thing, and these
are not infinite in number ; and to serve as attributes of subjects
there are the elements in the substance of subjects, and the con-
comitants, both finite in number. Therefore there must be a
first subject of which something is directly predicated, then a
predicate of the predicate, and the series finishes with a term
which is neither predicate nor subject to any term wider than
itself.
32. (B) (Second dialectical proof.) Propositions that have
others prior to them can be proved ; and if things can be proved,
we can neither be better off with regard to them than if we knew
them, nor know them without proof. But if a proposition is
capable of being known as a result of premisses, and we have
neither knowledge nor anything better with respect to these, we
shall not know the proposition. Therefore if it is possible to know
anything by demonstration absolutely and not merely as true
if certain premisses are true, there must be a limit to the inter-
mediate predications; for otherwise all propositions will need
proof, and yet, since we cannot traverse an infinite series, we shall
be unable to know them by proof. Thus if it is also true that we
are not better off than if we knew them, it will not be possible
to know anything by demonstration absolutely, but only as
following from an hypothesis.
8427. (C) (Analytical proof.) Demonstration is of per se attri-
butes of things. These are of two kinds: (a) elements in the
essence of their subjects, (b) attributes in whose essence their
subjects are involved (e.g. 'odd' is a (b) attribute of number,
plurality or divisibiiity an (a) attribute of it).
17. Neither of these two sets of attributes can be infinite in
number. Not the (b) attributes; for then there would be an
attribute belonging to ‘odd’ and including ‘odd’ in its own essence ;
and then number would be involved in the essence of all its (b)
attributes. So if there cannot be an infinite number of elements
in the essence of anything, there must be a limit in the upward
direction. What is necessary is that all such attributes must
belong to number, and number to them, so that there will be
a set of convertible terms, not of terms gradually wider and
wider.
25. Not the (a) attributes; for then definition would be im-
possible. Thus if all the predicates studied by demonstrative
science are fer se attributes, there is a limit in the upward direc-
tion, and therefore in the lower.
576 COMMENTARY
29. If so, the terms between any two terms must be finite in
number. Therefore there must be first starting-points of demon-
stration, and not everything can be provable. For if there are
first principles, neither can everything be proved, nor can proof
'extend indefinitely ; for either of these things implies that there
is never an immediate relation between terms; it is by inserting
terms, not by tacking them on, that what is proved is proved,
and therefore if proof extends indefinitely, there must be an in-
finite series of middle terms between any two terms. But this
is impossible, if predications are limited in both directions; and
that there is a limit we have now proved analytically.
In this chapter A. sets himself to prove that the first two
questions raised in ch. 19—Can demonstration involve an infinite
regress of premisses, (1) supposing the primary attribute fixed,
(2) supposing the ultimate subject fixed?—-must be answered
in the negative. The chapter is excessively difficult. The con-
nexion is often hard to seize, and in particular a disproportionate
amount of attention is devoted to proving a thesis which is at
first sight not closely connected with the main theme. A. offers
two dialectical proofs—the first, with its preliminaries, extending
from the beginning to 83531, the second from 83532 to 8436—and
one analytical proof extending from 8437 to 84328.
He begins (82537-8341) by arguing that the possibility of
definition shows that the attributes predicable as included in
the definition of anything cannot be infinite in number, since
plainly we cannot in defining run through an infinite series. But
that proof is not wide enough; he has also to show that the
attributes predicable of anything, though mot as parts of its
definition, must be finite in number. But as a preliminary to
this he delimits the sense in which he is going to use the verb.
‘predicate’ (8331-23). He distinguishes three types of assertion,
and analyses them differently: (1 4) assertions like τὸ λευκὸν
βαδίζει or τὸ μουσικόν ἐστι λευκόν; (1 b) assertions like τὸ μέγα
ἐκεῖνό (or τὸ λευκόν) ἐστι ξύλον; (2) assertions like τὸ ξύλον ἐστι
μέγα (or λευκόν) or ὁ ἄνθρωπος βαδίζει. (1b) When we say τὸ
λευκόν ἐστι ξύλον, we do not mean that white is a subject of
which being a log is an attribute, but that being white is an
attribute of which the log is the subject. And (1 a) when we say
τὸ μουσικόν ἐστι λευκόν, we do not mean that musical is a subject
of which being white is an attribute, but that someone who has the
attribute of being musical has also that of being white. But (2)
when we say τὸ ξύλον ἐστι λευκόν, we mean that the log is a genuine
I. 22 577
subject and whiteness a genuine attribute of it. This last type
of assertion is the only type that A. admits as genuine predication ;
the others he dismisses as either not predication at all, or predica-
tion only xarà συμβεβηκός, predication that is possible only as
an incidental consequence of the possibility of genuine predica-
tion. As a logical doctrine this leaves much to be desired ; it must
be admitted that all these assertions are equally genuine predica-
tions, that in each we are expressing knowledge about the subject
beyond what is contained in the use of the subject-term; and in
particular it must be admitted that A. is to some extent confused
by the Greek usage—one which had very unfortunate results
for Greek metaphysics—by which a phrase like τὸ λευκόν, which
usually stands simply for a thing having a quality, can be used
to signify the quality; it is this that makes an assertion like τὸ
λευκόν ἐστι ξύλον Or τὸ μουσικόν ἐστι λευκόν seem to A. rather
scandalous. But A. is at least right in saying (#20-1) that his
‘genuine predications’ are the kind that occur in the sciences.
The only examples he gives here of genuine subjects are ‘the log’
and ‘the man’, which are substances. The sciences make, indeed,
statements about things that are not substances, such as the
number seven or the right-angled triangle, but they at least
think of these as being related to their attributes as a substance
is related to its attributes (cf. 87436), and not as τὸ λευκόν is
related to ξύλον, or τὸ μουσικόν to λευκόν. He concludes (83221—3)
that the predications we have to consider are those in which there
is predicated of something either an element in its essence or that
it has a certain quality or is of a certain quantity or in a certain
relation, or doing or suffering something, or at a certain place,
or occurs at a certain time.
He next (83224-35) distinguishes, among genuine predications,
those which ‘indicate essence’ (i.e. definitions, which indicate
what the subject is, and partial definitions, which indicate what
it is a particularization of, i.e. which state its genus) from those
which merely indicate a quality, relation, etc., of the subject,
and groups the latter under the term συμβεβηκότα. But it must
be realized that these include not only accidents but also pro-
perties, which, while not included in the essence of their subjects,
are necessary consequences of that essence. The predication of
συμβεβηκότα is of course to be distinguished from the predication
κατὰ συμβεβηκός dealt with in the previous paragraph. A. repeats
here (*#30-2) what he has already pointed out, that συμβεβηκότα
depend for their existence on a subject in which they inhere—
that their esse (as we might say) is ?zesse—and takes occasion
4985 Pp
578 COMMENTARY
to denounce the Platonic doctrine of Forms as sinning against
this principle.
Now follows a passage (436-12) whose connexion with the
general argument is particularly hard to seize ; any interpretation
must be regarded as only conjectural. 'If B cannot be a quality
of A and A a quality of B—a quality of its own quality—two
terms cannot be predicated of each other as if each were a genuine
subject to the other (cf. 231), though if A has the quality B, we
can truly say "that thing which has the quality B is A" (as has
been pointed out in 41-23). There are two possibilities to be
considered. (1) (339-510) Can A be predicated as an element in
the essence of its own predicate (i.e. as its genus or differentia)?
This is impossible, because (as we have seen in 82537-83*1) the
series which starts with "man" and moves upwards through the
differentia "biped" to the genus "animal" must have a limit,
since definition of essence is possible and the enumeration of an
infinity of elements in the essence is impossible ; just as the series
which starts with "animal" and moves downwards through
"man" must have a limit in an individual man. Thus a term
cannot be predicated as the genus of its own genus, since that
would make man a species of himself. (2) (Pro-:7) The second
possibility to be examined is that a term should be predicated
of its own quality or of some attribute it has in another category
other than substance. Such an assertion can only be (as we have
seen in *1-23) an assertion κατὰ συμβεβηκός. All attributes in
categories other than substance are accidents and are genuinely
predicable only of substances, and thus limited in the downward
direction. And they are also limited in the upward direction,
since any predicate must be in one or other of the categories,
and both the attributes a thing can have in any category and the
number of the categories are limited.'
A.’s main purpose is to maintain the limitation of the chain
of predication at both ends, beginning with an individual sub-
stance and ending with the name of a category. But with this
is curiously intermingled a polemic against the possibility of
counter-predication. We can connect the two tliemes, it seems,
only by supposing that he is anxious to exclude not one but two
kinds of infinite chain; not only a chain leading ever to wider
and wider predicates, but also one which is infinite in the sense
that it returns upon itself, as a ring does (Phys. 20722). Such
a chain would be of the form ‘A is B, BisC...Y is Z,
Z is A’, and would therefore involve that A is predicable of
B as well as B of A ; and that is what he tries in this section
I. 22 579
to prove to be impossible, if ‘predication’ be limited to genuine
predication.
There follows a passage (17-31) in which A. sums up his theory
of predication. The main propositions he lays down are the
following: (1) A term and its definition are the only things that
can strictly be predicated of each other (518-19). (2) The ultimate
predicate in all strict predication is a substance (P2o—-2). (3)
Upwards from a substance there stretches a limited chain of
predications in which successively wider elements in its essence
are predicated (527-8). (4) Of these elements in the definition of
a substance can be predicated properties which they entail, and
of these also the series is limited (b26—8). (s) There are thus sub-
jects (ie. individual substances) from which stretches up a
limited chain of predication, and attributes (i.e. categories) from
which stretches down a limited chain of predication, such attri-
butes being neither predicates nor subjects to anything prior
to them, sc. because there is no genus prior to them (i.e. wider
than they are) (628-31). Thus A. contemplates several finite
chains of predication reaching upwards from an individual subject
like Callias. There is a main chain of which the successive terms
are Callias, ?nfima species to which Callias belongs, differentia
of that species, proximate genus, differentia of that genus, next
higher genus . . . category (i.e. substance). But also each of these
elements in the essence of the individual subject entails one or
more properties and is capable of having one or more accidental
attributes, and each of these generates a similar train of differ-
entiae and genera, terminating in the category of which the
property or accident in question is a specification—quality,
quantity, relation, etc.
The second dialectical proof (b32-8426) runs as follows : Wherever
there are propositions more fundamental than a given proposition,
that proposition admits of proof ; and where a proposition admits
of proof, there is no state of mind towards it that is better than
knowledge, and no possibility of knowing it except by proof.
But if there were an infinite series of propositions more funda-
mental] than it, we could not prove it, and therefore could not
know it. The finitude of the chain is a necessary precondition
of knowledge; nothing can be known by proof, unless something
can be known without proof.
The analytical proof (8437—28) runs as follows: Demonstration
is concerned with propositions ascribing predicates to subjects
to which they belong fer se. Such attributes fall into two classes—
the two which were described in 7334-53, viz. (1) attributes
580 COMMENTARY
involved in the definition of the subject (illustrated by plurality
or divisibility as belonging per se to number), (2) attributes
whose definition includes mention of the subjects to which they
belong. The latter are illustrated by ‘odd’ as belonging per se
to number; but since such καθ᾽ αὑτά attributes are said to be
convertible with their subjects (8422-5), ‘add’ must be taken to
stand for ‘odd or even’, which we found in 73439-40. The original
premisses of demonstration (if we leave out of account ἀξιώματα
and ὑποθέσεις) are definitions (72314-24), which ascribe to subjects
predicates of the first kind. From these original premisses (with
the help of the ἀξιώματα and ὑποθέσεις) are deduced propositions
predicating of their subjects attributes καθ᾽ αὐτό of the second
kind; and by using propositions of both kinds further proposi-
tions of the second kind are deduced.
καθ᾽ αὑτό attributes of the second kind are dealt with in 84318-
25, those of the first in 425-8. There cannot be an infinite chain
of propositions asserting καθ᾽ αὑτό attributes of the second kind,
e.g. 'number is either odd or even, what is either odd or even is
either a or b, etc.’; for thus, number being included in the
definition of ‘odd’ and of ‘even’, and ‘odd or even’ being included
in that of ‘a or δ᾽, number would be included in the definition of
‘a or δ᾽, and of any subsequent term in the series, and the defini-
tion of the term at infinity would include an infinity of preceding
terms. Since this is impossible (definition being assumed to be
always possible, and the traversing of an infinite series impossible ;
cf. 82537-83^1), no subject can have an infinite series of καθ᾽ aóró
attributes of the second kind ascending from it (8418-22). It
must be noted, however (222-5), that, since in such predications
the predicate belongs to the subject precisely in virtue of the
subject's nature, and to nothing else, in a series of such terms all
the terms after the first must be predicable of the first, and the
first predicable of all the others, so that it will be a series of
convertible terms, not of terms of which each is wider than the
previous one, ie. not an ascending but what may be called a
neutral series; thus it will be infinite as the circumference of a
circle is infinite, in the sense that it returns on itself, but not an
infinite series of the kind whose existence we are denying.
Again (425-8) καθ᾽ αὑτό terms of the first kind are all involved
in the essence of their subject, and these for the same reason
cannot be infinite in number.
We have already seen (in ch. 20) that if the series is finite in
both directions, there cannot be an infinity of terms between any .
two terms within the series. We have now shown, therefore, that
T. 22. 8337 —>r7 581
there must be pairs of terms which are immediately connected,
the connexion neither needing nor admitting of proof (84229-b2).
8327. ὅπερ λευκόν τι, ‘identical with a species of white’.
I3. ὅπερ kal ἐγένετο, ‘which is what we made it in our assertion’.
24-5. Ἔτι τὰ pév . . . κατηγορεῖται, ‘further, predicates that
indicate just what their subject is, or just what it is a species of’.
ὅπερ ἐκεῖνό τι is to be explained differently from ὅπερ λευκόν τι
in 37 and the other phrases of the form ómep . . . τι which occur in
the chapter. It plainly means not ‘just what a species of that
subject is’, but ‘just what that subject is a species of’, τι going
not with ἐκεῖνο but with ὅπερ.
30. ὅπερ yap ζῷόν ἐστιν ὁ ἄνθρωπος. More strictly ὅπερ ζῷόν
τι, ‘identical with a species of animal’. But A.’s object here is not
to distinguish genus from species, but both from non-essential
attributes.
32-5. rà yàp εἴδη... εἰσίν. τερετίσματα is applied literally to
buzzing, twanging, chirruping, twittering; metaphorically to
speech without sense. This is the harshest thing A. ever says
about the Platonic Forms, and must represent a mood of violent
reaction against his earlier belief. The remark just made (332),
that there is nothing white without there being a subject in
which whiteness inheres, leads him to express his disapproval
of the Platonic doctrine, which in his view assigned such a
separate existence to abstractions. Even if there were Platonic
Forms, he says, the sciences (whose method is the subject of the
Posterior Analytics) are concerned only with forms incorporated
in individuals.
I conjecture that after these words we should insert εἴδη μὲν
obv . . . ὁμώνυμον (7755-9), which is out of place in its present
position. It seems impossible to say what accident in the history
of the text has led to the misplacement.
36-8. Ἔτι εἰ... οὕτως. ποιότης is here used to signify an
attribute in any category. ποιότητες are then subdivided into
essential attributes (439-10) and non-essential attributes (10-17),
as in Met. 1020^13-18).
39-1. ἢ γάρ... . . κατηγορουμένου. These words are answered
irregulariy by οὐδε μὴν τοῦ ποιοῦ ἢ τῶν ἄλλων οὐδέν, Pro.
br2-17. ἀλλὰ δὴ . .. ποτέ, ‘but now to prove that . . .; the
proof is contained in the fact that. ...’ For this elliptical use
of ὅτι cf. An. Pr. 62932, 40,514. n may be right in reading ἀλλὰ
δῆλον ὅτι (the reading δή being due to abbreviation of δῆλον), but
the /ectio difficilior is preferable.
17. Ὑπόκειται. . . ἑνὸς κατηγορεῖσθαι is to be interpreted in
582 COMMENTARY
the light of the remainder of the sentence, ‘we assume that one
thing is predicated of one other thing’. The only exception is
that in a definitory statement a thing is predicated of itself (ὅσα
μὴ τί ἐστι, P18).
These words seem to make a fresh start, and I have accordingly
written 57 as the more appropriate particle.
19-24. συμβεβηκότα yàp . . . érépov. In all non-definitory
statements we are predicating concomitants of the subject—
either per se concomitants, i.e. properties (attributes καθ᾽ αὑτό of
the second of the two kinds defined in 73334-^3) or accidental
concomitants. Both alike presuppose a subject characterized by
them. Not only does ‘straight’ (a typical καθ᾽ αὑτό attribute) pre-
suppose a line, but ‘white’ (a typical accidental concomitant)
presupposes a body or a surface (8321-23). ‘For we do not class
as a concomitant anything that is said to be what it is said to be,
without being anything else’ (22-3).
8437-8. Λογικῶς μὲν οὖν . . . ἀναλυτικῶς δέ, cf. 82535-6 n.
II-I2. ἡ μὲν yàp . . . πράγμασιν. The use of the article (τῶν)
as a demonstrative pronoun, with a relative attached, is a relic
of the Homeric usage, found also in 85536 and not uncommon in
Plato (cf. esp. Prot. 320d3, Rep. 469b3, 510a2, Parm. 13oc1,
Theaet. 204 d 1).
I3. ὅσα τε yàp . . . ἐστι. Jaeger (Emend. Arist. Specimen,
49-52) points out that while the implication of one term in the
definition of another is expressed by ἐνυπάρχει, or ὑπάρχει, ἐν τῷ
τί ἐστι (73°34, 36, 7457, 84215), the inherence of an attribute in a
subject is expressed by ὑπάρχει, or ἐνυπάρχει, τινί (without ἐν),
and that when A. wants to say ‘A inheres in B as being implied
in its definition’, he says τινὶ ἐν τῷ τί ἐστιν ἐνυπάρχει, or ὑπάρχει
(73337, P1, 7408). He therefore rightly excises ἐν.
16-17. καὶ πάλιν ... ἐνυπάρχει. Mure reads ἀδιαίρετον, on the
ground that number is πλῆθος ἀδιαιρέτων (Met. 1085522). But
διαιρετόν is coextensive with ποσόν in general (Met. 102047).
Quantity or the divisible has for its species μέγεθος or τὸ συνεχές,
and πλῆθος or τὸ διωρισμένον (Phys. 204711), i.e. what is infinitely
divisible (De Caelo 26846) and what is divisible into indivisibles,
ie. units (Met. 102027-11). Thus διαιρετόν is in place here, as an
element in the nature of number.
18-19. πάλιν γὰρ... εἴη. Bonitz (Arist. Stud. iv. 21-2) points
out that, as in 73437 the sense requires ὑπαρχόντων, not évvrapxóv-
των (cf. n. ad loc.), so here we do not want ἐν before τῷ περιττῷ.
The lectio recepta ἂν ἐν is due to a conflation of the correct dv
with the corrupt ἐν.
I. 22. 83>19 — 84436 583
21. ὑπάρχειν ἐν τῷ ἑνί. ἐν should perhaps be omitted, as in
473 and 19. But on the whole it seems permissible here. ὑπάρχειν
ev τῷ ἑνί stands for ὑπάρχειν τῷ ἑνὶ ἐν τῷ τί ἐστιν.
22-5. ἀλλὰ piv... ὑπερτείνοντα. Having rejected in *18-22
the possibility of an infinite series of terms, each καθ᾽ αὑτό in the
second sense to its predecessor, A. now states the real position—
that, instead, there is a number of terms, each καθ᾽ αὑτό in this
sense to a certain primary subject (in the case in question, to
number) ; but these will be convertible with one another and with
the subject, not a series in which each term is wider than its
predecessor.
29. Ei δ᾽ οὕτω... πεπερασμένα. This has been proved in
ch. 20.
32. ὅπερ ἔφαμεν . . . ἀρχάς, in 72567.
36. ἐμβάλλεσθαι. Cf. παρεμπίπτειν in An. Pr. 4268 (where
see n.).
CHAPTER 23
Corollaries from the foregoing propositions
8453. It follows (1) that if the same attribute belongs to two
things neither of which is predicable of the other, it will not
always belong to them in virtue of something common to both
(though sometimes it does, e.g. the isosceles triangle and the
scalene triangle have their angles equal to two right angles in
virtue of something common to them).
9. For let B be the common term in virtue of which A belongs
to C and D. Then (on the principle under criticism) B must
belong to C and D in virtue of something common, and so on,
so that there would be an infinite series of middle terms between
two terms.
x4. But the middle terms must fall within the same genus,
and the premisses be derived from the same immediate premisses,
if the common attribute to be found is to be a per se attribute;
for, as we saw, what is proved of one genus cannot be transferred
to another.
19. (2) When A belongs to B, then if there is a middle term, it
is possible to prove that A belongs to B ; and the elements of the
proof are the same as, or at least of the same number as, the
middle terms; for the immediate premisses are elements—either
all or those that are universal. If there is o middle term, there
is no proof; this is 'the way to the first principles'.
24. Similarly if A does not belong to B, then if there is a middle
term, or rather a prior term to which A does not belong, there is
584 COMMENTARY
a proof; if not, there is not—No B is A is a first principle; and
there are as many elements of proof as there are middle terms;
for the propositions putting forward the middle terms are the
first principles of demonstration. As there are affirmative in-
demonstrable principles, so there are negative.
31. (a) To prove an affirmative we must take a middle term
that is affirmed directly of the minor, while the major is affirmed
directly of the middle term. So we go on, never taking a premiss
with a predicate wider than A but always packing the interval
till we reach indivisible, unitary propositions. As in each set of
things the starting-point is simple—in weight the mina, in melody
the quarter-tone, etc.—so in syllogism the starting-point is the
immediate premiss, and in demonstrative science intuitive
knowledge.
85x. (b) In negative syllogisms, (i) in one mood, we use no
middle term that includes the major. E.g., we prove that B is
not A from No C is A, All B is C ; and if we have to prove that
no C is A, we take a term between A and C, and so on. (ii) In
another mood, we prove that E is not D from All DisC, No E is
C ; then we use no middle term included in the minor term. (iii)
In the third available mood, we use no middle term that either
is included in the minor or includes the major.
8458. 4 yàp σχῆμά mt, Le. qua triangle.
'12. ἐμπίπτοιεν. Cf. παρεμπίπτειν in An. Pr. 4258 (where see n.).
ἀλλ᾽ ἀδύνατον, as proved in chs. 19-22.
I4. εἴπερ ἔσται ἄμεσα διαστήματα. Jaeger (Emend. Arist.
Specimen, 53-7) points out that the MS. reading (with ἔπειπερ)
could only mean 'since it would follow that there are immediate
intervals’. I.e. the argument would be a reductio ad absurdum.
But it is "of absurd, but the case, that there are immediate
intervals (011-13). He cures the passage by reading εἴπερ, which
gives the sense 'if there are to be' (as there must be) 'immediate
intervals’. For the construction cf. P16, 803302, 81418-19; εἰ,
ἔσται in 7736 ; εἰ μέλλει ἔσεσθαι in 80>35 ; εἴπερ 8et . . . εἶναι in 7203, 26.
I4-17. ἐν μέντοι τῷ αὐτῷ γένει... δεικνύμενα. The point of
this addition is to state that while the middle terms used to prove
the possession of the same καθ᾽ αὑτό attribute by different subjects
need not be identical, all the middle terms so used must fall
within the same genus (e.g. be arithmetical, or geometrical),
and all the premisses must be derived from the same set of ultimate
premisses, since, as we saw in ch. 7, propositions appropriate to one
genus cannot be used to prove conclusions about another genus.
I. 23. 8458-33 585
20-2. kai στοιχεῖα... καθόλου. The sentence is improved by
reading ταὐτά in 52r, but remains difficult; to bring out A.'s
meaning, his language must be expanded. 'And there are ele-
ments of the proof the same as, or more strictly as many as, the
middle terms; for the immediate premisses are elements—either
all of them (and these are of course one more numerous than the
middle terms) or those that are major premisses (and these are
exactly as many as the middle terms).' The suggestion is that in
a chain of premisses such as All B is A, All C is B, All D isC only
the first two are elements of the proof, since in a syllogism the
major premiss already contains implicitly the conclusion (cf.
86222—9, and 86530 εἰ ἀρχὴ συλλογισμοῦ ἡ καθόλου πρότασις ἄμεσος).
For καί (Pzr) = ‘or more strictly’ cf. Denniston, Greek Particles,
292 (7).
23-4. ἀλλ᾽ ἡ ἐπὶ τὰς ἀρχὰς ... ἐστίν. Cf. E.N. 109532 εὖ yàp
καὶ ὁ Πλάτων ἠπόρει τοῦτο καὶ ἐζήτει, πότερον ἀπὸ τῶν ἀρχῶν ἢ
ἐπὶ τὰς ἀρχάς ἐστιν ἡ ὁδός. As the imperfect tenses imply, the
reference is to Plato’s oral teaching rather than to Rep. 510 b-
5IIC.
25. εἰ μὲν... ὑπάρχει. ἢ πρότερον ᾧ οὐχ ὑπάρχει is a correction.
μέσον suggests something that links two extremes, and something
intermediate in extent between them; and in a syllogism in
Barbara the middle term must at least be not wider than the
major and not narrower than the minor. But in a negative
syllogism the middle term serves not to link but to separate the
extremes, and in a syllogism in Celarent nothing is implied about
the comparative width of the major and middle terms; they are
merely known to exclude each other. But the middle term at
least more directly excludes the major than the minor does.
31-8533. Ὅταν 86 . . . πίπτει. A. here considers affirmative
syllogisms, and takes account only of proof in the first figure,
ignoring the second, which cannot prove an affirmative, and the
third, which cannot prove a universal. If we want to prove that
all B is A, we can only do so by premisses of the form All C is
A, All BisC. If we want to prove either of these premisses, we
can only do so by a syllogism of similar form. Clearly, then, we
never take a middle wider than and inclusive of A, nor (though
A. does not mention this) one narrower than and included in B;
all the middle terms will fall within the ‘interval’ that extends
from B to A, and will break this up into shorter, and ultimately
into unitary, intervals.
31-3. Ὅταν δὲ... A. The editions have ὁμοίως τὸ A. But if
we start with the proposition All B is A, there is no guarantee that
586 COMMENTARY
we can find a term “directly predicable of B, and having A directly
predicable of it’; and in the next sentence A. contemplates a
further packing of the interval between B and A. n must be
right in reading ὁμοίως τὸ 4; the further packing will then be
of the interval between 4 and A.
35-6. ἔστι δ᾽... ἄμεσος. A comma is required after γένηται,
and none after ἕν.
ΒΕ. ἐν δ᾽ ἀποδείξει καὶ ἐπιστημῇ ὁ νοῦς, ‘in demonstrative
science the unit is the intuitive grasp of an unmediable truth’.
3-12. ἐν δὲ rois στερητικοῖς . . . βαδιεῖται. The interpreta-
tion of this passage depends on the meaning of ἔξω in 44, 9, 11.
Prima facie, ἔξω might mean (a) including or (b) excluded by.
But neither of these meanings will fit A.'s general purpose, which
is to show that a proposition is justified not by taking in terms
outside the 'interval' that separates the subject and predicate,
but by breaking the interval up into minimal parts (84533-5).
The only meaning of ἔξω that fits in with this is that in which
a middle term would be said to be outside the major term if it
included it, and outside the minor term if it were included in it.
Further, this is the only meaning that fits the detail of the
passage. Finally, it is the sense that ἔξω bears in 88235 ἢ τοὺς
μὲν εἴσω ἔχειν τοὺς δ᾽ ἔξω τῶν ὅρων.
A. considers first (21-7) the justification of a negative proposi-
tion by successive syllogisms in the first figure (i.e. Celarent).
"No B is A’ will be justified by premisses of the form No C is A,
All B is C. Here the middle term plainly does not include the
major. Further, if All B is C needs proof, the middle term to be
used will not include the major term C (shown in 84531-5 and now
silently assumed by A.). And if No C is A is to be proved, it
will be by premisses of the form No D is A, All C is D, where
again the middle term does not include the major. Thus in a
proof by Celarent no middle term used includes the major term
(8523-5). We may add, though A. does not, that no middle term
used is included in the minor.
A. next (27-10) considers a proof in Camestres. If we prove
No E is D from All D is C, No E is C, we see at once that here it
is ot true that no middle term used includes the major ; for here
the very first middle does so. But it is true that no middle term
used is included in the minor. The first middle term plainly is
not. And if we have to prove the minor premiss by Camestres,
it will be by premisses of the form All C is F, No E is F, where F
is not included in E.
The last case (210-12) is usually taken to be that of a proof in
I. 23. 84*35 — 85212 587
the third figure. But a reference to the third figure would be
irrelevant; for A. is considering only the proof of a universal
proposition, and that is why he ignored the third figure when
dealing with proofs of an affirmative proposition (84531—5).
Further, what he says, that the middle term never falls outside
either the minor or the major term, i.e. never is included in the
minor or includes the major, would not be true of a proof in the
third figure. For consider the proof of a negative in that figure,
say in Fesapo—No M is P, All M is S, Therefore some S is not P;
the very first middle term used is included in the minor.
ἐπὶ τοῦ τρίτου τρόπου refers not to the third figure, but to the
third (and only remaining) way of proving a universal negative,
viz. by Cesare in the second figure. (Cf. An. Pr. 42532 τὸ μὲν otv
καταφατικὸν τὸ καθόλου διὰ τοῦ πρώτου σχήματος δείκνυται μόνου,
καὶ διὰ τούτου μοναχῶς: τὸ δὲ στερητικὸν διά τε τοῦ πρώτου καὶ διὰ
τοῦ μέσου, καὶ διὰ μὲν τοῦ πρώτου μοναχῶς, διὰ δὲ τοῦ μέσου διχῶς.
Further, the three modes of proving an E proposition have been
mentioned quite recently in Am. Post. 79>16-20.) The form of
Cesare is No DisC, All E isC, Therefore No E is D. The middle
term neither includes the major nor is included in the minor.
Further, if we prove the premiss No D is C by Cesare, it will be
by premisses of the form No C is F, All D is £F, and if we
prove the premiss All E is C, it will be by premisses of the form
AllG is C, All E is G; and neither of the middle terms, F, G, in-
cludes the corresponding major or is included in the correspond-
ing minor.
Thus the general principle, that in the proof of a universal
proposition we never use a middle term including the major
or included in the minor, holds good with the exception (tacitly
admitted in *9-10) that in a proof in Camestres the middle term
includes the major.
One point remains in doubt. The fact that A. ignores the third
figure when dealing with affirmative syllogisms (84531—5) and the
fact that he ignores Ferio when dealing with negative syllogisms
in the first figure (85*5-7) imply that he is considering only
universal conclusions and therefore only universal premisses.
But in 8529 (ἢ μὴ παντῇ the textus receptus refers to a syllogism
in Baroco. It is true enough that in a proof or series of proofs
in Baroco the middle term is not included in the minor; but
either the remark is introduced fer incuriam or more probably
it is a gloss, introduced by a scribe who thought that 510-12 re-
ferred to the third figure, and therefore that A. was not confining
himself to syllogisms proving universal conclusions.
588 COMMENTARY
4. ἔνθα μὲν ὃ δεῖ ὑπάρχειν. ὃ δεῖ ὑπάρχειν can stand for the
predicate of the conclusion even when the conclusion is negative
(cf. 8022—5 n.).
5. εἰ γὰρ... À, ‘for this proof is effected by assuming that
all B is C and noC is A’.
10. ᾧ Set ὑπάρχειν. This reading is preferable to the easier
ᾧ ov δεῖ ὑπάρχειν. Cf. * 3n.
CHAPTER 24
Universal demonstration is superior to particular
85213. It may be inquired (1) whether universal or particular
proof is the better, (2) whether affirmative or negative, (3)
whether ostensive proof or reductio ad impossibile.
zo. Particular proof might be thought the better, (1) because
the better proof is that which gives more knowledge, and we know
a thing better when we know it directly than when we know it
in virtue of something else; e.g. we know Coriscus the musician
better when we know that Coriscus is musical than when we
know that man is musical; but universal proof proves that some-
thing else, not the thing itself, has a particular attribute (e.g.
that the isosceles triangle has a certain attribute not because it
is isosceles but because it is a triangle), while particular proof
proves that the particular thing has it:
31. (2) because the universal is not something apart from its
particulars, and universal proof creates the impression that it
is, e.g. that there is a triangle apart from the various kinds of
triangle; now proof about a reality is better than proof about
something unreal, and proof by which we are not led into error
better than that by which we are.
b4. In answer to (1) we say that the argument applies no more
to the universal than to the particular. If possession of angles
equal to two right angles belongs not to the isosceles as such
but to the triangle as such, one who knows that the isosceles has
the attribute has not knowledge of it as belonging essentially
to its subject, so truly as one who knows that the triangle has
the attribute. If 'triangle' 15 wider and has a single meaning,
and the attribute belongs to every triangle, it is not the triangle
qua isosceles but the isosceles qua triangle that has the attribute.
Thus he who knows universally, more truly knows the attribute
as essentially belonging to its subject.
15. In answer to (2) we say (a) that if the universal term is
univocal, it will exist not less, but more, than some of its parti-
I. 23. 8533— 24. 85816 589
culars, inasmuch as things imperishable are to be found among
universals, while particulars tend to perish; and (δ) that the fact
that a universal term has a single meaning does not imply that
there is a universal that exists apart from particulars, any more
than do qualities, relations, or activities; it is not the demonstra-
tion but the hearer that is the source of error.
23. (Positive arguments.) (1) A demonstration is a syllogism
that shows the cause, and the universal is more causal than the
particular (for if 4 belongs to B qua B, B is its own reason for
its having the attribute A; now it is the universal subject that
directly owns the attribute, and therefore is its cause) ; and there-
fore the universal demonstration is the better.
27. (2) Explanation and knowledge reach their term when we
see precisely why a thing happens or exists, e.g. when we know
the «timate purpose of an act. If this is true of final causes, it
is true of all causes, e.g. of the cause of a figure's having a certain
attribute. Now we have this sort of knowledge when we reach
the universal explanation ; therefote universal proof is the better.
8612. (3) The more demonstration is particular, the more it
sinks into an indeterminate manifold, while universal demonstra-
tion tends to the simple and determinate. Now objects are
intelligible just in so far as they are determinate, and therefore
in so far as they are more universal; and if universals are more
demonstrable, demonstration of them is moretruly demonstration.
10. (4) Demonstration by which we know two things is better
than that by which we know only one; but he who has a universal
demonstration knows also the particular fact, but not vice versa.
13. (5) To prove more universally is to prove a fact by a middle
term nearer to the first principle. Now the immediate proposition,
which js the first principle, is nearest of all. Therefore the more
universal proof is the more precise, and therefore the better.
22. Some of these arguments are dialectical; the best proof
that universal demonstration is superior is that if we have a more
general premiss we have potentially a less general one (we know
the conclusion potentially even if we do not know the minor
premiss) ; while the converse is not the case. Finally, universal
demonstration is intelligible, while particular demonstration
verges on sense-perception.
85*13-16. Οὔσης δ᾽... ἀποδείξεως. The three questions are
discussed in chs. 24, 25, 26. In the first question the contrast is
not between demonstrations using universal propositions and
those using particular or singular propositions ; for demonstration
590 COMMENTARY
always uses universal propositions (the knowledge that Coriscus
is musical (#25) is not an instance of demonstration, but an
example drawn from the sphere of sensuous knowledge, in a
purely dialectical argument in support of the thesis which A.
rejects, that particular knowledge is better than universal). The
contrast is that between demonstrations using universal pro-
positions of greater and less generality.
24. τὸν μουσικὸν Κορίσκον. Coriscus occurs as an example
also in the Sophistici Elenchi, the Physics, the Parva Naturalia,
the De Partibus, the De Generatione Animalium, the Metaphysics,
and the Eudemian Ethics. Coriscus of Scepsis was a member of
a school of Platonists with whom A. probably had associations
while at the court of Hermeias at Assos, c. 347-344. He is one of
those to whom the (probably genuine) Sixth Letter of Plato is
addressed. From Phys. 219920 ὥσπερ of σοφισταὶ λαμβάνουσιν
ἕτερον τὸ Κορίσκον ἐν Λυκείῳ εἶναι καὶ τὸ Κορίσκον ἐν ἀγορᾷ we may
conjecture that he became a member of the Peripatetic school,
and he was the father of Neleus, to whom Theophrastus left
A.’s library. The reference to him as ‘musical Coriscus’ recurs in
Met. 1015>18, 1026617. On A.’s connexion with him cf. Jaeger,
Entst. d. Met. 34 and Arist. 112-17, 268.
27-8. olov ὅτι... τρίγωνον, ‘e.g. it proves that the isosceles
triangle has a certain attribute not because it is isosceles but
because it is a triangle’.
37-?r. προϊόντες yap... τι. A. illustrates the point he is here
putting dialectically, by reference to a development of mathe-
matics which he elsewhere (74217-25) describes as a recent dis-
covery, viz. the discovery that the properties of proportionals
need not be proved separately for numbers, lines, planes, and
solids, but can be proved of them all qua sharing in a common
nature, that of being quanta. The Pythagoreans had worked out
the theory of proportion for commensurate magnitudes; it was
Eudoxus that discovered the general theory now embodied in
Euc. EL v, vi. In the present passage the supposed objector
makes a disparaging reference to the general proof—‘if they carry
on in this course they come to proofs such as that which shows
that whatever has a certain common character will be propor-
tional, this character not being that of being a number, line,
plane, or solid, but something apart from these'.
^s. ἅτερος λόγος, ‘the other argument’, i.e. that in 321-31.
II. τὸ δύο, i.e. τὸ τὰς γωνίας δυὸ ὀρθαῖς ἴσας ἔχειν.
23. Ἔτι εἰ xrÀ., ‘the same conclusion follows from the fact
that’, etc. ; cf. 86*ro n., 30-1 n.
I. 24. 85224 — 86430 591
25. τὸ δὲ καθόλου πρῶτον, ‘and the universal is primary’, i.e.
if the proposition All B is A is commensurately universal, the
presence of B'ness is the direct cause of the presence of A’ness.
36. ἐπὶ δὲ τῶν ὅσα αἴτια. For the construction cf. 84211—12 n.
38-86*1. ὅταν μὲν οὖν... εὐθύγραμμον. This is interesting
as being one of the propositions known to A. but not to be found
in Euclid a generation later; for other examples cf. De Caelo
287227-8, Meteor. 376*1—3, 7-9, P1-3, 10-12, and Heiberg, Math.
zu Arist. in Arch. z. Gesch. d. Math. Wissensch. xviii (1904), 26-7.
Cf. Heath, Mathematics in Aristotle, 62-4.
86*9. ἅμα yàp μᾶλλον rà πρός τι, ‘for correlatives increase
concomitantly'.
IO. Ἔτι εἰ αἱρετωτέρα x7A., cf. 85523 n.
22-9. ᾿Αλλὰ τῶν μὲν εἰρημένων . . . ἐνεργείᾳ. This is not a new
argument; it is the argument of #10-13 expanded, with explicit
introduction of the distinction of δύναμις and ἐνέργεια. Thus A.
is in fact saying that while some of the previous arguments are
dialectical, one of them is genuinely scientific.
Zabarella tries to distinguish this argument from that of 110-13
by saying that whereas the present argument rests on the fact
that knowledge that all B is A involves potential knowledge that
particular B's are A, the earlier argument rests on the fact
that knowledge that all B is A presupposes actual knowledge that
some particular B's are A. But this is not a natural reading of
910-13.
A. does not mean by τὴν προτέραν, τὴν ὑστέραν the major and
minor premiss of a syllogism; for (a) what he is comparing in
general throughout the chapter is not two premisses but two
demonstrations, or the conclusions of two demonstrations; (b)
it is not true that knowledge of a major premiss implies potential
knowledge of the minor, though it is true to say that in a sense
it implies potential knowledge of the conclusion ; (c) in theexample
(325-9) it is with knowledge of the conclusion. that A. contrasts
knowledge of the major premiss. ἡ προτέρα is the premiss of a
more general demonstration, ἡ ὑστέρα the premiss of a less general
demonstration. A. is comparing the first premiss in a proof of the
form All B is A, AUC is B, All D isC, Therefore All D is A, with
the first premissin a proof of the form ΑἹ] ( is A, All Dis C, There-
fore all Dis A.
It follows that ταύτην τὴν πρότασιν in ?27-8 means τὸ ἰσοσκελὲς
ὅτι δύο ὀρθαῖς, not τὸ ἰσοσκελὲς ὅτι τρίγωνον.
29-30. ἡ δὲ κατὰ μέρος... τελευτᾷ. If we imagine a series of
demonstrations of gradually lessening generality, the last member
592 COMMENTARY
of such a series would be a syllogism with an individual thing
as its minor term, and in that case the conclusion of the syllogism
is a fact which might possibly be apprehended by sense-per-
ception, as well as reached by inference.
CHAPTER 25
Affirmative demonstration is superior to negative
86*31. That an affirmative proof is better than a negative
is clear from the following considerations. (1) Let it be granted
that ceteris paribus, i.e. if the premisses are equally well known,
a proof from fewer premisses is better than one from more pre-
misses, because it produces knowledge more rapidly.
36. This assumption may be proved generally as follows: Let
there be one proof that E is A by means of the middle terms
B, Γ, A, and another by means of the middle terms Z, H. Then
the knowledge that 4 is A is on the same level as the knowledge,
by the second proof, that Eis A. But that 4 is A is known better
than it is known, by the first proof, that E is A; for the latter
is known by means of the former.
b4. Now an affirmative and a negative proof both use three
terms and two premisses; but the former assumes only that
something is, and the latter both that something is and that
something is not, and therefore uses more premisses, and is
therefore inferior.
ro. (2) We have shown that two negative premisses cannot
yield a conclusion; that to get a negative conclusion we must
have a negative and an affirmative premiss. We now point out
that if we expand a proof, we must take in several affirmative
premisses but only one negative. Let no B be A, and all Γ be B.
To prove that no B is A, we take the premisses No 4 is A, All
B is 4; to prove that all I" is B, we take the premisses All E is B,
Ali ris E. So we take in only one negative premiss.
22. The same thing is true of the other syllogisms ; an affirma-
tive premiss needs two previous affirmative premisses ; a negative
premiss needs an affirmative and a negative previous premiss.
Thus if a negative premiss needs a previous affirmative premiss,
and not vice versa, an affirmative proof is better than a negative.
30. (3) The starting-point of a syllogism is the universal im-
mediate premiss, and this is in an affirmative proof affirmative,
in a negative proof negative; and an affirmative premiss is prior
to and more intelligible than a negative (for negation is known
on the ground of affirmation, and affirmation is prior, as being
I. 25. 86333 — 38 593
is to not-being). Therefore the starting-point of an affirmative
proof is better than that of a negative; and the proof that has
the better starting-point is the better. Further, the affirmative
proof is more primary, because a negative proof cannot proceed
without an affirmative one.
86233-»9. ἔστω yap... χείρων. This argument is purely dia-
lectical, as we see from two facts. (1) What A. proves in ?33-57 is
that an argument which uses fewer premisses is superior to one
that uses more, if the premisses are equally well known. But
what he points out in 57-9 is that a negative proof uses more
kinds of premiss than an affirmative, since it needs both an
affürmative and a negative premiss. (2) The whole conception
that there could be two demonstrations of the same fact using
different numbers of equally well-known premisses (i.e. immediate
premisses, or premisses approaching equally near to immediacy)
is inconsistent with his view of demonstration, namely that of
a single fact there is only one demonstration, viz. that which
deduces it from the unmediable facts which are in reality the
grounds of the fact's being a fact.
34. αἰτημάτων ἢ ὑποθέσεων. ὑπόθεσις and αἴτημα are defined
in contradistinction to each other in 7627-34; there is no allusion
here to the special sense given to ὑπόθεσις in 72418-20.
byo-z2, ἐπειδὴ δέδεικται. . . ὑπάρχει. The proof is contained
in the treatment of the three figures in An. Pr. i. 4-6, and summed
up ib. 24. 41>6-7.
I5. ἐν ἁπαντὶ συλλογισμῷ, not only in each syllogism but in
each sorites, as A. goes on to show.
22-3. 6 δ᾽ αὐτὸς τρόπος . . . συλλογισμῶν. This may refer
either (a) to further expansions of an argument by the inter-
polation of further middle terms, or (b) to arguments in the second
or third figure. But in ^3o-3 A. contemplates only first-figure
syllogisms; for in the second figure a negative conclusion does
not require a negative major premiss; so that (a) is probably the
true interpretation here. :
30-1. ἔτι el . . . ἄμεσος. εἰ is to be explained as in 85523,
86410. The major premiss is called the starting-point of the
syllogism because knowledge of it implies potential knowledge
of the conclusion (322-9).
38. ἄνευ yàp τῆς δεικνυούσης . . . στερητική, because, as we
have seen in >ro-30, a negative proof requires an affirmative
premiss, which (if it requires proof) requires proof from affirma-
tive premisses.
4985 [9] q
594 COMMENTARY
CHAPTER 26
Ostensive demonstration 1s superior to reductio ad impossibile
8741. Since affirmative proof is better than negative, it is
better than reductio ad impossibile. The difference between
negative proof and reduciio is this: Let no B be A, and all C be B.
Then no C is A. That is a negative ostensive proof. But if we
want to prove that B is not A, we assume that it is, and that C is
B, which entails that C is A. Let this be known to be impossible;
then if C is admittedly B, B cannot be A.
12. The terms are similarly arranged; the difference depends
on whether it is better known that B is not A or that C is not A.
When the falsity of the conclusion (‘C is A’) is the better known,
that is veductio; when the major premiss (‘B is not A’) is the
better known, ostensive proof. Now 'B is not A’ is prior by
nature to 'C is not A’. For premisses are prior to the conclusion
from them, and ‘C is not A’ isa conclusion, ' B is not A’ a premiss.
For if we get the result that a certain proposition is disproved,
that does not imply that the negation of it is a conclusion and
the propositions from which this followed premisses; the pre-
misses of a syllogism are propositions related as whole and part,
but ‘C is not A’ and 'C is B’ are not so related.
25. If, then, inference from what is prior is better, and the
conclusions of both kinds of argument are reached from a nega-
tive proposition, but one from a prior proposition, one from
a later one, negative demonstration is better than reductio, and
a fortior: affirmative demonstration is so.
87*10. οὐκ ἄρα... ὑπάρχειν. Maier (Syll. d. Arist. 2 a. 231 n.)
conjectures Γ for the MS. reading B, on the ground that otherwise
this sentence would anticipate the result reached in the next
sentence. But with his emendation the present sentence becomes
a mere repetition of the previous one, so that nothing is gained.
The next sentence simply sums up the three that precede it.
12-25. oi μὲν οὖν Spor... ἀλλήλας. The two arguments, as
stated in #3-12, are (1) (Ostensive) No B is A, All C is B, There-
fore noC is A. (2) (Reductio) (a) If B is A, then—since C is B—C
is A. But (5) in fact C is not A; the conclusion of a syllogism
cannot be false and both its premisses true; 'C is B' is true; there-
fore 'B is A' is false. A. deliberately (it would seem) chooses a
reductio the effect of which is to establish not the conclusion to
which the ostensive syllogism led, but the major premiss of that
I. 26. 87410-28 595
syllogism. At the same time, to avoid complications about the
quantity of the propositions, he introduces them in an unquanti-
fied form. The situation he contemplates is this: (1) There may
be a pair of known propositions of the form 'B is not A', 'C is
B', which enable us to infer that C is not A. But (2), on the other
hand, we may, while knowing that C is B and that C is not A, not
know that B is not A, and be able to establish this only by con-
sidering what follows from supposing it to be false; then we use
reductio. The arrangement of the terms is as before (512); i.e.
in fact in both cases B is not A, C is B, end C is not A; the
difference is that we use 'B is not A’ to prove 'C is not A’ (as in
(1)) when 'B is not A’ is to us the better known proposition, and
‘C is not A’ to prove 'B is not A’ (as in (2 b)) when 'C is not A’
is the better known. But the two processes are not equally
natural (417-18); 'B is not A’ is in itself the prior proposition,
since it, with the other premiss 'C is B', constitutes a pair of
premisses related to one another as whole to part (322-3, cf.
An. Post. 4238-13, 47*10-14, 4937-501), the one stating a general
rule, the other bringing a particular case under it; while 'C is
not A’, with ‘C is B', does not constitute such a pair (and in fact
does not prove that B is not A, but only that some B is not A).
The second part of the reductio process is, as A. points out in
An. Pr. 41*23-30, 50?29-38, not a syllogism at all, but an argument
ἐξ ὑποθέσεως, involving besides the data that are explicitly
mentioned (Ὁ is not A’ and 'C is B") the axiom that premisses
(e.g. 'B is A’ and ‘C is B") from which an impossible conclusion
(e.g. ‘C is A’) follows cannot both be true.
It seems impossible to make anything of the MS. reading AI
xai AB in 224. For what A. says is ‘the only thing that can be
a premiss of a syllogism is a proposition which is to another'
(i.e. to the other premiss) 'either as whole to part or as part to
whole', and it would be pointless to continue 'but the propositions
AT ("C is not A") and AB ("B is not A") are not so related’ ; for
in the reductio there is no attempt to treat these propositions as
joint premisses; 'C is not A’ is datum, ‘B is not A’ conclusion.
Accordingly we must read ΑΓ xai ΒΓ, which do appear as joint
data in (2 b). The corruption was very likely to occur, in view
of the association of the propositions ‘C is not A’ and 'B is not A’
in 514, 17-18, 19-20.
28. ἡ ταύτης βελτίων ἡ κατηγορική. That affirmative proof
is superior to negative was proved in ch. 25.
596 COMMENTARY
CHAPTER 27
The more abstract science is superior to the less abstract
87*3x. One sctence is more precise than and prior to another,
(1) if the first studies both the fact and the reason, the second
only the fact ; (2) if the first studies what is not, and the second
what is, embodied in a subject-matter (thus arithmetic is prior
to harmonics) ; (3) if the first studies simpler and the second more
complex entities (thus arithmetic is prior to geometry, the unit
being substance without position, the point substance with
position).
87°31-3. ᾿Ακριβεστέρα δ᾽... διότι. At first sight it looks as
if we should put a comma after χωρὶς τοῦ ὅτι, and suppose A.
to be placing a science which studies both the fact and the reason,
and not the fact alone (if we take χωρίς adverbally), or not the
reason without the fact (if we take ywpis as a preposition), above
one which studies the reason alone. But it seems impossible to
reconcile either of these interpretations with A.'s general view,
and there is little doubt that T. 37. 9-11, P. 299. 27-8, and
Zabarella are right in taking ἀλλὰ μὴ χωρὶς τοῦ ὅτι τῆς τοῦ διότι to
mean, by hyperbaton, “but not of the fact apart from the know-
ledge of the reason’. A. will then be referring to such a situation
as is mentioned in 78539-79413, where he distinguishes mathe-
matical astronomy, which knows the reasons, from nautical
astronomy, which knows the facts, and similarly distinguishes
mathematical harmonics from ἡ κατὰ τὴν ἀκοήν, and mathematical
optics from τὸ περὶ τῆς ἴριδος, the empirical study of the rainbow.
The study of the facts without the reasons is of course only by
courtesy called a science at all, being the mere collecting of
unexplained facts.
Thus A. in the first place ranks genuine sciences higher than
mere collections of empirical data. He then goes on to rank pure
sciences higher than applied sciences (*33-4), and pure sciences
dealing with simple entities higher than those that deal with
more complex entities (534-7).
36. olov povas ... 8erós. The definition of the point is taken
from the Pythagoreans ; cf. Procl. in Euc. El. 95. 21 of Πυθαγόρειοι
τὸ σημεῖον ἀφορίζονται μονάδα προσλαβοῦσαν θέσιν. A.'s use of the
term οὐσία in defining the unit and the point is not strictly
justified, since according to him mathematical entities have no
existence independent of subjects to which they attach. But he
I. 27. 87431 — 28. 8754 597
can call them οὐσίαι in a secondary sense, since in mathematics
they are regarded not as attributes of substances but as subjects
of further attributes.
CHAPTER 28
What constitutes the unity of a science
87°38. A single science is one that is concerned with a single
genus, i.e. with all things composed of the primary elements of
the genus and being parts of the subject, or essential properties
of such parts. Two sciences are different if their first principles
are not derived from the same origin, nor those of the one from
those of the other. The unity of a science is verified when we
reach the indemonstrables; for they must be in the same genus
as the conclusions from them; and the homogeneity of the first
principles can in turn be verified by that of the conclusions.
87°38-9. Mia δ᾽ ἐπιστήμη . . . αὑτά. A science is one when its
subjects are species (μέρη) of a single genus, composed of the
same ultimate elements, and when the predicates it ascribes to
its subjects are fer se attributes of those species.
39-51. ἑτέρα δ᾽... ἑτέρων. When the premisses of two pieces
of reasoned knowledge are derived from the same ultimate
principles, we have two coordinate parts of one science ; when the
premisses of one are derived from the premisses of the other, we
have a superior and a subaltern branch of the same science;
cf. 78534—79216.
Pr. μήθ᾽ Grepat ἐκ τῶν ἑτέρων. The grammar requires drepa«.
The MSS. of T. and P. are divided between ἕτεραι and at ἕτεραι,
but P. seems to have read drepa« or a£ ἕτεραι (rois δὲ τῆς ἑτέρας
θεωρήμασιν ἀρχαῖς ἡ ἑτέρα χρῷτο, 303. 9-10).
1-4. τούτου δὲ... συγγενῆ. Since the conclusions of a science
must fall within the same genus (deal with the same subject-
matter) as its premisses, the homogeneity of the conclusions can
be inferred from that of the premisses, or vice versa.
CHAPTER 29
How there may be several demonstrations of one connexion
87>s. There may be several proofs of the same proposition,
(1) if we take a premiss linking an extreme term with a middle
term not next to it in the chain; (2) if we take middle terms from
different chains, e.g. pleasure is a kind of change because it is
598 COMMENTARY
a movement, and also because it is a coming to rest. But in such
a case one middle term cannot be universally deniable of the
other, since both are predicable of the same thing. This problem
should be considered in the other two figures as well.
8755-7. οὐ μόνον... Z, ic. if all Fis A, all A is I", all Z is 4,
and all B is Z, we may omit any two of the middle terms and use
as premisses for the conclusion All Bis A (1) All I is A, AIL B is
I, (2) Al 4 is A, All B is 4, or (3) All Z is A, AIL Bis Z, using
in (1) a middle term not directly connected with B, in (3) one not
directly connected with A, and in (2) one not directly connected
with either extreme.
14-15. οὐ μὴν... μέσων, i.e. each of the middle terms must
be predicable of some part of the other, since both are predicable
of pleasure.
16-18. ἐπισκέψασθαι δὲ... συλλογισμόν. For infinitivus vi
imperativa, cf. Bonitz, Index, 343?22—34.
CHAPTER 30
Chance conjunctions are not demonstrable
87^19. There cannot be demonstrative knowledge of a chance
event; for such an event is neither necessary nor usual, while
every syllogism proceeds from necessary or usual premisses, and
therefore has necessary or usual conclusions.
For A.’s doctrine of chance cf. Phys. ii. 4-6, A. Mansion, Intro-
duction à la Physique Aristotélicienne, ed. 2 (1946), and the Intro-
duction to my edition of the Physics, 38-41.
CHAPTER 31
There can be no demonstration through sense-perception
87528. It is impossible to have scientific knowledge by per-
ception. For even if perception is of a such and not of a mere
this, still what we perceive must be a this here now. For this
reason a universal cannot be perceived, and, since demonstrations
are universal, there cannot be science by perception. Even if it
had been possible to perceive that the angles of a triangle equal
two right angles, we should still have sought for proof of this.
So even if we had been on the moon and seen the earth cutting
off the sun's light from the moon, we should not have known the
cause of eclipse.
I. 29. 875 -— 31. 88416 599
882. Still, as a result of seeing this happen often we should
have hunted for the universal and acquired demonstration; for
the universal becomes clear from a plurality of particulars. The
universal is valuable because it shows the cause, and therefore
universal knowledge is more valuable than perception or intuitive
knowledge, with regard to facts that have causes other than
themselves; with regard to primary truths a different account
must be given.
9. Thus you cannot know a demonstrable fact by perception,
unless one means by perception just demonstrative knowledge.
Yet certain gaps in our knowledge are traceable to gaps in our
perception. For there are things which if we had seen them we
should not have had to inquire about—not that seeing con-
stitutes knowing, but because we should have got the universal
as a result of seeing.
87537. ὥσπερ φασί tives. The reference is to Protagoras’
identification of knowledge with sensation ; cf. Pl. Theaet. 151 e-
1§2 a.
8851. kai οὐ διότι ὅλως, ‘and not at all why it happens’. For
this usage of ὅλως with a negative cf. Bonitz, Index, 506. 1—10.
2-4. οὐ μὴν ἀλλ᾽... εἴχομεν. The knowledge of a universal
principle which supervenes on perception of particular facts is
not itself deduction but intuitive knowledge, won by induction
(216-17) ; but the principles thus grasped may become premisses
from which the particular facts may be deduced.
6-8. Gore περὶ τῶν τοιούτων... . . λόγος. What A. is saying
here is that where there is a general law that depends on a still
more general principle, the only way of really knowing it is to
derive it by demonstration from the more general principle. It
cannot be grasped by sensation, which can only yield awareness
of particular facts; nor by intellectual intuition, which grasps
only the most fundamental general principles. For the latter
point cf. ii. 19, especially rooPi2 νοῦς dv εἴη τῶν ἀρχῶν.
14-16. οἷον εἰ... καίει. This is a reference to Gorgias’ explana-
tion of the working of the burning-glass—fr. 5 Diels (= Theophr.
de Igne 73) ἐξάπτεται δὲ ἀπό τε τῆς Bédov . . . οὐχ, ὥσπερ Γοργίας
φησὶ καὶ ἄλλοι δέ τινες οἴονται, διὰ τὸ ἀπιέναι τὸ πῦρ διὰ τῶν πόρων.
600 COMMENTARY
CHAPTER 32
All syllogisms cannot have the same first principles
88:18. That the starting-points of all syllogisms are not the
same can be seen (1) by díalectical arguments. (a) Some syllogisms
are true, others false. À true conclusion may indeed be got from
false premisses, but that happens only once. 4 may be true of
C though A is untrue of B and B of C. But if we take premisses
to justify these premisses, these will be false, because a false
conclusion can only come from false premisses; and false pre-
misses are distinct from true premisses.
27. (b) Even false conclusions do not come from the same
premisses; for there are false propositions that are contrary or
incompatible.
30. Our thesis may be proved (2) from the principles we have
laid down. (2) Not even all true syllogisms have the same starting-
points. The starting-points of many true syllogisms are different
in kind, and not applicable to things of another kind (e.g. those
concerning units are not applicable to points). They would have
either to be inserted between the extreme terms, or above the
highest or below the lowest, or some would be inside and some
outside.
36. (δ) Nor can there be any of the common principles, from
which everything will be proved; for the genera of things are
different, and some principles apply only to quantities, others
only to qualities, and these are used along with the common
principles to prove the conclusion.
b3. (c) The principles needed to prove conclusions are not
much fewer than the conclusions; for the principles are the pre-
misses, and premisses involve either the addition of a term from
outside or the interpolation of one.
6. (d) The conclusions are infinite in number, but the terms
supposed to be available are finite.
7. (&) Some principles are true of necessity, others are con-
tingent.
9. It is clear, then, that, the conclusions being infinite, the
principles cannot be a finite number of identical principles. Let
us consider other interpretations of the thesis. (1) If it is meant
that precisely these principles are principles of geometry, these
of arithmetic, these of medicine, this is just to say that the sciences
have their principles; to call the principles identical because
they are self-identical would be absurd, for at that rate all things
would be identical.
I. 32. 88419-31 601
x5. Nor (2) does the claim mean that it is from all the principles
taken together that anything is proved. That would be too naive;
for this is not so in the manifest proofs of mathematics, nor is it
possible in analysis, since it is immediate premisses that are the
principles, and a new conclusion requires the taking in of a new
immediate premiss.
zo. (3) If it be said that the first immediate premisses are
the principles, we reply that there is one such peculiar to each
genus.
21. (4) If it is not the case that any conclusion requires all the
principles, nor that each science has entirely different principles,
the possibility remains that the principles of all facts are alike
in kind, but that different conclusions require different premisses.
But this is not the case; for we have shown that the principles
of things different in kind are themselves different in kind. For
principles are of two sorts, those that are premisses of demonstra-
tion, which are common, and the subject-genus, which is peculiar
(e.g. number, spatial magnitude).
88219. πρῶτον μὲν λογικῶς θεωροῦσιν. The arguments in 419-
3o are called dialectical because they take account only of the
general principles of syllogistic reasoning, and not of the special
character of scientific reasoning.
19-26. oi μὲν γὰρ... τἀληθῆ. This first argument is to the
effect that all syllogisms cannot proceed fzom the same premisses,
since broadly speaking true conclusions follow from true pre-
misses and false from false. A. has to admit that there are
exceptions; a true conclusion can follow from false premisses.
But this, he claims, can only happen once in a chain of reasoning,
since the false premisses from which the conclusion follows must
themselves have false premisses, which must in turn have false
premisses, and so on.
The argument is a weak one; for not both the premisses of
a false conclusion need be false, so that there may be a con-
siderable admixture of true propositions with false in a chain of
reasoning. A. himself describes the argument as dialectical (219).
27-30. ἔστι yap... ἔλαττον. ‘What is equal is greater’ and
‘what is equal is less’ are offered as examples of contrary false
propositions ; ‘justice is injustice’ and ‘justice is cowardice’, and
again ‘man is horse’ and ‘man is ox’ as examples of incompatible
false propositions. It is evident that no two propositions so
related can be derived from exactly the same premisses.
30-1. "Ex δὲ τῶν κειμένων . .. πάντων. The dialectical arguments
602 COMMENTARY
in *19-30 took account of the existence of false propositions;
the scientific arguments in *3o-b29, being based on τὰ κείμενα, on
what has been laid down in the earlier part of the book with
regard to demonstrative science, take account only of true proposi-
tions, since only true premisses (71>19-26), and therefore only
true conclusions, find a place in science.
31—6. ἕτεραι γὰρ... ὅρων. A. considers, first, propositions
which form the actual premisses of proof, i.e. θέσεις (ὑποθέσεις
and ὁρισμοί) (7214-16, 18-24). These, he says, are in the case of
many subjects generically different, and those appropriate to
one subject cannot be applied to prove propositions about
another subject. If we want to prove that B is A, any terms
belonging to a different field must be introduced either (1) as
terms predicable of B and having A predicable of them, or (2)
as terms predicable of A, or of which B is predicable, or (3) some
of them will be introduced as in (1) and some as in (2). In any
case we shall have terms belonging to one field predicated of
terms belonging to another field, which we have seen in ch. 7 to
be impossible in scientific proof. Such propositions could
obviously not express connexions καθ᾽ αὑτό.
36-53. ἀλλ᾽ οὐδὲ... κοινῶν. A. passes now to consider an-
other suggestion, that some of the ἀξιώματα (72216-18), like the
law of excluded middle, can be used to prove all conclusions. In
answer to this he points out that proof requires also special
principles peculiar to different subjects (ie. those considered in
8831-6), proof taking place through the ἀξιώματα along with such
special principles. The truth rather is that the special principles
form the premisses, and the common principles the rules according
to which inference proceeds.
53-7. ἔτι αἱ apyai . . . ἐνδεχόμεναι. A. has given his main
proof in ?31-5s, viz. that neither can principles proper to one main
genus be used to prove properties of another, nor can general
principles true of everything serve alone to prove anything. He
now adds, rather hastily, some further arguments. (x) The first
is that (a) the theory he is opposing imagines that the vast
variety of conclusions possible in science is proved from a small
identical set of principles; while in fact (b) premisses are not
much fewer than the conclusions derivable from them ; not much
fewer, because the premisses required for the increase of our
knowledge are got not by repeating our old premisses, but either
(if we aim at extending our knowledge) by adding a major higher
than our previous major or a minor below our former minor
(προσλαμβανομένου opov), or (if we aim at making our knowledge
I. 32. 88431 — ^29 603
more thorough) by interpolating a middle term between two of
our previous terms (ἐμβαλλομένου).
(b) is a careless remark. A. has considered the subject in An.
Pr. 42>16-26, where he points out that if we add a fresh premiss
to an argument containing * premisses or »+1 terms, we get
n new conclusions. Thus (i) from two premisses ‘A is B', 'B is
C' we get one conclusion, ‘A is C', (ii) from three premisses ‘A is
B','B isC', ' is D', we get three conclusions, ‘A is C', ‘A is δ᾽
'B is D', (iii) from four premisses ‘A is B', ‘B is C', 'C is D',
‘D is E' we get six conclusions ‘A is C’, ‘A is D’, ‘A is E', 'B is
D', ‘B is E', Ὁ is E'—and so on. With * premisses we have
nin-1) conclusions, and as » becomes large the disparity between
the number of the premisses and that of the conclusions becomes
immense. That is what happens when the new terms are added
from outside (προστιθεμένου 42518, προσλαμβανομένου 8855). The
same thing happens if new terms are interpolated (xdv eis τὸ
μέσον δὲ παρεμπίπτῃ 42023, ἐμβαλλομένου 8855), and A. concludes
'so that the conclusions are much more numerous than either
the terms or the premisses’ (4225-6). It is only if the number of
premisses is itself comparatively small that it can be said to be
‘little less than the number of the conclusions’; one is tempted
to say that if A. had already known the rule which he states in
the Prior Analytics he would hardly have written as he does here,
and that An. Pr. i. 25 must be later than the present chapter.
The next sentence (b6—7) is cryptic enough, but can be inter-
preted so as to give a good sense. ‘If the ἀρχαί of all syllogisms
were the same, the terms which, combined into premisses, have
served to prove the conclusions already drawn—and these terms
must be finite in number—are all that are available for the
proving of all future conclusions, to whose number no limit can
be set. But in fact a finite number of premisses can be combined
only into a finite number of syllogisms.'
If this interpretation be correct, the argument is an ingenious
application of A.'s theory that there is no existing infinite but
only an infinity of potentiality (PAys. iii. 6-8).
Finally (b7-8) A. points out that some principles are apodeictic,
some problematic; this, taken with the fact that conclusions
have a modality varying with that of their premisses (cf. Ax. Pr.
41527-31), shows that not all conclusions can be proved from the
same premisses.
9-29. Οὕτω μὲν οὖν. . . μέγεθος. A. turns now to consider
other interpretations of the phrase 'the first principles of all
604 COMMENTARY
syllogisms are the same’. Does it mean (1) that the first principles
of all geometrical propositions are identical, those of all arithmeti-
cal propositions are identical, and those of all medical propositions
are identical? To say this is not to maintain the identity of all
first principles but only the self-identity of each set of first
principles, and to maintain this is to maintain nothing worth
maintaining (Pro—r5).
(2) The claim that all syllogisms have the same principles can
hardly mean the claim that any proposition requires the whole
mass of first principles for its proof. That would be a foolish
claim. We can see in the sciences that afford clear examples of
proof (i.e. in the mathematical sciences) that it is not so in fact ;
and we can see by attempting the analysis of an argument that
it cannot be so; for each new conclusion involves the bringing
in of a new premiss, which therefore cannot have been used in
proving the previous conclusions (15-20).
(3) The sentence in ^2o-1 has two peculiar features. (a) The
first is the phrase τὰς πρώτας ἀμέσους προτάσεις. πρῶτος is very
frequently used in the same sense as ἄμεσος, but if that were its
meaning here A. would almost certainly have said πρώτας
καὶ ἀμέσους (cf. e.g. 71521). The phrase as wc have it must point
to primary immediate premisses as distinct from the immediate
premisses in general which have been previously mentioned.
(This involves putting a comma after προτάσεις and treating
ταύτας as a repetition for the sake of emphasis; cf. 7257-8 and
many examples in Kühner, Gr. Gramm. § 469. 4 b.) (6) The same
point emerges in the phrase μία ἐν ἑκάστῳ γένει. This must mean
that out of all the principles proper to a subject-matter and not
available for the study of other subject-matters, there is one that
is primary. Zabarella is undoubtedly right in supposing this to
be the definition of the subject-matter of the science in question,
e.g. of number or of spatial magnitude (cf. 528-9) ; for it is from
the subject's essential nature that its consequential properties
are deduced.
(4) (P2179) If what is maintained is neither (2) nor (1) but an
intermediate view, that the first principles of all proof are identi-
cal in genus but different in species, the answer is that, as we
have already proved in ch. 7, generically different subjects have
generically different principles. Proof needs not only common
principles (the axioms) but also special principles relating to the
subject-matter of the science, viz. the definitions of the terms
used in the science, and the assumptions of the existence of the
primary subjects of the science (cf. 72214-24).
I. 32. 8859-29 605
Cherniss (A.’s Criticism of Plato and the Academy, i. 73 n.)
argues with much probability that this fourth view is that of
Speusippus, who insisted on the unity of all knowledge, the know-
ledge of any part of reality depending on exhaustive knowledge
of all reality, and all knowledge being a knowledge of similarities
(ὁμοιότης = συγγένεια). Cf. 97*6—11 n.
CHAPTER 33
Ofinion
88>30. Knowledge differs from opinion in that knowledge is
universal and reached by necessary, i.e. non-contingent, premisses.
There are things that are true but contingent. Our state of mind
with regard to them is (1) not knowledge; for then what is con-
tingent would be necessary ; nor (2) intuition (which is the start-
ing-point of knowledge) or undemonstrated knowledge (which is
apprehension of an immediate proposition). But the states of
mind capable of being true are intuition, knowledge, and opinion ;
so it must be opinion that is concerned with what is true or false,
but contingent.
89°3. Opinion is the judging of an unmediated and non-
necessary proposition. This agrees with the observed facts; for
both opinion and the contingent are insecure. Besides, a man
thinks he has opinion, not when he thinks the fact is necessary—
he then thinks he knows—but when he thinks it might be other-
wise.
xx. How then is it possible to have opinion and knowledge of
the same thing? And if one maintains that anything that is
known could be opined, will not that identify opinion and know-
ledge? A man who knows and one who opines will be able to
keep pace with each other through the chain of middle terms till
they reach immediate premisses, so that if the first knows, so
does the second ; for one may opine a reason as well as a fact.
16. We answer that if a man accepts non-contingent proposi-
tions as he does the definitions from which demonstration pro-
ceeds, he will be not opining but knowing ; but if he thinks the
propositions are true but not in consequence of the very nature
of the subject, he will have opinion and not genuine knowledge—
both of the fact and of the reason, if his opinion is based on the
immediate premisses ; otherwise, only of the fact.
23. There cannot be opinion and knowledge of what is com-
pletely the same; but as there can be false and true opinion of
what is in a sense the same, so there can be knowledge and opinion.
606 COMMENTARY
To maintain that true and false opinion have strictly the same
object involves, among other paradoxical consequences, that one
does not opine what one opines falsely. But since ‘the same’ is
ambiguous, it is possible to opine truly and falsely what is in one
sense the same, but not what is so in another sense. It is impos-
sible to opine truly that the diagonal of a square is commen-
surate with the side; the diagonal, which is the subject of both
opinions, is the same, but the essential nature ascribed to the
subjects in the two cases is not the same.
33. So too with knowledge and opinion. If the judgement be
‘man is an animal’, knowledge is of ‘animal’ as a predicate that
cannot fail to belong to the subject, opinion is of it as a predicate
that need not belong; or we may say that knowledge is of man
in his essential nature, opinion is of man but not of his essential
nature. The object is the same because it is in both cases man,
but the mode in which it is regarded is not the same.
38. It is evident from this that it is impossible to opine and
know the same thing at the same time; for that would imply
judging that the fact might be otherwise, and that it could not.
In different persons there may be knowledge and opinion of the
same thing in the sense just described, but in the same person
this cannot happen even in that sense; for then he would be
judging at the same time, for example, that man is essentially an
animal and that he is not.
bg, The question how the remaining functions should be as-
signed to understanding, intuitive reason, science, art, practical
wisdom, and philosophical knowledge belongs, rather, in part to
physics and in part to ethics.
88>35-7. ἀλλα piv... προτάσεως. Though the phrase ém-
στήμη ἀποδεικτική is common in A., the phrase which is implied
as its opposite, ἐπιστήμη ἀναπόδεικτος, occurs only here and in
12?19-2o0. Where ἐπιστήμη is used without qualification it means
demonstrative knowledge; with the qualification ἀναπόδεικτος it
means mental activity which shares with demonstrative know-
ledge the characteristics of possessing subjective certainty and
grasping necessary truth, but differs from it in being immediate,
not ratiocinative. Now this is exactly the character which A.
constantly ascribes to νοῦς, and which the identification of νοῦς
with the ἀρχὴ ἐπιστήμης (b36) implies νοῦς to possess. Finally, in
8931 ἐπιστήμη ἀναπόδεικτος does not appear alongside of νοῦς,
ἐπιστήμη (i.e. ἐπιστήμη ἀποδεικτική), and δόξα. It must therefore
be mentioned here not as anything distinct from νοῦς but as
I. 33. 88535 — 89332 607
another name for it; and I have altered the punctuation accord-
ingly. Just as καί in an affirmative statement can have explicandi
magis quam copulandi vim (Bonitz, Index, 357513-20), so can οὐδέ
in a negative sentence.
89*3-4. τοῦτο δ᾽... ἀναγκαίας. ἐπιστήμη ἀναπόδεικτος has
been defined as ὑπόληψις τῆς ἀμέσου προτάσεως, i.e. of a premiss
which is unmediable because its predicate belongs directly and
necessarily to its subject. δόξα is ὑπόληψις τῆς ἀμέσου προτάσεως
καὶ μὴ ἀναγκαίας, i.e. of a premiss which is ἄμεσος for another
reason, viz. that (whether it has been reached by incorrect reason-
ing or without reasoning; for opinion may occur in either case),
it has not been mediated, i.e. derived by correct reasoning from
necessary premisses.
17-18. ὥσπερ [ἔχει] τοὺς ὁρισμούς. Neither ἔχει, the reading
of the best MSS., nor ἔχειν, which is adopted by Bekker and
Waitz, gives a tolerable sense, and I have treated the word as an
intruder from the previous line.
25-8. καὶ yàp . . . ψευδῶς. The view referred to is the sceptical
view discussed in Met. I' which denies the law of contradiction.
In holding that a single thing B can both have a certain attribute
A and not have it, such thinkers imply that there can be both
a true and a false opinion that B is A (or that B is not A). This
was not the doctrine of a single school; it was rather a view of
which A. found traces in many of his predecessors—Heraclitus
(Met. 1012424, 34) and his school (1o1o*10), Empedocles (100915),
Anaxagoras (1009327, 525), Democritus (1009227, Pr1, 15), Prota-
goras (1009%6).
Besides the many paradoxical consequences which A. shows in
the Metaphysics to follow from this view, there is (he here says)
the self-contradictory consequence that what a man opines
falsely he does not opine at all. This consequence arises in the
following way: if the object of true and of false opinion is (as
these thinkers allege) the same, anyone who entertains this object
must be thinking truly; so that if a man be supposed to be
thinking falsely, it turns out that he cannot really be thinking
what he was supposed to be thinking falsely.
29-32. τὸ μὲν γὰρ... αὐτό. There cannot be a true opinion
that the diagonal of a square is commensurate with the side.
There can indeed be a true opinion that the diagonal is not
commensurate, and a false opinion that it is commensurate, and
these opinions are 'of the same thing' in so far as they are both
about the diagonal. But the essential nature (as it would be
stated in a definition) ascribed to the subject is different in the
608 COMMENTARY
two cases; not that ‘commensurate’ or ‘not commensurate’ is
included in the definition, but that since properties follow from
essence, it would only be by having a different essence that the
diagonal, which is in fact not commensurate, could be com-
mensurate.
33-7- ὁμοίως δὲ... αὐτό. A. has pointed out that a true and
a false judgement with the same subject and the same predicate
must differ in quality. He now insists that knowledge and opinion
about the same subject and the same predicate differ in modality.
He takes as his example the statement ‘man is an animal’ (cf.
b4). The knowledge that man is an animal is ‘of animal’, but of
it as a predicate that cannot fail to belong to man; the opinion
that man is an animal is also ‘of animal’ but of it as a predicate
that belongs, but need not belong, to man. Or, to put the matter
with reference to the subject, the one is 'of what man essentially
is’, the other is ‘of man’, but not ‘of what man essentially is’.
For the phrase ἡ μὲν ὅπερ ἀνθρώπου ἐστίν, strict grammar would
require ἡ μὲν τούτου ἐστὶν ὅπερ ἄνθρωπός ἐστιν. But ὅπερ ἄνθρωπος
has through constant usage almost coalesced into one word, so
that the genitive inflection can come at the end. Cf. Met. 1007422,
23, 28 ὅπερ ἀνθρώπῳ εἶναι.
b2-3. ἐν ἄλλῳ . . . οἷόν τε. Two people can respectively know
and opine what is the same proposition in the sense explained
in #33-7 (there should be no comma before ὡς εἴρηται in 2) ; i.e.
two propositions with the same subject and predicate but different
modalities ; one person cannot at one time know and opine what
is the same proposition even in this sense, still less a strictly self-
identical proposition.
7-9. Ta δὲ λοιπὰ . . . ἐστιν. A. has in this chapter considered
the difference between knowledge and opinion, because know-
ledge (i.e. demonstrative knowledge) is the subject of the Posterior
Analytics. But a full discussion of how the operations of thought
are to be assigned respectively to διάνοια (discursive thought)
and its species—émor7jun (knowledge pursued for its own sake),
τέχνη (knowledge applied to production), and φρόνησις (knowledge
applied to conduct)—and to νοῦς (intuitive reason) and σοφία
(metaphysical thought, the combination of νοῦς and ἐπιστήμη),
is a matter for the sciences that study the mind itself—psy-
chology (here included under physical science) and ethics. νοῦς
is in fact discussed in De An. iii. 4-7 and in E.N. vi. 6, ἐπιστήμη
in E.N. vi. 3, τέχνη ib. 4, φρόνησις ib. 5, σοφία ib. 7.
I. 33. 89733 —>g 609
CHAPTER 34
Quick wit
89»1o. Quick wit is a power of hitting the middle term in an
imperceptible time; e.g., if one sees that the moon always has
its bright side towards the sun, and quickly grasps the reason,
viz. that it gets its light from the sun ; or recognizes that someone
is talking to a rich man because he is borrowing from him; or
why two men are friends, viz. because they have a common
enemy. On seeing the extremes one has recognized all the middle
terms.
BOOK II
CHAPTER 1
There are four types of inquiry
89523. The objects of inquiry are just as many as the objects
of knowledge; they are (1) the that, (2) the why, (3) whether the
thing exists, (4) what it is. The question whether a thing is this
or that (e.g. whether the sun does or does not suffer eclipse)
comes under (i), as is shown by the facts that we cease from
inquiring when we find that the sun does suffer eclipse, and do not
begin to inquire if we already know that it does. When we know
(1) the that, we seek (2) the why.
31. Sometimes, on the other hand, we ask (3) whether the
thing (e.g. a centaur, or a god) is, simply, not is thus or thus
qualified, and when we know that it is, inquire (4) what it is.
In the first Book A. has considered demonstration both as
proving the existence of certain facts and as giving the reason
for them. In the second Book he is:to consider demonstration as
leading up to definition. By way of connecting the subjects of
the two Books, he now starts with an enumeration of all possible
subjects of inquiry, naming first the two that have been con-
sidered in the first Book—the question ‘why’ and the preliminary
question of the ‘that’—and going on to the two to be considered
in the second Book, the question what a certain thing is, with the
preliminary question whether the thing exists.
It is probable that A. meant primarily by the four phrases τὸ
ὅτι, τὸ διότι, εἰ ἔστι, τί ἐστι the following four questions: (1)
whether a certain subject has a certain attribute, (2) why it has
1985 RI
610 COMMENTARY
it, (3) whether a certain subject exists, (4) what it is: and the
examples given in this chapter conform to these distinctions.
The typical example of (1) is ‘whether the sun suffers eclipse’,
of (2) ‘why it does’, of (3) ‘whether a god exists’, of (4) ‘what
a god is’, But the phrases ὅτι ἔστι and εἰ ἔστι do not in themselves
suggest the distinction between the possession of an attribute by
a subject and the existence of a subject, and the phrase τί ἔστι does
not suggest that only the definition of a subject is in question.
Naturally enough, then, the distinctions become blurred in the
next chapter. In 89538-9o*5 the distinction formerly conveyed by
the phrases ὅτι ἔστιν and εἰ ἔστιν is conveyed by the phrases εἰ
ἔστιν ἐπὶ μέρους (= ef ἐστι τί, 9033), whether a subject is qualified
in this or that particular way, i.e. whether it has a certain
attribute) and εἰ ἔστιν ἁπλῶς (whether a certain subject exists at
all). Further, even εἰ ἔστιν ἁπλῶς comes to be used so widely in
90?4-5 as to include the inquiry whether night, which is surely
an attribute rather than a subject (ie. a substance), exists.
Again, the question τί ἐστι, which was originally limited to the
problem of defining subjects, is extended to include the problem
of defining such an attribute as eclipse (9o*15). It has always to
be remembered that A. is making his vocabulary as he goes, and
has not succeeded in making it as clear-cut as might be wished.
8925. eis ἀριθμὸν θέντες. This curious phrase should probably
be taken (as it is by P., E., Zabarella, and Pacius) to mean 'intro-
ducing a plurality of terms', i.e. ascribing a particular attribute
to the subject, as against a proposition which says that a certain
subject exists. Waitz takes the phrase to mean 'stating more than
one possibility'. But that is not part of the essence of the inquiry
as to the ore.
CHAPTER 2
They are all concerned with a middle term
89536. When we inquire whether a thing is thus or thus
qualified, or whether a thing exists, we are asking whether there
is a middle term; when we know that a thing is thus or thus
qualified, or that a thing exists, i.e. the answer to the particular
or to the general question, and go on to ask why it is thus or
thus qualified, or what it is, we are asking what the middle term
is. By the 'that' or particular question I mean a question like
‘does the moon suffer eclipse?’, i.e. ‘is it qualified in a particular
way?'; by the general question a question like ‘does the moon
exist ?' or ‘does night exist?’
90*s. Thus in all inquiries we are asking whether there is
il. r. 89525 611
a middle term, or what it is; for the cause is the middle term, and
we are always seeking the cause. ‘Does the moon suffer eclipse?’
means ‘Is there a cause of this?’ If we know there is, we ask
what itis. For the cause of the existence of a thing's substantial
nature, or of an intrinsic or incidental property of it, is the
middle term.
14. In all such cases the what and the why are the same. What
is eclipse? Privation of light from the moon by the interposition
of the earth. Why does eclipse happen? Because the light fails
when the earth is interposed. What is harmony? An arithmetical
ratio between a high and a low note. Why does the high note
harmonize with the low? Because the ratio between them is
expressible in numbers.
24. That our search is for the middle term is shown by cases
in which the middle term is perceptible. If we have not perceived
it we inquire whether the fact (e.g. eclipse) exists; if we were
on the moon, we should not have inquired either whether or why
eclipse exists; it would have been at once obvious. For from
perceiving the particular facts, that the earth was interposed and
that the moon was eclipsed, one would have grasped the universal
connexion.
31. Thus to know the what is the same as knowing the why,
i.e. why a thing exists, or why it has a certain attribute.
There are two perplexing statements in this chapter. One is
the statement that when we are asking whether a certain con-
nexion of subject and attribute exists (τὸ ὅτι) or whether a certain
thing exists (εἰ ἔστι), we are inquiring whether there is a μέσον,
and that this inquiry precedes the inquiry what the μέσον is
(8937-901). The other is the statement that in all four of the
inquiries enumerated in 8924-5 we are asking either whether
there is a μέσον or what it is (9075-6). By μέσον A. means not any
and every term that might serve to establish a conclusion (as
a symptom may establish the existence of that of which it is
a symptom), but the actual ground in reality of the fact to be
explained (9036-7). His meaning therefore must be that, since
everything that exists must have a cause, to inquire whether
a certain connexion of subject and attribute, or a certain thing,
exists is implicitly to inquire whether something that is its cause
exists. This is intelligible enough when the inquiry is whether,
or why, a certain complex of subject and attribute, or of subject
and event, exists (ὅτε ἔστι or διὰ τί ἔστι). It is also intelligible
when the inquiry is whether a certain attribute (or event) exists
612 COMMENTARY
(εἰ ἔστι applied to an attribute or event) or what it is (τί ἐστι
applied to an attribute or event). For since an attribute can
exist only in a subject, εἰ ἔστε here reduces itself to ὅτι ἔστι,
and A. holds that τί ἐστι reduces itself to διὰ τί ἔστι, i.e. that the
proper definition of an attribute is a causal definition explaining
why the attribute inheres in its subject. But how can ed ἔστι or
τί ἐστι applied to a substance be supposed to be concerned with
a middle term? A substance does not inhere in anything; there
are no two terms between which a middle term is to be found.
A. gives no example of what he means by the μέσον in such a
case, and in this chapter the application of the questions εἰ ἔστι
and τί ἐστι to substances is overshadowed by its application to
attributes and events, which is amply illustrated (90*15—23). He
does not seem to have thought out the implications of his view
where it is the εἰ ἔστι or the τί ἐστι of a substance that is in ques-
tion, and the only clue we have to his meaning is his statement
that by μέσον he means αἴτιον. As regards the εἰ ἔστι of substances,
then, he will be saying that since they, no less than attributes,
must have a sufficient ground of their being, to inquire whether
a certain substance exists is by implication to inquire whether
something that is its cause exists. As regards the ri ἐστι of sub-
stances he will be saying that to inquire what a certain substance
is, is to inquire what its cause is; i.e. that its definition, no less
than that of an attribute, should be causal, that a substance
should be defined by reference either to a final or to an efficient
cause. This is the doctrine laid down in Met. xo41226—xai διά
τί ταδί, otov πλίνθοι καὶ λίθοι, οἰκία ἐστίν ; φανερὸν τοίνυν ὅτι ζητεῖ τὸ
αἴτιον: τοῦτο δ᾽ ἐστὶ τὸ τί ἦν εἶναι, ὡς εἰπεῖν λογικῶς, ὃ ἐπ᾽ ἐνίων μέν
ἐστι τίνος ἕνεκα, οἷον ἴσως ἐπ᾽ οἰκίας ἢ κλίνης, ἐπ᾽ ἐνίων δὲ τί ἐκίνησε
πρῶτον: αἴτιον γὰρ καὶ todro- (cf. 1041>4-g, 1043*14-21). But it
cannot be said that A. remains faithful to this view ; the definitions
he offers of substances far more often proceed per genus et differen-
tiam without any mention of a caüse.
The general upshot is that the questions εἰ ἔστι and ri ἐστι,
which in ch. x referred to substances, have in ch. 2 come to refer
so much more to attributes and events that the former reference
has almost receded from A.’s mind, though traces of it still
remain.
89539. ἢ τὸ ὅτι... ἁπλῶς. τὸ ἐπὶ μέρους further characterizes
τὸ ὅτι, making it plain that this refers to the question whether
a certain subject has a certain particular attribute (e.g. whether
the moon suffers eclipse, 9033). τὸ ἁπλῶς further characterizes
τὸ εἰ ἔστιν, indicating that this refers to the question whether
II. 2. 89539 — 90*33 613
a certain subject (e.g. the moon, *s) or a certain attribute (e.g. the
deprivation of light which we call night, ib.) exists at all.
90*3-4. εἰ yap . . . ri, ‘whether the subject has or has not some
particular attribute'.
5. ἢ νύξ. The mention of night here, where we should expect
only substances to be in A.’s mind, is surprising, but the words
are sufficiently vouched for by P. 338. 13 and E. 2o. 11-18. Cf.
the introductory n. on ch. 1.
10. ἢ τοῦ μὴ ἁπλῶς. Both sense and grammar require us to
read τοῦ for the τό of the MSS., as Bonitz points out in Ar.
Stud. iv. 28 n.
II. ἢ κατὰ συμβεβηκός. This can hardly refer to pure acci-
dents, for with these A. holds that science has nothing to do.
Zabarella is probably right in thinking that the reference is to
attributes which result from the operation of one thing on another,
while τῶν καθ᾽ αὑτό refers to attributes springing simply from the
essential nature of the thing that has them.
13-14. τὸ δὲ τὶ... μή. ἔκλειψιν, an attribute of moon or sun;
ἰσότητα ἀνισότητα, alternative attributes of a pair of triangles;
ἐν μέσῳ ἢ μή, being in the centre of the universe or not (the ques-
tion discussed in De Caelo 293*15-15), alternative attributes one
of which must belong to the earth.
18-23. ri ἐστι... λόγος; The Pythagoreans had discovered
the dependence of consonance on the ratios between the lengths of
vibrating strings—that of the octave on the ratio 1: 2, of the fifth
on the ratio 2: 3, of the fourth on the ratio 3: 4; see Zeller-Mondolfo,
il. 454-5.
29-30. καὶ yàp . . . ἐγένετο, ‘and so, since it would have been
also clear that the moon is now in eclipse, the universal rule would
have become clear from the particular fact’. The ydp clause is
anticipatory ; cf. Denniston, Greek Particles, 69—70.
33. ὅτι δύο ὀρθαί, that the subject (the triangle, cf. #13) has
angles equal to two right angles.
CHAPTER 3
There is nothing that can be both demonstrated and defined
go*35. We must now discuss how a definition is proved, and
how reduced to demonstration, what definition is and what things
are definable. First we state some difficulties. It may be asked
whether it is possible to know the same thing, in the same respect,
by definition and by demonstration.
b3,. (A) <Not everything that can be demonstrated can be
614 COMMENTARY
defined.) (1) Definition is of the what, and the what is universal
and affirmative; but some syllogisms are negative and some are
particular.
4. (2) Not even all affirmative facts proved in the first figure
are objects of definition. The reason for this discrepancy is that
to know a demonstrable fact is to have a demonstration of it,
so that if demonstration of such facts is possible, there cannot be
also definition of them, since if there were, one could know the
fact by having the definition, without the demonstration.
13. (3) The point may be made by induction. We have never
come to recognize the existence of a property, whether intrinsic or
incidental, by defining it.
16. (4) Definition is the making known of an essence, but
such things are not essences.
18. (B) Can everything that can be defined be demonstrated?
(x) We may argue as before, that to know something that is
demonstrable is to have demonstration of it; but if everything
that is definable were demonstrable, we should by defining it
know it without demonstrating it.
24. (2) Thestarting-points of demonstration are definitions, and
there cannot be demonstration of the starting-points of demonstra-
tion; either there will be an infinite regress of starting-points or
the starting-points are definitions that are indemonstrable.
28. (C) Can some things be both defined and demonstrated?
No, for (1) definition is of essence ; but the demonstrative sciences
assume the essence of their objects.
43. (2) Every demonstration proves something of something,
but in definition one thing is not predicated of another— neither
genus of differentia nor vice versa.
38. (3) What a thing is, and that a connexion of subject and
attribute exists, are different things; and different things demand
different demonstrations, unless one demonstration is a part of
the other (as the fact that the isosceles triangle has angles equal
to two right angles is part of the fact that every triangle has
this property); but these two things are not part and whole.
91?7. Thus not everything that is definable is demonstrable,
nor vice versa ; nor is anything at all both definable and demon-
strable. Thus definition and demonstration are not the same,
nor is one a part of the other ; for if they were, their objects would
be similarly related.
90°37. διαπορήσαντες πρῶτον περὶ αὑτῶν. The fact that the
chapter (as also chs. 4-7) is aporematic implies that it is dialecti-
II. 3. 902337 — 9139 615
cal, using sometimes arguments that A. could not have thought
really convincing.
br. οἰκειοτάτη τῶν ἐχομένων λόγων, ‘most appropriate to the
discussions that are to follow’, not ‘to those that have preceded’.
For the meaning cf. Bonitz, Index, 306*48—58.
7-17. εἶτα οὐδὲ... οὐσίαι. A.’s point here is that while
demonstration is of facts such as that every triangle has its angles
equal to two right angles, or in general that a certain subject has
a certain property, definition is of the essence of a subject. In
bi4—16 it is assumed that both rà καθ᾽ αὑτὸ ὑπάρχοντα and τὰ
συμβεβηκότα are objects of demonstration, so that the distinction
is not between properties and accidents, but (as in *r1) between
properties following simply from the essential nature of their
subject and those that follow upon interaction between the subject
and something else; for accidents cannot be demonstrated.
10. τὸ ἀποδεικτόν, though rather poorly supported by MSS.
here, is confirmed by 21 and is undoubtedly the right reading.
16. τά γε τοιαῦτα, i.e. τὰ καθ᾽ αὑτὸ ὑπάρχοντα καὶ τὰ συμβεβη-
κότα, such as that the angles οὗ a triangle are equal to two right
angles (58-9).
19. ti Sai; I have accepted B's reading, as being more likely
to have been corrupted than τί δ᾽. For τί δαί cf. Denniston, Greek
Particles, 262-4. The colloquial phrase is particularly appropriate
in a dialectical passage like the present one.
25. δέδεικται πρότερον, in 72518-25 and 84229-2.
34-8. ἐν δὲ τῷ ὁρισμῷ... ἐπίπεδον. A. takes ὁρισμός here as
being not a sentence such as ἄνθρωπός ἐστι ζῷον δίπουν, but simply
a phrase such as ζῷον δίπουν, put forward as the equivalent of
ἄνθρωπος. In such a phrase the elements are not related by way
of assertion or denial, but by way of qualification or restriction
of the genus by the addition of the differentia.
91*8-9. οὔτε ὅλως... ἔχειν. The MSS. have wove for οὔτε.
But (1) we can hardly imagine A. to reason so badly as to say
‘(a) not everything that is definable is demonstrable, (b) not
everything that is demonstrable is definable, therefore (c) nothing
is both definable and demonstrable'. And (2) in the course of the
chapter (b), (a), and (c) have been proved separately in 9053-19,
19-27, 28-91*6, (c) not being deduced from (a) and (b). Therefore
we must read οὔτε, which Pacius already read. Whether he had
any authority for the reading we do not know. Hayduck's
grounds for suspecting the whole sentence (Obs. Crit. im aliquot
locos Árist. 14—15) are insufficient.
616 COMMENTARY
CHAPTER 4
It cannot be demonstrated that a certain phrase is the definition
of a certain term
g1*12. We must now reconsider the question whether definition
can be demonstrated. Syllogism proves one term true of another
by means of a middle term; now a definition states what is both
(1) peculiar and (2) essential to that whose definition it is. But
then (1) the three terms must be reciprocally predicable of each
other. For if A is peculiar to C, A must be peculiar to B, and
B toC.
18. And (2) if A is essential to the whole of B, and B to the
whole of C, A must be essential to C ; but unless we make both
assumptions the conclusion will not follow; i.e. if A is essential
to B but B is not essential to everything of which it is predicated.
Therefore both premisses must express the essence of their subjects.
And so the essence of the subject will be expressed in the middle
term before it is expressed in the definition we are trying to prove.
26. In general, if we want to prove what man is, let C be man,
and A the proposed definition. If a conclusion is to follow, A
must be predicated of the whole of a middle term B, which will
itself express the essence of man, so that one is assuming what
one ought to prove.
33. We must concentrate our attention on the two premisses,
and on direct connexions at that ; for that is what best brings out
our point. Those who prove a definition by reliance on the
convertibility of two terms beg the question. If one claims that
soul is that which is the cause of its own life, and that this is a
self-moving number, one is necessarily begging the question in
saying that the soul is essentially a self-moving number, in the
sense of being identical with this.
br. For if A is a consequent of B and B of C, it does not follow
that A is the essence of C (it may only be true of C) ; nor does this
follow if A is that of which B is a species, and is predicated of
all B. Every instance of being a man is an instance of being an
animal, as every man is an animal; but not so as to be identical
with it. Unless one takes both the premisses as stating the
essence of their subjects, one cannot infer that the major term is
the essence of the minor; but if one does take them so, one has
already assumed what the definition of C is.
g1°12. Ταῦτα μὲν οὖν... διηπορήσθω. This does not mean
that A. has come to the end of the aporematic part of his dis-
II. 4. 913212-31 617
cussion of definition ; his positive treatment of the question begins
with ch. 8. What he says is ‘so much for éhese doubts’ ; there are
more to come, in chs. 4-7.
13-14. καθάπερ viv . . . ὑπέθετο, i.e. in ch. 3.
16. ταῦτα δ᾽ ἀνάγκη ἀντιστρέφειν, ‘terms so related must be
reciprocally predicable’. The phrase is rather vague, but A.’s
meaning is made clear by the reason given for the statement,
which follows in 716-18: ‘Since the definitory formula is to be
proved to be peculiar to the term defined, all three terms used
in the syllogism must be coextensive. For, definition being a
universal affirmative statement, the proof of it must be in
Barbara: All B is A, All C is B, Therefore all C is 4. Now if B
were wider than the extreme terms, which are ex hypothest
coextensive, the major premiss would be untrue; and if it were
narrower than they are, the minor would be untrue. Therefore
it must be equal in extent to them.’
23. μὴ καθ᾽ ὅσων... ἐστιν, ‘but B is not included in the
essence of everything to which it belongs'. The phrase would be
easier if we supposed a second τὸ B, after the comma, to have
fallen out.
24-5. ἔσται ἄρα... ἐστιν. The comma read by the editors
after τοῦ Γ must be removed.
26. ἐπὶ τοῦ μέσου... εἶναι. ἐπί, because it is a£ the stage
represented by the middle term (ie. by the premiss which
predicates this of the minor) that we first find the τί ἐστι (of the
minor), before we reach the conclusion.
30-1. τοῦτο δ᾽... ἄνθρωπος. The reading is doubtful. All the
external evidence is in favour of rovrov, and τούτου would natur-
ally refer to B ; then the words would mean ‘and there will be
another definitory formula intermediate between C and B' (as
B is, between C and A), 'and this new formula too will state the
essence of C (man). Le. A.’s argument will be intended to
show that an infinite regress is involved in the attempt to prove
a definition. Then in ?33-5 A. would go on to say ‘but we should
study the matter in the case where there are but two premisses,
and no prosyllogism'. But there are difficulties in this interpreta-
tion. (a) A. does not, on this interpretation, show that the
original middle term B must be a definition of C, which would be
the proper preliminary to showing that the new middle term
(say, D) must be a definition of C. (b) He gives no reason why 'C
is B' must be supported by a prosyllogism. (c) He uses none of
the phrases by which he usually points to an infinite regress (e.g.
eis τὸ ἄπειρον βαδιεῖται). He simply says that the proposed proof
618 COMMENTARY
begs the question, and he points not to D and the further terms
of an infinite series in justification of the charge, but simply says
(4331-2) that in assuming All C is B (ie. is definable as B) the
person who is trying to prove the definition of C as A is assuming
the correctness of another definition of C.
It seems probable, then, that there is no reference to an infinite
regress. In that case, τούτου must refer to A, and the meaning
must be ‘and there will be another definitory formula than A
intermediate between C and A (i.e. B), and this will state the
essence of man’. But, κατὰ τοῦ B being the emphatic words in
the previous clause, it is practically certain that τούτου would
necessarily refer to B and not to A. This being so, it is better to
adopt Bonitz's conjecture roóro (Arist. Stud. iv. 23), which is
read by one of the best MSS. of Anonymus.
31-2. kai yàp τὸ B... ἄνθρωπος. Bonitz (Arist. Stud. iv. 23)
is almost certainly right in reading ἔσται for ἐστὶ; cf. 324, 26, 30, 59.
37-1. οἷον εἴ rs . . . ὄν. The definition of soul as ἀριθμὸς
αὐτὸς αὑτὸν κινῶν was put forward by Xenocrates (Plut. Mor.
ror2 D). A. refers to it in De An. 404529, 408532, without naming
its author.
53. ἀλλ᾽ ἀληθὲς... μόνον. If we keep the reading of most of
the MSS. (ἀλλ᾽ ἀληθὲς ἦν εἰπεῖν ἔσται μόνον), we must put ἔσται
in inverted commas and interpret the clause as meaning ἀλλ᾽
ἀληθὲς ἦν εἰπεῖν ‘€orat τῷ Γ τὸ A’ μόνον, ‘it was only true to predi-
cate A of C', not to assume their identity. But n (confirmed by
E. 62. 25 ἀλλα μόνον ἔσται αὐτοῦ ἀληθῶς κατηγορούμενον) gives what
is probably the right reading. Of the emendations Mure’s ap-
pears to be the best.
9-10. πρότερον ἔσται... Β. The grammar of the sentence
is best corrected by treating 76 B as a (correct) gloss.
CHAPTER 5
It cannot be shown by division that a certain phrase is the
definition of a certain term
gt>1z. Nor does the method of definition by division syllogize.
The conclusion nowhere follows from the premisses, any more than
does that of an induction. For (1) we must not put the conclusion
as a question nor must it arise by mere concession ; it must arise
from the premisses, even if the respondent does not admit it.
Is man an animal or a lifeless thing? The definer assumes that
man is an animal; he has not proved it. Again, every animal is
II. 4. 91431 — 5. 91524 619
either terrestrial or aquatic; he assumes that man is terrestrial.
(2) He assumes that man is the whole thus produced, terrestrial
animal; it makes no difference whether the stages be many or
few. (Indeed, those who use the method do not prove by
syllogism even what might be proved.) For the whole formula
proposed may be true of man but not indicate his essence. (3)
There is no guarantee against adding or omitting something or
passing over some element in the being of the thing defined.
28. These defects are disregarded; but they may be obviated
by taking none but elements in the essence, maintaining con-
secutiveness in division, and omitting nothing. This result is
necessarily secured if nothing is omitted in the division ; for then
we reach without more ado a class needing no further division.
32. But there is no syllogism in this; if this process gives
knowledge, it gives it in another way, just as induction does.
For as, in the case of conclusions reached without the middle
terms, if the reasoner says 'this being so, this follows', one can
ask ‘why?’, so too here we can say ‘why?’ at the addition of
each fresh determinant. The definer can say, and (as he thinks)
show by his division, that every animal is 'either mortal or
immortal’. But this whole phrase is not a definition, and even
if it were proved by the process of division, definition is still not
a conclusion of syllogism.
gr>12-13. ᾿Αλλὰ μὴν... εἴρηται. The Platonic method of
definition by division (illustrated in the SofAstes and Politicus)
has already been discussed 'in that part of our analysis of argu-
ment which concerns the figures of syllogism’, ie. in An. Pr.
i.31. The value of division as a preliminary to definition is brought
out in 9627-976.
16. οὐδὲ τῷ δοῦναι elvai, ‘nor must it depend on the respon-
dent’s conceding it’.
18. εἶτ᾽ ἔλαβε ζῷον, i.e. then, when the respondent answers
‘animal’, the questioner assumes that man is an animal.
20-1. καὶ τὸ εἶναι... τοῦτο. Bekker’s and Waitz’s comma be-
fore τὸ ὅλον is better away ; τὸ ὅλον is the whole formed by ζῷον
πεζόν (cf. τὸ πᾶν, 525). The point made here is a fresh one (made
more clearly in 524-6). Even if the assumption that man is an
animal and is two-footed is true, what guarantee have we that
man is just this complex, ‘two-footed animal’, Le. that this is
his essence?
23-4. ἀσυλλόγιστος μὲν οὖν... συλλογισθῆναι. The process
of division is liable not only to assume that the subject has
620 COMMENTARY
attributes that it cannot be proved to have, but also to assume
that it has attributes that it could be proved to have.
μὲν οὖν ‘nay rather’, introducing a stronger point against the
method A. is criticizing than that introduced before. 'The
speaker objects to his own words, virtually carrying on a dialogue
with himself’ (Denniston, The Greek Particles, 478).
26. μὴ μέντοι. . . δηλοῦν, ‘the definitory formula may not
succeed in showing what the thing is, or what it was to be the
thing’; no real distinction is meant to be drawn between the two
phrases.
26-7. ἔτι τί κωλύει... οὐσίας ; The process of division may (r)
introduce attributes that are properties or accidents of the subject,
not part of its essence. It may (2) fail to state the final differentia
of the subject. Or (3) it may pass over an intermediate differentia.
E.g. substance is divisible into animate and inanimate, and
animate substance into rational and irrational. If then we define
man as rational substance, we shall have omitted an intermediate
differentia.
30. αἰτούμενον τὸ πρῶτον, ‘postulating the next differentia at
each stage’.
30-2. τοῦτο δ᾽... εἶναι. Waitz omits εἰ... ἐλλείπει (as well
as the second τοῦτο δ᾽ dvayxaiov), on the ground that these words
are a mere repetition of the previous sentence; but there seems
to be just enough of novelty in the clause to make it not pointless.
On the other hand, the repetition of τοῦτο δ᾽ ἀναγκαῖον is highly
suspicious; it may so easily have arisen from the words having
been first omitted, then inserted in the margin, and then drawn
into the text at two different points. Besides, they would have
to mean two quite different things. The first τοῦτο δ᾽ ἀναγκαῖον
would mean 'and this result is necessarily achieved', the second
‘and this condition must be fulfilled’. The second τοῦτο δ᾽
ἀναγκαῖον might be saved if we read (with A and d) τοῦτο δ᾽
ἀναγκαῖον ἄτομον ἤδη εἶναι, ‘and the result so produced must
necessarily be a formula needing no further differentiation'. But
the balance of probability is in favour of the reading I have
adopted.
32. ἄτομον yàp ἤδη Set εἶναι. The sense would not be seriously
altered if we adopted B's original reading εἴδει (for ἤδη); but the
idiomatic ἤδη is rather the more likely. ἄτομον must be taken in
a special sense. The correct definitory formula will not be indi-
visible, unless the term to be defined happens to be an tnfima
species; but it will be unsuitable for further division, since a
further division would only yield too narrow a formula.
II. 5. gtb26— 9234 621
92*3-4. ὁ δὲ τοιοῦτος. . . ὁρισμός. Bonitz's conjecture of
συλλογισμός for ὁρισμός (Arist. Stud. iv. 27) gives a good sense, but
does not seem to be required, and has no support in the MS.
evidence.
CHAPTER 6
Attempts to prove the definition of a term by assuming the definition
either of definition or of the contrary term beg the question
9276. Is it possible to demonstrate the definition on the basis
of an hypothesis, assuming that the definition is the complex
composed of the elements in the essence and peculiar to the
subject, and going on to say ‘these are the only elements in
the essence, and the complex composed by them is peculiar to
the subject’? For then it seems to follow that this is the essence
of the subject.
9. No; for (1) here again the essence has been assumed, since
proof must be through a middle term. (2) As we do not in a
syllogism assume as a premiss the definition of syllogism (since
the premisses must be related as whole and part), so the definition
of definition must not be assumed in the syllogism which is to
prove a definition. These assumptions must lie outside the pre-
misses. To anyone who doubts whether we have effected a
syllogism we must say ‘yes, that is what a syllogism is’; and to
anyone who says we have not proved a definition we must say
'yes; that is what definition meant'. Hence we must have
already syllogized without including in our premisses a definition
of syllogism er of definition.
20. Again, suppose that one reasons from a hypothesis. E.g.
‘To be evil is to be divisible; for a thing to be contrary is to be
contrary toits contrary ; good is contrary to evil, and the indivisible
tothedivisible. Therefore to be good is to be indivisible.' Here too
one assumes the essence in trying to prove it. 'But not the same
essence', you say. Granted, but that does not remove the objec-
tion. No doubt in demonstration, too, we assume one thing to
be predicable of another thing, but the term we assume to be true
of the minor is not the major, nor identical in definition and
correlative to it.
27. Both to one who tries to prove a definition by division and
to one who reasons in the way just described, we put the same
difficulty : Why should man be 'two-footed terrestrial animal’ and
not animal avd terrestrial and two-footed? The premisses do not
show that the formula is a unity ; the characteristics might simply
622 COMMENTARY
belong to the same subject just as the same man may be musical
and grammatical.
92*6-9. "AAA’ ápa . . . ἐκείνῳ. In this proposed proof of a
definition the assumption is first laid down, as a major premiss,
that the definition of a given subject must (1) be composed of
the elements in its essence, and (2) be peculiar to the subject.
It is then stated, as a minor premiss, that (1) such-and-such
characteristics alone are elements in the essence, and (2) the whole
so constituted is peculiar to the subject. Then it is inferred that
the whole in question is the definition of the subject. (The method
of proof is that which A. himself puts forward in Top. 15337—22
as the method of proving a definition ; and that which he criticizes
in 420-33 is that which he puts forward in 153324- 24; Maier
(2 b. 78 n. 3) infers that the present chapter must be later than
that part of the Topics. This is very likely true, but Cherniss
(Aristotle's Criticism of Plato and the Academy, i. 34 n. 28) shows
that the inference is unsound; the Topics puts these methods
forward not as methods of demonstrating a definition, but as
dialectical arguments by which an opponent may be induced
to accept one.)
This analysis shows that Pacius is right in reading ἴδιον after
ἐστιν in *8. Cf. the application of ἴδιος to the definition in 91415,
Top. 1o1?19-23, 140*33-4.
9-19. ἢ πάλιν... ri. On this proposed proof A. makes two
criticisms: (1) (149-10) that the proof really begs the question that
the proposed complex of elements is the definition of the subject,
whereas it ought to prove this by a middle term. It begs the
question in the minor premiss; for if 'definition' just means
'formula composed of elements in the essence, and peculiar to
the subject' (which is what the major premiss says), then when
we say in the minor premiss ‘ABC is the formula composed of
elements in the essence of the subject and peculiar to it', we are
begging the question that ABC is the definition of the subject.
(2) (à11-19) that just as the definition of syllogism is not the major
premiss of any particular syllogism, the definition of definition
should not be made the major premiss of any syllogism aimed at
establishing a definition. He is making a similar point to that
which he makes when he insists that neither of the most general
axioms—the laws of contradiction and of excluded middle—
which are presupposed by all syllogisms, should be made the
major premiss of any particular syllogism (77*10-12, 88936-b3).
He is drawing in fact the very important distinction between
II. 6. 9236-27 623
premisses from which we reason and principles according to
which we reason.
9. πάλιν, because A. has made the same point in chs. 4 and 5
passim.
II-IQ. ἔτι ὥσπερ. .. rt. The premisses of a syllogism should
be related as whole and part, ie. (in the first figure, the only
perfect figure) the major premiss should state a rule and the
minor premiss bring a particular type of case under this rule, the
subject of the major premiss being also the predicate of the minor.
But if the major premiss states the general nature of syllogism
and the minor states particular facts, the minor is not related
to the major as part to whole, since it has no common term with
it. The facts on which the conclusion is based will be all contained
in the minor premiss, and the major will be otiose. The true
place of the definition of syllogism is not among the premisses
of a particular syllogism, nor that of the definition of definition
among the premisses by which a particular definition is proved
(if it can be proved) ; but when we have syllogized and someone
doubts whether we have, we may say ‘yes; that is what a syllo-
gism is’, and when we have proved a definition, and this is
challenged, we may say ‘yes; that is what definition is'—but we
must first have syllogized, or (in particular) proved our definition,
before we appeal to the definition of syllogism or of definition.
14-16. καὶ πρὸς τὸν ἀμφισβητοῦντα... συλλογισμός. Bonitz
(Arist. Stud. iv. 29) points out that, with the received punctuation
(εἰ συλλελόγισται 7) μὴ τοῦτο, ἀπαντᾶν), τοῦτο is not in its idiomatic
position.
18. ἢ τὸ τί ἦν εἶναι. The argument requires the reading τό,
not τοῦ, and this is confirmed by T. 47. 17-19, P. 356. 4-6, E. 85. 11.
20—7. Κἂν ἐξ ὑποθέσεως . . . ἀντιστρέφει. The use of the
τόπος ἀπὸ τοῦ ἐναντίου is discussed in Top. 153°26-24. It was one
of the grounds on which Eudoxus based his identification of
the good with pleasure (Eth. Nic. 1172518—20). The description of
evil as divisible and of good as indivisible, also, is Academic;
it was one of Speusippus' grounds for denying that pleasure is
good. He described the good as ἴσον, and pleasure (and pain) as
μεῖζον καὶ ἔλαττον (Eth. Nic. 1173*15-17 λέγουσι δὲ τὸ μὲν ἀγαθὸν
ὡρίσθαι τὴν δὲ ἡδονὴν ἀόριστον εἶναι ὅτι δέχεται τὸ μᾶλλον καὶ τὸ
ἧττον, 115354-6 ὡς γὰρ Σπεύσιππος ἔλυεν, οὐ συμβαίνει ἡ λύσις,
ὥσπερ τὸ μεῖζον τῷ ἐλάττονι καὶ τῷ ἴσῳ ἐναντίον" οὐ γὰρ ἂν φαίη
ὅπερ κακόν τι εἶναι τὴν ἡδονήν), and identified the ἴσον with the
ἀδιαίρετον (ἄσχιστον γὰρ ἀεὶ καὶ ἑνοειδὲς τὸ ἴσον, frag. 4. 53, ed.
Lang), and the ἀόριστον (i.e. the μεῖζον καὶ ἔλαττον) with the
624 COMMENTARY
imperfect (Met. 109213). On this whole question cf. Cherniss,
Ar.’s Criticism of Plato and the Academy, i. 36-8.
2x. τὸ δ᾽ ἐναντίῳ... elvai, ‘and to be one of two contraries
is to be the contrary of the other’. Bonitz's emendations (Arist.
Stud. i. 8 n. 2, iv. 23-4) are required by the argument.
24-7. kai yàp . . . ἀντιστρέφει, ‘for here too (cf. *9 n.) he
assumes the definition in his proof; but he assumes it in order to
prove the definition. You say "Yes, but a different definition".
I reply, "Granted, but that does not remove the objection, for
in demonstration also one assumes indeed that this is true of
that, but the term one assumes to be true of the minor term is
not the very term one is proving to be true of it, nor a term which
has the same definition as this, i.e. which is correlative with it’’.’
In *25 Bekker and Waitz have ἕτερον μέντοι ἔστω, but the
proper punctuation is already found in Pacius. ἔστω is the
idiomatic way of saying ‘granted’; cf. Top. 176223 ἀποκριτέον δ᾽
ἐπὶ μὲν τῶν δοκούντων τὸ 'éorw' λέγοντα.
The point of A.’s answer comes in καί (sc. καὶ ὅ; for the grammar
cf. H.A 494717, Part. An. 694*7, Met. ggo*4, Pol. 1317*4) ἀντι-
στρέφει. Good and evil are correlative, and in assuming the
definition of evil one is really assuming the definition of good.
27-33. πρὸς ἀμφοτέρους .. . γραμματικός. A.’s charge is that
the processes of definition he is attacking, though they can build
up a complex of attributes each of which is true of the subject,
cannot show that these form a real unity which is the very
essence of the subject; the complex may be only a series of
accidentally associated attributes (as ‘grammatical’ and ‘musical’
are when both are found in a single man). The difficulty is that
which A. points out at length in Met. Z. 12 and attempts to solve
in H. 6 by arguing that the genus is the potentiality of which the
species are the actualizations. It is clear how the difficulty
applies to definition by division; it is not so clear how it applies
to definitions by hypothesis such as have been considered in
320-7. But the answer becomes clear if we look at Top. 153?23-
b24, where A. describes a method of discovering the genus and the
successive differentiae of a term by studying those of its contrary.
30. ζῷον πεζὸν . . . δίπουν. T. 47. 9, P. 357. 24, and E. 87. 34
preserve the proper order ζῷον πεζὸν Bímovv.—working from
general to particular (cf. Top. 103427, 133*3, 58). In the final
clause again, where the MSS. read ζῷον xai πεζόν, and Bonitz
(Arist. Stud. iv. 32-3) reads ζῷον δίπουν καὶ πεζόν, P. 357. 22 and
E. 88. 1 seem to have the proper reading ζῷον xai πεζὸν xai
δίπουν.
II. 6. 92*21-30 625
CHAPTER 7
Neither definition. and syllogism nor their objects are the same;
definition proves nothing; knowledge of essence cannot be got etther
by definition or by demonstration
92°34. How then is one who defines to show the essence? (1)
He will not prove it as following from admitted facts (for that
would be demonstration), nor as one proves a general conclusion
by induction from particulars; for induction proves a connexion
or disconnexion of subject and attribute, not a definition. What
way is left? Obviously he will not prove the definition by appeal
to sense-perception.
b4. (2) How can he prove the essence? He who knows what
a thing is must know that it is; for no one knows what that which
is not is (one may know what a phrase, or a word like 'goat-deer',
means, but one cannot know what a goat-deer is). But (a) if he
is to prove what a thing is and that it is, how can he do so by
the same argument? For definition proves one thing, and so does
demonstration ; but what man is and that man is are two things.
I2. (b) We maintain that any connexion of a subject with an
attribute must be proved by demonstration, unless the attribute
is the essence of the subject ; and to be is not the essence of any-
thing, being not being a genus. Therefore it must be demonstra-
tion that shows that a thing is. The sciences actually do this; the
geometer assumes what triangle means, but proves that it exists.
What then will the person who defines be showing, except what
the triangle is? Then while knowing by definition what it is, he
will not know that it is; which is impossible.
19. (c) It is clear, if we consider the methods of definition now
in use, that those who define do not prove existence. Even if
there is a line equidistant from the centre, why does that which has
been thus defined exist? and why is this the circle? One might
just as well call it the definition of mountain-copper. For
definitions do not show either that the thing mentioned in the
definitory formula can exist, or that it is that of which they claim
to be definitions; it is always possible to ask why.
26. If then definition must be either of what a thing is or of
what a word means, and if it is not the former, it must be simply
a phrase meaning the same as a word. But that is paradoxical ;
for (a) there would then be definitions of things that are not
essences nor even realities; (b) all phrases would be definitions;
for to any phrase you could assign a name; we should all be
4085 Ss
626 COMMENTARY
talking definitions, and the Iliad would be a definition; (c) no
demonstration can prove that this word means this ; and therefore
definitions cannot show this.
35. Thus (1) definition and syllogism are not the same; (2)
their objects are not the same; (3) definition proves nothing;
(4) essence cannot be known either by definition or by demons-
tration.
This is a dialectical chapter, written by A. apparently to clear
his own mind on a question the answer to which was not yet clear
to him. The chapter begins with various arguments to show that
a definition cannot be proved. (1) (92*35-53) A person aiming at
establishing a definition uses neither deduction nor induction,
which A. here as elsewhere (An. Pr. 685r13-14, E.N. 1139^26-8)
takes to be the only methods of proof. (2) One who knows what
a thing is must know that it exists. But (a) (b4-11) definition
has a single task, and it is its business to show what things are,
and therefore not its business to show that things exist. (6)
(512-18) To show that things exist is the business of demonstra-
tion, and therefore not of definition. (c) (P19-25) It can be seen
by an induction from the modes of definition actually in use that
they do not prove the existence of anything corresponding to
the definitory formula, nor that the latter is identical with the
thing to be defined.
Concluding from these arguments that definition cannot prove
the existence of anything, A. now infers (626-34) that it must
simply declare the meaning of a word, and points out that this
interpretation of it is equally open to objection. Finally, he sums
up the results of his consideration of definition up to this point.
92535—6 οὔτε ὁρισμός... ὄρισμός refers to ch. 3, 37-8 πρὸς δὲ
τούτοις... γνῶναι to chs. 4-7.
9257. τραγέλαφος, cf. An. Pr. 49223 n.
8-9. ἀλλα phy. . . δείξει; Waitz reads ἀλλὰ μὴ εἰ δείξει τί
ἐστι, καὶ ὅτι ἔστι; καὶ πῶς τῷ αὐτῷ λόγῳ δείξει; His μή is a mis-
print. In reading καὶ πῶς he is following the strongest MS.
tradition. This reading involves him in putting a comma before
καὶ ὅτι ἔστι and in treating this as a question. But in the absence
of dpa it is difficult to treat it as a question ; and Bekker’s reading,
which I have followed, has very fair evidence behind it.
12-15. Εἶτα καὶ... ἔστιν. The sense requires us to read ὅ τι
ἐστιν, not ὅτι ἔστιν. ‘Everything that a thing is (i.e. its possession
of all the attributes it has) except its essence is shown by demon-
stration. Now existence is not the essence of anything (being
IT. 7. 9257-34 627
not being a genus). Therefore there must be demonstration that
a thing exists.’ For οὐ yàp γένος τὸ ov cf. Met. 99822-7.
16. ὅτι δ᾽ ἔστι, δείκνυσιν. Mure remarks that ‘triangle is for
the geometer naturally a subject and not an attribute; and in
that case ὅτι δ᾽ ἔστι should mean not “that it exists", but "that
it has some attribute’, e.g. equality to two right angles. It is
tempting to read ἐστὶ ri.’ But that would destroy A.’s argument,
which is about existential propositions and is to the effect that
since it is the business of demonstration to prove existence, it
cannot be the business of definition to do so. A.’s present way
of speaking of τρίγωνον as one of the attributes whose existence
geometry proves, not one of the subjects whose existence it
assumes, agrees with what he says in 71414 and what his language
suggests in 76235 and in 93531-2.
17. τί ov... τρίγωνον; The vulgate reading τί οὖν δείξει ὁ
ὁριζόμενος τί ἐστιν; 7) τὸ τρίγωνον; gives no good sense. P. 361.
18-20 6 γοῦν ὁριζόμενος kai τὸν ὁρισμὸν ἀποδιδοὺς τί dpa δείξει; ἢ
πάντως παρίστησι τί ἐστι τρίγωνον καθὸ τρίγωνον, E. 98. 13-14
ὁ οὖν ὁρισμὸς δεικνὺς τὸ τρίγωνον τί λοιπὸν δείξει ἢ τί ἐστι; and An.
559. 24-5 τί οὖν δείκνυσιν 6 ὁριζόμενος καὶ τὸ τί ἐστιν ἀποδιδούς
τινος; ἢ τὸ τί ἐστιν ἐκεῖνο ὃ ὁρίζεται; point to the reading I have
adopted. τί... 7 — τί ἄλλο ἤ, cf. Pl. Cri. 53e and Kühner,
Gr. Gramm. li. 2. 304 n. 4.
21. ἀλλὰ διὰ τί ἔστι τὸ ὁρισθέν; It is necessary to accent ἐστι,
if this clause is to mean anything different from that which
immediately follows. The first clause answers to 523-4 οὔτε...
ὅροι, the second to P24 οὔτε... ὁρισμοί.
24. ἀλλ᾽ ἀεὶ ἔξεστι λέγειν τὸ διὰ τί, as in Pz1 or in 91537-9.
28—9. πρῶτον μὲν yàp . . . εἴη. οὐσιῶν cannot here mean 'sub-
stances', for there would be nothing paradoxical in saying that
things that are not substances can be defined. It must mean
'definable essences'.
32-3. ἔτι οὐδεμία... av. The best supported reading omits
ἀπόδειξις. But the ellipse seems impossible here; ἀπόδειξις or
ἐπιστήμη is needed to balance ὁρισμοί (634). The reading of d
ἀπόδειξις elev dv points to the original reading having been
ἀπόδειξις ἀποδείξειεν dy. In most of the MSS. ἀπόδειξις disappeared
by haplography, and in some ἐπιστήμη was inserted to take its
place.
34. οὐδ᾽ oi Spicpot . . . προσδηλοῦσιν, “and so, by analogy,
definitions do not, in addition to telling us the nature of a thing,
prove that a word means so-and-so'.
628 COMMENTARY
CHAPTER 8
The essence of a thing that has a cause distinct from itself cannot be
demonstrated, but can become known by the help of demonstration
931. We must reconsider the questions what definition is and
whether there can be demonstration and definition of the essence.
To know what a thing is, is to know the cause of its being; the
reason is that there is a cause, either identical with the thing or
different from it, and if different, either demonstrable or indemon-
strable ; so if it is different and demonstrable, it must be a middle
term and the proof must be in the first figure, since its conclusion
is to be universal and affirmative.
g. One way of using a first-figure syllogism is the previously
criticized method, which amounts to proving one definition by
means of another; for the middle term to establish an essential
predicate must be an essential predicate, and the middle term
to establish an attribute peculiar to the subject must be another
such attribute. Thus the definer will prove one, and will not prove
another, of the definitions of the same subject.
x4. That method is not demonstration; it is dialectical
syllogism. But let us see how demonstration can be used. As we
cannot know the reason for a fact before we know the fact, we
cannot know what a thing is before knowing that itis. That a thing
is, we know sometimes fer accidens, sometimes by knowing part of
its nature—e.g. that eclipse is a deprivation of light. When our
knowledge of existence is accidental, it is not real knowledge and
does not help us towards knowing what the thing is. But where
we have part of the thing's nature we proceed as follows: Let
eclipse be A, the moon C, interposition of the earth B. To ask
whether the moon suffers eclipse is to ask whether B exists, and
this is the same as to ask whether there is an explanation of A;
if an explanation exists, we say A exists.
35. When we have got down to immediate premisses, we know
both the fact (that A belongs to C) and the reason; otherwise
we know the fact but not the reason. If B' is the attribute of
producing no shadow when nothing obviously intervenes, then
if B' belongs to C, and A to B’, we know that the moon suffers
eclipse but not why, and that eclipse exists but not what it is.
The question why is the question what B, the real reason for
A, is—whether it is interposition or something else; and this
real reason is the definition of the major term—eclipse is blocking
by the earth.
by. Or again, what is thunder? The extinction of fire in a
IL. 8 629
cloud. Why does it thunder? Because the fire is quenched in
the cloud. IfC is cloud, A thunder, B extinction of fire, B belongs
to C and A to B, and B is the definition of A. If there is a further
middle term explaining B, that will be one of the remaining
definitions of thunder.
15. Thus there is no syllogism or demonstration proving the
essence, yet the essence of a thing, provided the thing has a cause
other than itself, becomes clear by the help of syllogism and
demonstration.
A. begins the chapter by intimating (931-3) that he has reached
the end of the ἀπορίαι which have occupied chs. 3-7, and that he
is going to sift what is sound from what is unsound in the argu-
ments he has put forward, and to give a positive account of what
definition is, and try to show whether there is any way in which
essence can be demonstrated and defined. The clue he offers is
a reminder of what he has already said in 9014-23, that to know
what a thing is, is the same as knowing why it is (93*3-4). The
cause of a thing's being may be either identical with or different
from it (35-6). This is no doubt a reference to the distinction
between substance, on the one hand, and properties and events
on the other. A substance is the cause of its own being, and there
is no room for demonstration here; you just apprehend its nature
directly or fail to do so (cf. 93521-5, 9429-10). But a property or
an event has an αἴτιον other than itself. There are two types of
case which A. does not here distinguish. There are permanent
properties which have a ground (not a cause) in more fundamental
attributes of their subjects (as with geometrical properties, 33-5).
And there are events which have a cause in other events that
happen to their subjects (as with eclipse, 63-7, or thunder, 57-12).
Further (46) some events, while they have causes, cannot be
demonstrated to follow from their causes; A. is no doubt referring
to τὰ ἐνδεχόμενα ἄλλως ἔχειν, of which we at least cannot ascertain
what the causes are. But (36-9) where a thing has a cause other
than itself and proof is possible, the cause must occur as the
middle term, and (since what is being proved is a universal
connexion of a certain subject and a certain aftribute) the proof
must be in the first figure.
One attempt to reach definition by an argument in the first
figure is that which A. has recently criticized (ὁ viv ἐξητασμένος,
*10), viz. the attempt (discussed in 9114-11) to make a syllogism
with a definition as its conclusion. In such a syllogism the middle
term must necessarily be both essential and peculiar to the subject
630 COMMENTARY
(9311-12, cf. 91415-16), and therefore the minor premiss must
itself be a definition of the subject, so that the definer proves one
and does not prove another of the definitions of the subject
(93212-13), in fact proves one by means of another (as A. has
already pointed out in 91225-32, 69-11). Such an attempt cannot
be a demonstration (93214--15, cf. gr>10). It is only a dialectical
inference of the essence (93415). It is this because, while syllogisti-
cally correct, it is, as A. maintains (91231—2, 36-7, *g—11), a petitio
principi1. In attempting to prove a statement saying what the
essence of the subject is, it uses a premiss which already claims
to say this.
A. now begins (93215) to show how demonstration may be used
to reach a definition. He takes up the hint given in ?3-4, that to
know what a thing—i.e. a property or an event (for he has in
effect, in ?5-9, limited his present problem to this)—is, is to
know why itis. Just as we cannot know why a thing is the case
without knowing that it is the case, we cannot know what a
thing is without knowing that it is (416-20). In fact, when we
are dealing not with a substance but with a property or event,
whose esse is inesse in subjecto, to discover its existence is the
same thing as discovering the fact that it belongs or happens
to some subject, and to discover its essence is the same thing
as to discover why it belongs to that subject. Now when a fact
is discovered by direct observation or by inference from a mere
symptom or concomitant, it is known before the reason for it is
known ; but sometimes a fact is discovered to exist only because,
and therefore precisely when, the reason for it is discovered to
exist; what never happens is that we should know why a fact
exists before knowing that it exists (416-20).
Our knowledge that a thing exists may (1) be accidental (221),
Le. we may have no direct knowledge of its existence, but have
inferred it to exist because we know something else to exist of
which we believe it to be a concomitant. Or (2) (421-4) it may be
accompanied by some knowledge of the nature of the thing—of
its genus (e.g. that eclipse is a loss of light) or of some other
element in its essence. In case (1) our knowledge that it exists
gets us nowhere towards knowing what is its essence; for in fact
we do not really know that it exists (3524-7).
It is difficult at first sight to see how we could infer the existence
of something from that of something else without having some
knowledge of the nature of that whose existence we infer; but it
is possible to suggest one way in which it might happen. If we
hear some one whom we trust say 'that is a so-and-so', we infer the
Il. 8 631
existence of a so-and-so but may have no notion of its nature. It
is doubtful, however, whether A. saw the difficulty, and whether,
if he had, he would have solved it in this way.
A. turns (#27) to case (2), that in which we have some inkling
of the nature of the thing in question, as well as knowledge that
it exists, e.g. when we know that eclipse exists and is a loss of
light. This sets us on the way to explanation of why the moon
suffers eclipse. At this point A.'s account takes a curious turn.
He represents the question whether the moon suffers eclipse as
being solved not, as we might expect, by direct observation or
by inference from a symptom, but by asking and answering the
question whether interposition of the earth between the sun and
the moon—which would (if the moon has no light of its own) both
prove and explain the existence of lunar eclipse—exists. He takes
in fact the case previously (in 117—18) treated as exceptional, that
in which the fact and the reason are discovered together. He adds
that we really know the reason only when we have inferred the
existence of the fact in question through a series of immediate
premisses (535-6) ; i.e. (if N be the fact to be explained) through
a series of premisses of the form 'A (a directly observed fact)
directly causes B, B directly causes C . . . M directly causes Ν᾽.
But, as though he realized that this is unlikely to happen, he
turns to the more usual case, in which our premisses are not
immediate. We may reason thus: ‘Failure to produce a shadow,
though there is nothing between us and the moon to account for
this, presupposes eclipse, The moon suffers such failure, Therefore
the moon must be suffering eclipse’. Here our minor premiss is
not immediate, since the moon in fact fails to produce a shadow
only because it is eclipsed; and we have discovered the eclipse
of the moon without explaining it (236-53). Having discovered
it so, we then turn to ask which of a variety of causes which might
explain it exists, and we are satisfied only when we have answered
this question. Thus the normal order of events is this: we begin
by knowing that there is such a thing as eclipse, and that this
means some sort of loss of light. We first ask if there is any
evidence that the moon suffers eclipse and find that there is, viz.
the moon's inability to produce a shadow, at a time when there
are no clouds between us and it. Later we find that there is an
explanation of lunar eclipse, viz. the earth's coming between the
moon and the sun.
The conclusion that A. draws (515-20) is that while there is no
syllogism with a definition as its conclusion (the conclusion drawn
being not that eclipse is so-and-so but that the moon suffers
632 COMMENTARY
eclipse), yet a regrouping of the contents of the syllogism yields
the definition ‘lunar eclipse is loss of light by the moon in con-
sequence of the earth’s interposition between it and the sun’.
9376. κἂν ἡ ἄλλο, ἢ ἀποδεικτὸν ἢ ἀναπόδεικτον. This does
not mean that the cause may, or may not, be demonstrated, in
the sense of occurring in the conclusion of a demonstration. What
A. means is that the cause may, or may not, be one from which
the property to be defined may be proved to follow.
9-16. els μὲν δὴ τρόπος... ἀρχῆς. Pacius takes the τρόπος
referred to to be that which A. expounds briefly in 43-9 and fully
in *16-614. But this interpretation will not do. A. would not
admit that the syllogism he contemplates in 53-5 (‘That which is
blocked from the sun by the earth's interposition loses its light,
The moon is so blocked, Therefore the moon loses its light") is
not a demonstration but a dialectical syllogism (214-15). Pacius
has to interpret A.'s words by saying that while it is a demonstra-
tion as proving that the moon suffers eclipse, it is a dialectical
argument if considered as proving the definition of eclipse. But
A. in fact offers no syllogism proving that ‘eclipse is so-and-so’ ;
the moon is the only minor term he contemplates.
Again, the brief mention of a method in *3-9 by no means
amounts to an ἐξέτασις (10) of it. The parallels I have pointed out
above (pp. 629-30) show that 91214-^11is the passage referred to.
Pacius has been misled, not unnaturally, by supposing vóv to refer
to what immediately precedes. But it need not do this; cf. Plato
Rep. 414 b, referring to 382 a, 389 b, and 611 b referring to 435 b ff.
Pacius interprets ὃν δὲ τρόπον ἐνδέχεται (415) to mean ‘how the
dialectical syllogism can be constructed’ ; on our interpretation it
means ‘how demonstration can be used to aid us in getting a
definition’.
10. τὸ δι᾽ ἄλλου του τί ἐστι δεικνύσθαι. The meaning is made
much clearer by reading τὸν for the MS. reading τό, and the
corruption is one which was very likely to occur.
24. καὶ ψυχήν, ὅτι αὐτὸ αὑτὸ κινοῦν, a reference to Plato's
doctrine in Phaedr. 245 c-246 a, Laws 895 e-896 a; cf. οτἈ37-ῦτ.
34. τοῦ ἔχειν δύο ὀρθὰς, i.e. of the triangle’s having angles
equal to two right angles.
b12. καὶ ἔστι ye... ἄκρου. ye lends emphasis: ‘and B is, you
see, a definition of the major term A’.
20. ἐν rois διαπορήμασιν. Ch. 2 showed that definition of
something that has a cause distinct from itself is not possible
without demonstration, ch. 3 that a definition cannot itself be
demonstrated.
IT. 8. 93*6— 9. 93°27 633
CHAPTER 9
What essences can and what cannot be made known by demonstration
93°21. Some things have a cause other than themselves;
others have not. Therefore of essences some are immediate and
are first principles, and both their existence and their definition
must be assumed or made known in some other way, as the
mathematician does with the unit. Of those which have a middle
term, a cause of their being which is distinct from their own
nature, we may make the essence plain by a demonstration,
though we do not demonstrate it.
93521. Ἔστι 86 . . . ἔστιν. By the things that have a cause
other than themselves A. means, broadly speaking, properties
and accidents; by those that have not, substances, the cause of
whose being lies simply in their form. But it is to be noted that
he reckons with the latter certain entities which are not sub-
stances but exist only as attributes of subjects, viz. those which
a particular science considers as if they had independent existence,
and treats as its own subjects, e.g. the unit (P25). τὰ yap μαθήματα
περὶ εἴδη éariv: οὐ yàp καθ᾽ ὑποκειμένου τινός" εἰ yàp καθ᾽ ὑποκειμένου
τινὸς τὰ γεωμετρικά ἐστιν, ἀλλ᾽ οὐχ ἦ γε καθ᾽ ὑποκειμένου (79*7—10).
23-4. ἃ καὶ εἶναι... ποιῆσαι. Of ἀρχαί generally A. says in
E.N. 1098>3 ai μὲν ἐπαγωγῇ θεωροῦνται (where experience of more
than one instance is needed before we seize the general principle),
ai δ᾽ αἰσθήσει (where the perception of a single instance is enough
to reveal the general principle), ai δ᾽ ἐθισμῷ τινί (where the ἀρχαί
are moral principles), xai ἄλλαι δ᾽ ἄλλως. But we can be rather
more definite. The existence of substances, A. would say, is dis-
covered by perception; that of the quasi-substances mentioned
in the last note by abstraction from the data of perception. The
definitions of substances and quasi-substances are discovered by
the method described in ch. 13 (here alluded to in the words ἄλλον
τρόπον φανερὰ ποιῆσαι), Which is not demonstration but requires
a direct intuition of the genus the subject belongs to and of the
successive differentiae involved in its nature. Both kinds of ἀρχαί
—the ὑποθέσεις (assumptions of existence) and the ὁρισμοί (for
the distinction cf. 72#18-24)—-should then be laid down as assump-
tions (ὑποθέσθαι δεῖ).
25-7. τῶν δ᾽ ἐχόντων μέσον... ἀποδεικνύντας. τὸ τί ἐστι must
be ‘understood’ as the object of δηλῶσαι. καὶ ὧν... οὐσίας is
explanatory of τῶν ἐχόντων μέσον. ὥσπερ εἴπομεν refers to ch. 8.
Waitz's δ᾽ (instead of δι᾽) is a misprint.
634 COMMENTARY
CHAPTER 10
The types of definition
93°29. (1) One kind of definition is an account of what a word
or phrase means. When we know a thing answering to this exists,
we inquire why it exists; but it is difficult to get the reason for the
existence of things we do not know to exist, or know only per
accidens to exist. (Unless an account is one merely by being
linked together—as the Iliad is—it must be one by predicating
one thing of another in a way which is not merely accidental.)
38. (2) A second kind of definition makes known why a thing
exists. (1) pointsout but does not prove ; (2) isa sort of demonstra-
tion of the essence, differing from demonstration in the arrange-
ment of the terms. When we are saying why it thunders we say
^it thunders because the fire is being quenched in the clouds';
when we are defining thunder we say 'the sound of fire being
quenched in clouds’. (There is of course also a definition of thunder
as ‘noise in clouds’, which is the conclusion of the demonstration
of the essence.)
94*9. (3) The definition of unmediable terms is an indemon-
strable statement of their essence.
II. Thus definition may be ((3) above) an indemonstrable
account of essence, ((2) above)—a syllogism of essence, differing
in grammatical form from demonstration, or ((1) above) the con-
clusion of a demonstration of essence. It is now clear (2) in what
sense there is demonstration of essence, (b) in the case of what
terms this is possible, (c) in how many senses 'definition' is used,
(d) in what sense it proves essence, (e) for what terms it is possible,
(f) how it is related to demonstration, (g) in what sense there can
be demonstration and definition of the same thing.
The first two paragraphs of this chapter fall into four parts
which seem at first sight to describe four kinds of definition—
9329-37, 38-94*7, 94*7-9, 9-10; and T. sr. 3-26 and P. 397. 23-8
interpret the passage so. As against this we have A.’s definite
statement in 94411-14 (and in 75531-2) that there are just three
kinds; P. attempts to get over this by saying that a nominal
definition, such as is described in the first part of the chapter, is
not a genuine definition.
Let us for brevity'ssake refer to the supposed four kinds as the
first, second, third, and fourth kind. In 93538-9 the second kind
is distinguished from the first by the fact that it shows why the
II. ro 635
thing defined exists; and this is just how the second kind is
distinguished from the thivd—-the second says, for instance,
‘thunder is a noise in clouds caused by the quenching of fire’,
the third says simply ‘thunder is a noise in clouds’. In fact,
there could be no better example of a nominal definition than this
latter definition of thunder. In answer to this it might be said
that while a nominal definition is identical in form with a defini-
tion of the third kind, they differ in their significance, thc one
being a definition of the meaning of a word, without any implica-
tion that a corresponding thing exists, the other a definition of
the nature of a thing which we know to exist. But this, it seems,
is not A.’s way of looking at the matter. In 72418-24 definition is
distinguished from ὑπόθεσις as containing no implication of the
existence of the definiendum; and in 76532-6 this distinction is
again drawn.
Further, A.'s statement that a definition of the first kind can
originate a search for the cause of the definiendum (9332) is a
recapitulation of what he has said in the previous chapter (221—57),
and the definition of thunder which occurs in this chapter as an
example of the third kind of definition (9457-8) occurs in that
chapter as an example of the kind of definition we start from in
the search for the cause of the definiendum (93222-3).
It seems clear, then, that the 'third kind' of definition is
identical with the first. Further, it seems a mistake to say that
A. ever recognizes nominal definition by that name. The mis-
take starts from the supposition that in 9330 λόγος ἕτερος óvo-
parans is offered as an alternative to λόγος τοῦ τί σημαΐνει τὸ
ὄνομα. But why érepos? For if λόγος ὀνοματώδης means nominal
definition, that is just the same thing as λόγος τοῦ τί σημαίνει τὸ
ὄνομα. Besides, ὀνοματώδης means ‘of the nature of a name’, and
a nominal definition is not in the least of the nature of a name.
λόγος ἕτερος ὀνοματώδης is, we must conclude (and the form of
the sentence is at least equally compatible with this interpreta-
tion), alternative not to λόγος τοῦ τί σημαίνει τὸ ὄνομα but to τὸ
ὄνομα, and means ‘or another noun-like expression’. Definitions
of such expressions (e.g. of εὐθεῖα γραμμή, ἐπίπεδος ἐπιφάνεια,
ἀμβλεῖα γωνία) are found at the beginning of Euclid, and were
very likely found at the beginning of the Euclid of A.’s day, the
Elements of Theudius.
As we have seen in ch. 8, it is, according to A.’s doctrine, things
that have no cause of their being, other than themselves, i.e.
substances, that are the subjects of indemonstrable definition.
Thus definitions. of the first kind are non-causal definitions of
636 COMMENTARY
attributes or events, those of the second kind causal definitions
of the same. The sentence at 9477-9 does not describe a third
kind ; having referred to the causal definition of thunder (45), A.
reminds the reader that there can also be a non-causal definition
of it. There are only three kinds, and the 'fourth kind' is really
a third kind, definition of substances. The three reappear in
reverse order in 94?11-14.
93°31. οἷον τί onpaive . . . τρίγωνον. The vulgate reading
olov τὸ τί σημαίνει τί ἐστιν ἦ τρίγωνον seems impossible. P.’s
interpretation in 372. 17--18 οἷον παριστᾷ τί σημαίνει τὸ ὄνομα τοῦ
τριγώνου καθὸ τρίγωνον seems to show that he read οἷον τί σημαίνει
τρίγωνον (or τρίγωνον ἧ τρίγωνον). τί ἐστιν has come in through a
copyist’s eye catching these words in the next line.
Since the kind of definition described in the present passage
and in 9427-9 is distinguished from the definition of immediate
terms (9429-10) (i.e. of the subjects of a science, whose definition
is not arrived at by the help of a demonstration assigning a cause
to them, but is simply assumed), τρίγωνον is evidently here thought
of not as a subject of geometry but as a predicate which attaches
to certain figures. À. more often treats it as a subject, a quasi-
substance, but the treatment of it as an attribute is found else-
where, in 71°14, 76*33-6, and gz^15—16.
32-3. χαλεπὸν δ᾽... ἔστιν, ‘it is difficult to advance from a
non-causal to a causal definition, unless besides having the non-
causal definition we know that the thing definitely exists’.
34. εἴρηται πρότερον, 424-7.
36. 9 μὲν συνδεσμῷ, ὥσπερ ἡ ᾿Ιλιάς, cf. 92532.
36-7. ὁ 86 . . . συμβεβηκός. A definition is a genuine pre-
dication, stating one predicate of one subject, and not doing so
κατὰ συμβεβηκός, i.e. not treating as grammatical subject what
is the metaphysical predicate and vice versa (cf. 81523-9, 8311—23).
9476-7. καὶ ὡδὶ μὲν... ὁρισμός. As Mure remarks, ‘Demon-
stration, like a line, is continuous because its premisses are parts
which are conterminous (as linked by middle terms), and there
is a movement from premisses to conclusion. Definition resembles
rather the indivisible simplicity of a point'.
9. τῶν Gpéeowv. For the explanation cf. 93521-5.
I2. πτώσει, ‘in grammatical form’, another way of saying what
A. expresses in 32 by τῇ θέσει, ‘in the arrangement of the terms’.
II. 10. 93°31 — 94712 637
CHAPTER 11
Each of four types of cause can function as middle term
94°20. We think we know a fact when we know its cause.
There are four causes—the essence, the conditions that necessitate
a consequent, the efficient cause, the final cause; and in every
case the cause can appear as middle term in a syllogism that
explains the effect.
24. For (1) the conditions that necessitate a consequent must
be at least two, linked by a single middle term. We can exhibit
the matter thus: Let A be right angle, B half of two right angles,
C the angle in a semicircle. Then B is the cause of C’s being A ;
for B= A, andC = B. B is identical with the essence of A,
since it is what the definition of A points to.
35. (2) The essence, too, has previously been shown to function
as middle term.
36. (3) Why were the Athenians made war on by the Medes?
The efficient cause was that they had raided Sardis. Let A be
war, B unprovoked raiding, C the Athenians. Then B belongs
to C, and A to B. Thus the efficient cause, also, functions as
middle term.
*8. (4) So too when the cause is a final cause. Why does a man
walk? In order to be well. Why does a house exist? In order
that one's possessions may be safe. Health is the final cause of
the one, safety of the other. Let walking after dinner be C,
descent of food into the stomach B, health A. Then let B attach
to C, and A to B; the reason why A, the final cause, attaches to
C is B, which is as it were the definition of A. But why does B
attach to C? Because A is definable as B. The matter will be
clearer if we transpose the definitions. The order of becoming here
is the opposite of the order in efficient causation ; there the middle
term happens first, here the minor happens first, the final cause
last.
27. The same thing may exist for an end and as the result of
necessity—e.g. the passage of light through a lantern; that which
is fine-grained necessarily passes through pores that are wider
than its grains, and also it happens in order to save us from
stumbling. If things can be from both causes, can they also
happen from both? Does it thunder both because when fire is
quenched there must be a hissing noise and (if the Pythagoreans
are right) as a means to alarming the inhabitants of Tartarus?
34. There are many such cases, especially in natural processes
638 COMMENTARY
and products; for nature in one sense acts for an end, nature in
another sense acts from necessity. Necessity itself is twofold;
one operating according to natural impulse, the other contrary to
it (e.g. both the upward and the downward movement of stones
are necessary, in different senses).
9553. Of the products of thought, some (e.g. a house or a statue)
never come into being by chance or of necessity, but only for
an end; others (e.g. health or safety) may also result from chance.
It is, properly speaking, in contingent affairs, when the course of
events leading to the result's being good is not due to chance,
that things take place for an end—either by nature or by art.
No chance event takes place for an end.
This chapter is one of the most difficult in A.; its doctrine is
unsatisfactory, and its form betrays clearly that it has not been
carefully worked over by A. but is a series of jottings for further
consideration. The connexion of the chapter with what precedes
is plain enough. As early as ch. 2 he has said (9025) συμβαίνει dpa
ἐν ἁπάσαις ταῖς ζητήσεσι ζητεῖν ἢ εἰ ἔστι μέσον ἢ τί ἐστι τὸ μέσον.
τὸ μὲν γὰρ αἴτιον τὸ μέσον, ἐν ἅπασι δὲ τοῦτο ζητεῖται, and in
chs. 8 and ro he has shown that the scientific definition of any of
the terms of a science except the primary subjects of the science
is a causal definition; but he has not considered the different
kinds of cause, and how each can play its part in detinition. He
now sets himself to consider this question. In the first paragraph
he sets himself to show that in the explanation of a result by any
one of four types of cause, the cause plays the part of (‘is exhibited
through’, 94223) the middle term. Three of the causes named in
421-3 are familiar to students of A.—the formal, efficient, and
final cause. The place usually occupied in his doctrine by the
material cause is here occupied by τὸ τίνων ὄντων ἀνάγκη τοῦτ᾽
εἶναι. This pretty clearly refers to the definition of syllogism as
given in An. Pr. 24>18-20, and the reference to the syllogism is
made explicit in 94224-7. He is clearly, then, referring to the
relation of ground to consequent. The ground of the conclusion
of a syllogism is the two premisses taken together, but in order to
make his account of this sort of αἴτιον fit into his general formula
that the αἴτιον functions as middle term in the proof of that
whose αἴτιον it is, he represents this αἴτιον as being the middle
term—the middle term, we must understand, as related in a
certain way to the major and in a certain way to the minor.
In Phys. 195216-19 the premisses are described as being the
ἐξ οὗ or material cause of the conclusion, alongside of other more
II. 11 639
typical examples of the material cause (rà μὲν yàp στοιχεῖα τῶν
συλλαβῶν xai ἡ ὕλη τῶν σκευαστῶν Kai τὸ πῦρ Kai τὰ τοιαῦτα τῶν
σωμάτων καὶ τὰ μέρη τοῦ ὅλου καὶ αἱ ὑποθέσεις τοῦ συμπεράσματος),
sc. as being ἃ quasi-material which is reshaped in the conclusion ;
cf. Met. 1013%17-21. Both T. and P. take A. to be referring in the
present passage to the material cause, and to select the relation
of premisses to conclusion simply as an example of the relation
of material cause to effect. But even if the premisses may by
a metaphor be said (as in Phys. 195*16-19) to be an example of
the material cause, it is inconceivable that if A. had here meant
the material cause in general, he should not have illustrated it
by some literal example of the material cause. Besides, the
material cause could not be described as τὸ τίνων ὄντων ἀνάγκη
τοῦτ᾽ εἶναι. It does not necessitate that whose cause it is; it is
only required to make this possible. Although in Phys. 195416-19
A. includes the premisses of a syllogism as examples of the material
cause, he corrects this in 200415-30 by pointing out that their
relation to the conclusion is the converse of the relation of a
material cause to that whose cause itis. The premisses necessitate
and are not necessitated by the conclusion; the material cause is
necessitated by and does not necessitate that whose αἴτιον it is.
Nor could the material cause be described as identical with the
formal cause (94334-5). It may be added that both the word
ὕλη and the notion for which it stands are entirely absent from
the Organon. It could hardly be otherwise; ὕλη is ἄγνωστος καθ᾽
αὐτήν (Met. 10369); it does not occur as a term in any of our
ordinary judgements (as apart from metaphysical judgements),
and it is with judgements and the inferences that include them
that logic is concerned. The term ὑποκείμενον, indeed, occurs in
the Organon, but then it is used not as equivalent to ὕλη, but as
standing either for an individual thing or for a whole class of
individual things; the analysis of the individual thing into matter
and form belongs not to logic but to physics (as A. understands
physics) and to metaphysics, and it is in the Metaphysics and the
physical works that the word ὕλη is at home.
A., then, is not putting forward his usual four causes. It may be
that this chapter belongs to an early stage at which he had not
reached the doctrine of the four causes. Or it may be that,
realizing that he could not work the material cause into his
thesis that the cause is the middle term, he deliberately substi-
tutes for it a type of αἴτιον which will suit his thesis, namely, the
ground of a conclusion as the αἴτιον of the conclusion. Unlike
efficient and final causation, in both of which there is temporal
640 COMMENTARY
difference between cause and effect (623-6), in this kind of necessi-
tation there is no temporal succession; ground and consequent
are eternal and simultaneous. And since mathematics is the
region in which such necessitation is most clearly evident, A.
naturally takes his example from that sphere (228-34).
The four causes here named, then, are formal cause, ground
(τίνων ὄντων ἀνάγκη τοῦτ᾽ εἶναι), efficient cause, final cause. But
A.’s discussion does not treat these as all mutually exclusive.
He definitely says that the ground is the same as the formal
cause (434-5). Further, he has already told us (in chs. 8, ro) that
the middle term in a syllogism wkich at the same time proves
and explains the existence of a consequence is an element in the
definition of the consequence, i.e. in its formal cause (the general
form of the definition of a consequential attribute being ‘A is
a B caused in C by the presence of D’). It is not that the middle
term in a demonstration is sometimes the formal cause of the
major term, sometimes its ground, sometimes its efficient cause,
sometimes its final cause. It is always its formal cause (or
definition), or rather an element in its formal cause; but this
element is in some cases an eternal ground of the consequent
(viz. when the consequence is itself an eternal fact), in some cases
an efficient or a final cause (when the consequence is an event) ;
the doctrine is identical with that which is briefly stated in Met.
1041227—30, φανερὸν τοίνυν ὅτι ζητεῖ τὸ αἴτιον" τοῦτο δ᾽ ἐστὶ τὸ τί
ἦν εἶναι, ὡς εἰπεῖν λογικῶς, ὃ ἐπ’ ἐνίων μέν ἐστι τίνος ἕνεκα, οἷον
ἴσως ἐπ᾽ οἰκίας ἢ κλίνης, én’ ἐνίων δὲ τί ἐκίνησε πρῶτον" αἴτιον γὰρ
καὶ τοῦτο. Cf. ib. 1044236 τί δ᾽ ὡς τὸ εἶδος; τὸ τί ἦν εἶναι. τί δ᾽ ὡς
οὗ ἕνεκα; τὸ τέλος. ἴσως δὲ ταῦτα ἄμφω τὸ αὐτό. In chs. 8 and 10
(e.g. 9393-12, 38-9427) the doctrine was illustrated by cases in
which the element-in-the-definition which serves as middle term
of the corresponding demonstration was in fact an efficient cause.
Lunar eclipse is defined as ‘loss of light by the moon owing to
the interposition of the earth’, thunder as ‘noise in clouds due
to the quenching of fire in them’. In this chapter A. attempts to
show that in other cases the element-in-the-definition which serves
as middle term of the corresponding demonstration is an eternal
ground, and that in yet others it is a final cause.
The case of the eternal ground is illustrated by the proof of the
proposition that the angle in a semicircle is a right angle (#28—34).
The proof A. has in mind is quite different from Euclid’s proof
(El. iii. 31). It is only hinted at here, but is made clearer by Met.
1051427 ἐν ἡμικυκλίῳ ὀρθὴ καθολου διὰ τί; ἐὰν ἴσαι τρεῖς, ἥ τε βάσις
δύο καὶ ἡ ἐκ μέσου ἐπισταθεῖσα ὀρθή, ἰδόντι δῆλον τῷ ἐκεῖνο (1.6.
II. x1 641
ὅτι δύο ὀρθαὶ τὸ τρίγωνον (1051*24), that the angles of a triangle
equal two right angles) εἰδότι. From O, the centre of the circle,
Ω.
Ν Ρ
OQ perpendicular to the diameter NP is drawn to meet the
circumference, and NQ, PQ are joined. Then, NOQ and POQ
being isosceles triangles, ZOQN = ONQ, and ZOQP = OPQ.
Therefore OON --OQP (= NQP) = ONQ+OPQ, and therefore
= half of the sum of the angles of NOP, i.e. of two right angles,
and therefore = one right angle. (Then, using the theorem that
angles in the same segment of a circle are equal (Euc. iii. 21), A.
must have inferred that any angle in a semicircle is a right
angle.) In this argument, NQP’s being the half of two right
angles is the ground of its being one right angle, or rather the
causa cognoscendi of this. (This is equally true of the proof inter-
polated in the part of Euclid after iii. 31, and quoted in Heath,
Mathematics in Aristotle, 72; but A. probably had in mind in the
present passage the proof which he clearly uses in the Metaphysics.)
But A.’s comment ‘this, the ground, is the same as the essence
of the attribute demonstrated, because this is what its definition
points to’ (4334-5) is a puzzling statement. Reasoning by analogy
(it would appear) from the fact that, e.g., thunder may fairly be
defined as ‘noise in clouds due to the quenching of fire in them’,
A. seems to contemplate some such definition of the rightness of
the angle in a semicircle as ‘its being right in consequence of being
the half of two right angles’; and for this little can be said. The
analogy between the efficient cause of an event and the causa
cognoscendi of an eternal consequent breaks down; the one can
fairly be included in the definition of the event, the other cannot
be included in the definition of the consequent.
Two comments may be made on A.'s identification of the
ground of a mathematical consequent with the definition of the
consequent. (1) The definition of ‘right angle’ in Euclid (and
probably in the earlier Elements known to A.) is: ὅταν εὐθεῖα ἐπ᾽
εὐθεῖαν σταθεῖσα τὰς ἐφεξῆς γωνίας ἴσας ἀλλήλαις ποιῇ, ὀρθὴ ἑκατέρα
τῶν ἴσων γωνιῶν ἐστι (El. i, Def. 10). Thus the right angle is
defined as half of the sum of a certain pair of angles, and it is not
unnatural that A. should have treated this as equivalent to
4085 Tt
642 COMMENTARY
defining it as the half of two right angles. (2) While it is not
defensible to define the rightness of the angle in a semicircle as
its being right by being the half of two right angles, there is
more to be said for a similar doctrine applied to a geometrical
problem, instead of a geometrical theorem. The squaring of a
rectangle can with some reason be defined as 'the squaring of it
by finding a mean proportional between the sides’ (De An.
413*13—20).
A. offers no separate proof that the formal cause of definition
functions as middle term. He merely remarks (335-6) that that
has been shown before, i.e. in chs. 8 and ro, where he has shown
that the cause of an attribute, which is used as middle term in
an inference proving ¢hat and explaining why a subject has the
attribute, is also an element in the full definition (i.e. in the formal
cause) of the attribute.
With regard to the efficient cause (36-68) A. makes no attempt
to identify it with the formal cause, or part of it. He merely points
out that where efficient causation is involved, the event, in con-
sequence of whose happening to a subject another event happens
to that subject, functions as middle term between that subject
and the later event. The syllogism, in the instance he gives,
would be: Those who have invaded the country of another people
are made war on in return, The Athenians have invaded the
country of the Medes, Therefore the Athenians are made war on
by the Medes.
With regard to the final cause (58-23) A. similarly argues that
it too can function as the middle term of a syllogism explaining
the event whose final cause it is. He begins by pointing out
(58-12) that where a final cause is involved, the proper answer
to the question ‘why?’ takes the form ‘in order that . . .'. He
implies that such an explanation can be put into syllogistic form,
with the final cause as middle term ; but this is in fact impossible.
If we are to keep the major and minor terms he seems to envisage
in the example he takes, i.e. 'given to walking after dinner' and
‘this man’, the best argument we can make out of this is: Those
who wish to be healthy walk after dinner, This man wishes to be
healthy, Therefore this man walks after dinner. And here it is
not ‘health’ but ‘desirous of being healthy’ that is the middle
term. If, on the other hand, we say ‘Walking after dinner pro-
duces health, This man desires health, Therefore this man walks
after dinner’, we abandon all attempt at syllogistic form. A. is
in fact mistaken in his use of the notion of final cause. It is never
the so-called final cause that is really operative, but the desire
II. zr 643
of an object ; and this desire operates as an efficient cause, being
what corresponds, in the case of purposive action, to a mechanical
or chemical cause in physical action.
Up to this point A. has tried to show how an efficient cause may
function as middle term (236-68) and how a final cause may do so
(58-12). He now (12-20) sets himself to show that an efficient
cause and a final cause may as it were play into each other's hands,
by pointing out that between a purposive action (such as walking
after dinner) and the ultimate result aimed at (e.g. health) there
may intervene an event which as efficient cause serves to explain
the occurrence of the ultimate result, and may in turn be teleo-
logically explained by the result which is its final cause. He offers
first the following quasi-syllogism: Health (A) attaches to the
descent of food into the stomach (B), Descent of food into the
stomach attaches to walking after dinner (C), Therefore health
attaches to walking after dinner. A. can hardly be acquitted of
failing to notice the ambiguity in the word ὑπάρχειν. In his
ordinary formulation of syllogism it stands for the relation of
predicate to subject, but here for that of effect to cause; and
‘A is caused by B, B is caused by C, Therefore A is caused by C',
while it is a sound argument, is not a syllogism.
A. adds (19-20) that here B is ‘as it were’ a definition of A,
i.e. that just as lunar eclipse may be defined by means of its
efficient cause as ‘failure of light in the moon owing to the inter-
position of the earth’ (ch. 8), so health may be defined as ‘good
condition of the body due to the descent of food into the stomach’.
This is only ‘as it were’ a definition of health, since it states not
the whole set of conditions on which health depends, but only
the condition relating to the behaviour of food.
‘But instead of asking why A attaches to C’ (A. continues in
b20-3) ‘we may ask why B attaches to C; and the answer is
"because that is what being in health is—being in a condition
in which food descends into the stomach." But we must transpose
the definitions, and so everything will become plainer.’ It may
seem surprising that A. should attempt to explain by reference to
the health produced by food's descent into the stomach (sc. and
the digestion of it there) the sequence of the descent of food upon
a walk after dinner—a sequence which seems to be sufficiently
explained on the lines of efficient causation. And in particular,
it is by no means easy to see what syllogism or quasi-syllogism
he has in mind; the commentators are much puzzled by the
passage and have not been very successful in dealing with it. We
shall be helped towards understanding the passage if we take
644 COMMENTARY
note of the very strong teleological element in A.’s biology
(especially in the De Partibus Animalium), and consider in parti-
cular the following passages: Phys. 200415 ἔστι δὲ τὸ ἀναγκαῖον ἔν
τε τοῖς μαθήμασι kai ἐν τοῖς κατὰ φύσιν γιγνομένοις τρόπον τινὰ
παραπλησίως" ἐπεὶ γὰρ τὸ εὐθὺ τοδί ἐστιν, ἀνάγκη τὸ τρίγωνων δύο
ὀρθαῖς ἴσας éyew- ἀλλ᾽ οὐκ ἐπεὶ τοῦτο, ἐκεῖνο" ἀλλ᾽ εἴ γε τοῦτο μὴ
ἔστιν, οὐδὲ τὸ εὐθὺ ἔστιν. ἐν δὲ τοῖς γιγνομένοις ἕνεκά του ἀνάπαλιν,
εἰ τὸ τέλος ἔσται ἢ ἔστι, καὶ τὸ ἔμπροσθεν ἔσται ἢ ἔστιν" εἰ
δὲ μή, ὥσπερ ἐκεῖ μὴ ὄντος τοῦ συμπεράσματος ἡ ἀρχὴ οὐκ ἔσται, καὶ
ἐνταῦθα τὸ τέλος καὶ τὸ οὗ ἕνεκα. Part. An. 639» )η6 ἀνάγκη δὲ
τοιάνδε τὴν ὕλην ὑπάρξαι, εἰ ἔσται οἰκία ἢ ἄλλο τι τέλος"
καὶ γενέσθαι τε καὶ κινηθῆναι δεῖ τόδε πρῶτον, εἶτα τόδε, καὶ τοῦτον
δὴ τὸν τρόπον ἐφεξῆς μέχρι τοῦ τέλους καὶ οὗ ἕνεκα γίνεται ἕκαστον
καὶ ἔστιν. ὡσαύτως δὲ καὶ ἐν τοῖς φύσει γινομένοις. ἀλλ᾽ ὁ τρόπος τῆς
ἀποδείξεως καὶ τῆς ἀνάγκης ἕτερος, ἐπί τε τῆς φυσικῆς καὶ τῶν
θεωρητικῶν ἐπιστημῶν. ἡ γὰρ ἀρχὴ τοῖς μὲν τὸ ὄν, τοῖς δὲ τὸ
ἐσόμενον" ἐπεὶ γὰρ τοιόνδε ἐστὶν ἡ ὑγίεια ἢ ὁ ἄνθρωπος, ἀνάγκη
τόδ᾽ εἶναι ἢ γενέσθαι, ἀλλ᾽ οὐκ ἐπεὶ τόδ᾽ ἔστιν ἢ γέγονεν, ἐκεῖνο ἐξ
ἀνάγκης ἔστιν ἢ ἔσται.
In the light of these passages we can see that A.’s meaning
must be that instead of the quasi-syllogism (1) (couched in terms
of efficient causation) ‘since descent of food into the stomach
produces health, and walking after dinner produces such descent,
walking after dinner produces health’ (611-20), we can have the
quasi-syllogism (2) (couched in terms of final causation) ‘since
health presupposes descent of food into the stomach, therefore
if walking after dinner is to produce health it must produce
such descent’.
In δεῖ ματαλαμβάνειν τοῦς λόγους, λόγους might mean ‘reason-
ings’, but the word has occurred in 5rg in the sense of definition,
and it is better to take it so here. A.'s point is this: In the quasi-
syllogism (1) above, we infer that walking after dinner produces
health because it produces what is ‘as it were’ the definition of
health. Now transpose the definition ; instead of defining health
as a good condition of body caused by descent of food into the
stomach, define descent of food into the stomach as movement
of food necessitated as a precondition of health, and we shall see
that in the quasi-syllogism (2) we are inferring that if walking
after dinner is to produce that by reference to which descent of
food into the stomach is defined (viz. health), it must produce
descent of food into the stomach.
The order of becoming in final causation, A. continues (23-6),
is the opposite of that in efficient causation. In the latter the
II. 11 645
middle term must come first ; in the former, C, the minor term,
must come first, and the final cause last. Here the type of
quasi-syllogism hinted at in 20-1 is correctly characterized. C,
the minor term (walking after dinner), happens first ; A, the final
cause and middle term (health), happens last; and B, the major
term (descent of food into the stomach), happens between the
two. But what does À. mean by saying that in efficient causation
the middle term must come first? In the last syllogism used to
illustrate efficient causation (in h18-2o) not the middle term B
(descent of food) but the minor term C (walking after dinner)
happens first. A. is now thinking not of that syllogism but of
the main syllogism used to illustrate efficient causation (in
336-58). There the minor term (the Athenians) was not an event
but a set of substances; A. therefore does not bring it into the
time reckoning, and in saying that the middle term happens first
means only that it happens before the major term.
A. has incidentally given an example of something that
happens both with a view to an end and as a result of necessity,
viz. the descent of food into the stomach, which is produced by
walking after dinner and is a means adopted by nature for the
production of health. He now (b27-9533) points out in general
terms the possibility of such double causation of a single event.
He illustrates this (1) by the passage of light through the pores
of a lantern. This may occur both because a fine-grained sub-
stance (light) must be capable of passing through pores which
are wider than its grains (A. adopts, as good enough in a mere
illustration of a general principle, Gorgias' theory, which is not
his own, of the propagation of light (cf. 88¢14-16 n.)), and because
nature desires to provide a means that will save us from stumbling
in the dark. A. illustrates the situation (2) by the case of thunder.
This may occur both because the quenching of fire is bound to
produce noise and— A. again uses for illustrative purposes a view
he does not believe in—to terrorize the inhabitants of Tartarus.
Such double causation is to be found particularly in the case
of combinations that nature brings into existence from time to
time or has permanently established (rots xarà φύσιν συνιστα-
μένοις kai συνεστῶσιν, 635). Natural causation is probably meant
to be distinguished from mathematical necessitation, which never
has purpose associated with it, and from the purposive action of
men, which is never necessitated. A study of various passages
in the De Partibus Animalium (6582-7, 663522-664*11, 67922530)
shows that A. considers the necessary causation to be the primary
causation in such cases, and the utilization for an end to be a sort
646 COMMENTARY
of afterthought on nature’s part (πῶς δὲ τῆς ἀναγκαίας φύσεως
ἐχούσης rois ὑπάρχουσιν ἐξ ἀνάγκης ἡ κατὰ τὸν λόγον φύσις ἕνεκά
του κατακέχρηται, λέγωμεν, 663>22-4).
Incidentally (94537-9523) A. distinguishes the natural necessity
of which he has been speaking from a form of necessity which is
against nature; this is illustrated by the difference between the
downward movement of stones which A. believes to be natural
to them and the upward movement which may be impressed upon
them by the action of another body—a difference which plays a
large part in his dynamics (cf. my edition of the Physics, pp. 26-
33).
From natural products and natural phenomena A. turns (95*3-6)
to consider things that are normally produced by purposive
action ; some of these, he says, are never produced by chance or
by natural necessity, but only by purposive action; others may
be produced either by purposive action or by chance—e.g. health
or safety. This point is considered more at length in Met. 1034*9—
21, where the reason for the difference is thus stated: αἴτιον δὲ
ὅτι τῶν μὲν ἡ ὕλη ἡ ἄρχουσα τῆς γενέσεως ἐν TH ποιεῖν καὶ γίγνεσθαί
τι τῶν ἀπὸ τέχνης, ἐν ἡ ὑπάρχει τι μέρος τοῦ πράγματος --ἡ μὲν
τοιαύτη ἐστὶν οἵα κινεῖσθαι ὑφ᾽ αὑτῆς ἡ δ᾽ οὔ, καὶ ταύτης ἡ μὲν ὡδὶ
οἷα τε ἡ δὲ ἀδύνατος. ‘Chance production is identical in kind with
the second half of the process of artistic production. The first
half, the νόησις, is here entirely absent. The process starts with
the unintended production of the first stage in the making, which
in artistic production is intended. This may be produced by
external agency, as when an unskilled person happens to rub
a patient just in the way in which a doctor would have rubbed
him ex arte, and thus originates the curative process. Or again,
it may depend on the initiative resident in living tissue; the sick
body may itself originate the healing process' (Aristotle's Meta-
physics, ed. Ross, i, p. cxxi).
Zabarella makes 953-6 the basis of a distinction between what
he calls the non-conjectural arts, like architecture and sculpture,
which produce results that nothing else can produce, and produce
them with fair certainty, and conjectural arts, like medicine or
rhetoric, which merely contribute to the production of their
results (nature, in the case of medicine, or the state of mind of
one's hearers, in that of rhetoric, being the other contributing
cause)—so that, on the one hand, these arts may easily fail to
produce the results they aim at, and on the other the causes
which commonly are merely contributory may produce the
results without the operation of art.
II. 11. 9458 — 9538 647
Finally (46-9), A. points out that teleology is to be found,
properly speaking, in these circumstances: (1) ἐν ὅσοις ἐνδέχεται
kai ὧδε καὶ ἄλλως, i.e. when physical circumstances alone do not
determine which of two or more events shall follow, when (2)
the result produced is a good one, and (3) the result produced is
not the result of chance. He adds that the teleology may be
either the (unconscious) teleology of nature or the (conscious)
teleology of art. Thus, as in Met. 1032*12-13, A. is working on the
assumption that events are produced by nature, by art (or, more
generally, by action following on thought), or by chance. The
production of good results by nature, and their production by art,
are coupled together as being teleological. With the present
rather crude account should be compared the more elaborate
theory of chance and of necessity which A. develops in the
Physics (cf. my edition, 38-44).
It is only by exercising a measure of goodwill that we can con-
sider as syllogisms some of the 'syllogisms' put forward by A.
in this chapter. But after all he does not use the word ‘syllogism’
here. What he says is that any of the four causes named can serve
as μέσον between the subject and the attribute, whose connexion
is to be explained. He had the conception, as his account of
the practical syllogism shows (E.N. 1144%31-3 of yàp συλλογισμοὶ
τῶν πρακτῶν ἀρχὴν ἔχοντές εἰσιν ᾿ἐπείδη τοιόνδε τὸ τέλος καὶ τὸ
ἄριστον᾽), of quasi-syllogisms in which the relations between terms,
from which the conclusion follows, are other than those of subject
and predicate; i.e. of something akin to the ‘relational inference’
recognized by modern logic, in distinction from the syllogism.
94°8. Ὅσων δ᾽ αἴτιον τὸ ἕνεκα τίνος. The editors write ἕνεκά
τινος, but the sense requires ἕνεκα τίνος as in 12 (cf. τὸ τίνος
ἕνεκα, * 23).
32-4. ὥσπερ εἰ... φοβῶνται, ‘as for instance if it thunders
both because when the fire is quenched there must be a hissing
noise, and (if things are as the Pythagoreans say) to intimidate
the inhabitants of Tartarus’. It seems necessary to insert ὅτι,
and this derives support from T. 52. 26 xai ἡ βροντή, διότι τε
ἀποσβεννυμένου krÀ., and E. 153. 11 διὰ τί βροντᾷ; ὅτι πῦρ dmo-
σβεννύμενον κτλ.
9576-8. μάλιστα δὲ... τέχνῃ. The received punctuation (ὅταν
μὴ ἀπὸ τύχης ἡ γένεσις 2. ὥστε τὸ τέλος ἀγαθὸν ἕνεκά του γίνεται καὶ
ἢ φύσει ἢ τέχνῃ) is wrong ; the comma after ἦ must be omitted, and
one must be introduced after ἀγαθόν. Further, τέλος must be
understood in the sense of result, not of end.
648 COMMENTARY
CHAPTER 12
The inference of past and future events
95 10. Similar effects, whether present, past, or future, have
similar causes, correspondingly present, past, or future. This
is obviously true in the case of the formal cause or definition
(e.g. of eclipse, or of ice), which is always compresent with that
whose cause it is.
22. But experience seems to show that there are also causes
distinct in time from their effects. Is this really so?
27. Though here the earlier event is the cause, we must reason
from the later. Whether we specify the interval between the
events or not, we cannot say 'since this has happened, this later
event must have happened’; for during the interval this would
be untrue.
35. And we cannot say 'since this has happened, this other
will happen'. For the middle term must be coeval with the major ;
and here again the statement would be untrue during the interval.
Pr. We must inquire what the bond is that secures that event
succeeds event. So much is clear, that an event cannot be con-
tiguous with the completion of another event. For the completion
of one cannot be contiguous with the completion of another,
since completions of events are indivisible limits, and therefore,
like points, cannot be contiguous ; and similarly an event cannot
be contiguous with the completion of an event, any more than
a line can with a point; for an event is divisible (containing an
infinity of completed events), and the completion of an event is
indivisible.
13. Here, as in other inferences, the middle and the major term
must be immediately related. The manner of inference is: Since
C has happened, A must have happened previously; If D has
happened, C must have happened previously; Therefore since
D has happened, A must have happened previously. But in
thus taking middle terms shall we ever reach an immediate
premiss, or will there (owing to the infinite divisibility of time)
always be further middle terms, one completed event not being
contiguous with another? At all events, we must start from an
immediate connexion, that which is nearest to the present.
25. So too with the future. The manner of inference is: If
D is to be, C must first be; If C is to be, A must first be; Therefore
if D is to be, A must first be. Here again, subdivision is possible
ad infinitum; yet we must get an immediate proposition as
starting-point.
II. 12 649
31. Inference from past to earlier past illustrated.
35. Inference from future to earlier future illustrated.
38. We sometimes see a cycle of events taking place; and this
arises from the principle that when both premisses are convertible
the conclusion is convertible.
96:8. Probable conclusions must have probable premisses ; for
if the premisses were both universal, so would be the conclusion.
17. Therefore there must be immediate probable premisses,
as well as immediate universal premisses.
A. starts this chapter by pointing out that if some existing
thing A is the cause (i.e. the adequate and commensurate cause)
of some existing thing B, A is also the cause of B's coming to
be when it is coming to be, was the cause of its having come to
be if it has come to be, and will be the cause of its coming to be
if it comes to be in the future. He considers first (414-24) causes
simultaneous with their effects, i.e. formal causes which are an
element in the definition of that whose causes they are, as 'inter-
position of the earth' is an element in the definition of lunar
eclipse as 'loss of light owing to the interposition of the earth'
(cf. ch. 8), or as 'total absence of heat' is an element in the
definition of ice as ‘water solidified owing to total absence of
heat'.
Jt is to be noted that, while in such cases the causes referred
to are elements in the formal cause (or definition) of that whose
cause they are, they are at the same time its efficient cause; for
formal and efficient causes are, as we have seen (ch. 11, intro-
ductory note), not mutually exclusive. What A. is considering
in this paragraph is in fact efficient causes which he considers
to be simultaneous with their effects.
From these cases A. proceeds (324—537) to consider causes that
precede their effects in time; and here we must take him to be
referring to the general run of material and efficient causes. He
starts by asking whether in the time-continuum an event past,
future, or present can have as cause another event previous to it,
as experience seems to show (ὥσπερ δοκεῖ ἡμῖν, 525). He assumes
provisionally an affirmative answer to this metaphysical question,
and proceeds to state a logical doctrine, viz. that of two past
events, and therefore also of two events still being enacted, or
of two future events, we can only infer the occurrence of the
earlier from that of the later (though even here the earlier is of
course the originative source of the later (#28-9)). (A) He con-
siders first the case of inference from one past event to another.
650 COMMENTARY
We cannot say “since event A has taken place, a later event B
must have taken place'—either after a definite interval, or without
determining the interval (231-4). The reason is that in the
interval (A. assumes that there is an interval, and tries to show
this later, in 63-12) it is untrue to say that the later event has
taken place; so that it can never be true to say, simply on the
ground that event A has taken place, that event B must have
taken place (34-5). So too we cannot infer, simply on the ground
that an earlier future event will take place, that a later future
event must take place (435-6).
(B) A. now turns to the question of inference from a past to
a future event (436). We cannot say ‘since A has taken place,
B will take place'. For (1) the middle term must be coeval with
the major, past if it is past, future if it is future, taking place if it
is taking place, existing if it is existing. A. says more than he
means here; for what he says would exclude the inference ofa
past event from a present one, no less than that of a future from
a past one. He passes to a better argument: (2) We cannot say
‘since A has existed, B will exist after a certain definite interval’,
nor even ‘since A has existed, B will sooner or later exist’; for
whether we define the interval or not, in the interval it will not
be true that B exists; and if A has not caused B to exist within
the interval, we cannot, simply on the ground that A has existed,
say that B ever will exist.
From the logical question as to the inferability of one event
from another, A. now turns (Pri) to the metaphysical question
what the bond is that secures the occurrence of one event after
the completion of another. The discussion gives no clue to A.’s
answer, and we must suppose that he hoped by attacking the
question indirectly, as he does in >3-37, to work round to an
answer, but was disappointed in this hope. He lays it down that
since the completion of a change is an indivisible limit, neither
a process of change nor a completion of change can be contiguous
to a completion of change (53-5). He refers us (bro-12), for a
fuller statement, to the Physics. The considerations he puts for-
ward belong properly to φυσικὴ ἐπιστήμη, and for a fuller dis-
cussion of them we must indeed look to the PAysics, especially to
the discussion of time in iv. 10-14 and of the continuous in vi.
In Phys. 227*6 he defines the contiguous (ἐχόμενον) as ὃ ἂν ἐφεξῆς
ὃν ἅπτηται. Le. two things that are contiguous must (1) be succes-
sive, having no third thing of the same kind between them (226534-
227*6), and (2) must be in contact, ie. having their extremes
together (226523); lines being in contact if they meet at a point,
II. 12 651
planes if they meet at a line, solids if they meet at a plane, periods
of time or events in time if they meet at a moment. Now the
completion of a change is indivisible and has no extremes (since
it occurs at a mornent, as A. proves in 23530-2367), just as a
point has not. It follows that two completions of change cannot
be contiguous (9554-6). Nor can a process of change be contiguous
to the completion of a previous change, any more than a line can
be contiguous to a point (66-9); for as a line contains an infinity
of points, a process of change contains an infinity of completions
of change (bg-1o)—a thesis which is proved in 236532-237?17.
From his assumption that there is an interval between two
events in a causal chain (434, ^1), and from his description of them
as merely successive (13), it seems that A. considers himself
to have proved that they are not continuous or even contiguous.
But this assumption rests on an ambiguity in the words yeyovds,
γενόμενον, γεγενημένον (which he treats as equivalent). He has
shown that two completions of change cannot be contiguous,
any more than two points, and that a process of change cannot
be contiguous to a completion of change, any more than a line
can be to a point. But he has not shown that two past processes
of change cannot be contiguous, one beginning at the moment at
which the other ends.
In inference from effect to cause (A. continues, 14), as in all
scientific inference («ai ἐν τούτοις, 515), there must be an immediate
connexion between our middle term and our major, the event
we infer from and the event we infer from it (bx4-15). Wherever
possible we must break up an inference of the form 'Since D
has happened, A must have happened’ into two inferences of the
form ‘Since D has happened, C must have happened’, ‘Since C
has happened, A must have happened’—C being the cause (the
causa cognoscendi) of our inference that A has happened (16-21).
But in view of the point we have proved, that no completion of
change is contiguous with a previous one, the question arises
whether we can ever reach two completions of change C and A
which are immediately connected (22-4). However this may be,
A. replies, we must, if inference is to be possible, start from an
immediate connexion, and from the first of these, reckoning back
from the present.
A. does not say how it is that, in spite of the infinite divisibility
of time, we can arrive at a pair of events immediately connected.
But the answer may be gathered from the hint he has given
when he spoke of becoming as successive (513). Events, as he has
tried to show, cannot be contiguous, but they can be successive;
652 COMMENTARY
there may be a causal train of events ACD such that there is no
effect of A between A and C, and no effect of C between C and
D, though there is a lapse of time between each pair; and then
we can have the two immediate premisses ‘C presupposes A,
D presupposes C', from which we can infer that D presupposes A.
So too with the inferring of one future event from another
(525-8); we can infer the existence of an earlier from that of a
later future event. But there is a difference. Speaking of past
events we could say ‘since C has happened’ (b16); speaking of
future events we can only say ‘tf C is to happen’ (29).
Finally, A. illustrates by actual examples (ἐπὶ τῶν ἔργων, 532)
inference from a past event to an earlier past event (b32-5), and
from a future imagined event to an earlier future event (35-7).
To the main discussion in the chapter, A. adds two further
points: (1) (b38—9627) he remarks that certain cycles of events
can be observed in nature, such as the wetting of the ground,
the rising of vapour, the formation of cloud, the falling of rain,
the wetting of the ground. . . . He asks himself the question how
this can happen. His example contains four terms, but the
problem can be stated more simply with three terms. The
problem then is: If C entails B and B entails A, under what
conditions will A entail C? He refers to his previous discussion
of circular reasoning. In Am. Pr. ii. 5 he has shown that if we
start with the syllogism All B is A, All C is B, Therefore all C
is A, we can prove the major premiss from the conclusion and
the converse of the minor premiss, and the minor premiss from
the conclusion and the converse of the major premiss. And in
An. Post. 7376-20 he has pointed out that any of the six proposi-
tions All B is A, All C is A, All B is C, AIC is B, All A is B,
All A is C can be proved by taking a suitable pair out of the other
five. This supplies him with his answer to the present problem.
A will entail C if the middle term is convertible with each of the
extreme terms; for then we can say B entails C, A entails B,
Therefore A entails C. (2) (9658-19) he points out that, since the
conclusion from two universal premisses (in the first figure) is
a universal proposition, the premisses of a conclusion which only
states something to happen for the most part must themselves
(i.e. both or one of them) be of the same nature. He concludes
that if inference of this nature is to be possible, there must be
immediate propositions stating something to happen for the most
part.
9528-9. ἀρχὴ 86 . . . γεγονότα. This is best interpreted (as
by P. 388. 4-8, 13-16, and E. 164. 34-165. 3) as a parenthetical
II. 12. 95*28 — 96°18 653
reminder that even if we infer the earlier event from the later,
the earlier is the originating source of the later. γεγονότα stands
for mpoyeyovóra.
b3-5. ἢ δῆλον... ἄτομα. γεγονός (or γενόμενον) here means
not ἃ past process of change; for that could not be said to be
indivisible. It means the completion of a past change, of which
A. remarks in Phys. 23635-7 that it takes place at a moment, i.e.
is indivisible in respect of time.
18. 6 ἐστιν ἀρχὴ τοῦ χρόνου. The now is the starting-point
of time in the sense that it is the point from which both past and
future time are reckoned; cf. Phys. 219>11 τὸ δὲ viv τὸν χρόνον
ὁρίζει, ἦ πρότερον kai ὕστερον, 220*4 καὶ συνεχής re δὴ ὁ χρόνος TH
νῦν, καὶ διήρηται κατὰ τὸ νῦν, and for A.’s whole doctrine of the
relation between time and the now cf. 218%6-220826, 233>33-234%9.
24. ὥσπερ ἐλέχθη, in 53-6.
24-5. ἀλλ᾽ ἄρξασθαί ye... πρώτου. A.’s language in P15 and
31 shows that the reading dz’ ἀμέσου is right. xai ἀπὸ τοῦ viv
πρώτου is ambiguous. It may mean (1) that we must start from
the present, ie. must work back from a recently past event to
one in the more remote past. Or more probably (so P. 394. 14,
An. 577. 24) (2) the whole phrase ἀπ᾽ ἀμέσου καὶ ἀπὸ τοῦ viv πρώτου
may mean ‘from a connexion that is immediate and is the first
of the series, reckoning back from the present’.
34. εἴπερ καὶ οἰκία γέγονεν. The sense requires this reading,
which is confirmed by E. 176. 19. The writer of the archetype of
our MSS. has been misled by λίθους γεγονέναι and θεμέλιον
γεγονέναι.
g6*1. ἐν τοῖς πρώτοις, i.e. in 7356--20 (cf. An. Pr. ii. 5).
18. ἀρχαὶ ἄμεσοι, ὅσα. ὅσα is in apposition to ἀρχαί.
CHAPTER 13
The use of division (a) for the finding of definitions
96:20. We have shown how the essence of a thing is set out
in the terms of a syllogism, and in what sense there is or is not
demonstration or definition of essence. Let us state how the
elements in a definition are to be searched for. Of the attributes
of a subject, some extend beyond it but not beyond its genus.
‘Being’, no doubt, extends beyond the genus to which ‘three’
belongs; but 'odd' extends beyond 'three' but not beyond its
genus.
32. Such elements we must take till we get a collection of
654 COMMENTARY
attributes of which each extends, but all together do not extend,
beyond the subject ; that must be the essence of the subject.
by. We have shown previously that the elements in the ‘what’
of a thing are true of it universally, and that universal attributes
of a thing are necessary to it; and attributes taken in the above
manner are elements in the ‘what’; therefore they are necessary
to their subjects.
6. That they are the essence of their subjects is shown as
follows: If this collection of attributes were not the essence of
the subject, it would extend beyond the subject ; but it does not.
For we may define the essence of a thing as the last predicate
predicable in the ‘what’ of the individual instances.
15. In studying a genus one must (1) divide it into its primary
infimae spectes, (2) get the definitions of these, (3) get the category
to which the genus belongs, (4) study the special properties in
the light of the common attributes.
2x. For the properties of the things compounded out of the
primary infimae spectes will follow from the definitions, because
definition and what is simple is the source of everything, and the
properties belong only to the simple species per se, to the complex
species consequentially.
25. The method of division according to differentiae is useful
in the following way, and in this alone, for inferring the ‘what’ of
a thing. (1) It might, no doubt, seem to be taking everything
for granted; but it does make a difference which attribute we
take before another. If every successive species, as we pass
from wide to narrow, contains a generic and a differential element,
we must base on division our assumption of attributes.
35- (2) It is the only safeguard against omitting anything that
belongs to the essence. If we divide a genus not by the primary
alternatives but by alternatives that come lower, not the whole
genus will fall into this division (not every animal, but only every
winged animal, is whole-winged or split-winged). If we divide
gradually we avoid the risk of omitting anything.
97*6. (3) The method is not open to the objection that one who
is defining by division must know everything. Some thinkers
say we cannot know the difference between one thing and others
without knowing each of these, and that we cannot know each
of these without knowing its difference from the original thing;
for two things are or are not the same according as they are or
are not differentiated. But in fact (4) many differences attach,
but not per se, to things identical in kind.
14. And (b) when we take opposites and say 'everything falls
Il. 13 655
here or here', and assume that the given thing falls in a particular
one of the divisions, and know this one, we need not know all the
other things of which the differentiae are predicated. If one
reaches by this method a class not further differentiated, one has
the definition ; and the statement that the given thing must fall
within the division, if the alternatives are exhaustive, is not an
assumption.
23. To establish a definition by division we must (x) take
essential attributes, (2) arrange them properly, (3) make sure
that we have got them all. (x) is secured by the possibility of
establishing such attributes by the topic of 'genus'.
28. (2) is secured by taking the first attribute, i.e. that which
is presupposed by all the others; then the first of the remaining
attributes; and so on.
35. (3) is secured by taking the differentiation that applies to
the whole genus, assuming that one of the opposed differentiae
belongs to the subject, and taking subsequent differentiae till
we reach a species not further differentiable, or rather one which
(including the last differentia) is identical with the complex term
to be defined. Thus there is nothing superfluous, since every
attribute named is essential to the subject; and nothing missing,
since we have the genus and all the differentiae.
by, In our search we must look first at things exactly like, and
ask what they have in common; then at other things like in
genus to the first set, and in species like one another but unlike
the first set. When we have got what is common to each set, we
ask what they all have in common, till we reach a single definition
which will be the definition of the thing. If we finish with two
or more definitions, clearly what we are inquiring about is not
one thing but more than one.
rs. E.g. we find that certain proud men have in common
resentment of insult, and others have in common indifference to
fortune. If these two qualities have nothing in common, there
are two distinct kinds of pride. But every definition is wn?versal.
28. It is easier to define the particular than the universal, and
therefore we must pass from the former to the latter; for am-
biguities more easily escape notice in the case of universals than
in that of infimae species. As in demonstrations syllogistic
validity is essential, clearness is essential in definitions; and this
is attained if we define separately the meaning of a term as
applied in a single genus (e.g. ‘like’ not in general but in colours
or in shapes, or 'sharp' in sound), and only then pass to the
general meaning, guarding thus against ambiguity. To avoid
656 COMMENTARY
reasoning in metaphors, we must avoid defining in metaphors
and defining metaphorical terms.
In this chapter A. returns to the subject of definition. In
chs. 3-7 he has considered it aporematically and pointed out
apparent objections to the possibility of ever establishing a defini-
tion of anything. In chs. 8-10 he has pointed out the difference
between the nominal definition, whether of a subject or of an
attribute, and the causal definition of an attribute, and has
shown that, while we cannot demonstrate the definition of an
attribute, we can frame a demonstration which may be recast
into the form of a definition. He has also intimated (9321-4) that
a non-causal definition must either be taken for granted or made
known by some method other than demonstration. This method
he now proceeds to expound. In 96*24~14 he points out that the
definition of a species must consist of those essential attributes
of the species which singly extend beyond it but collectively do
not. In Prs-25 he points out that a knowledge of the definitions
of the simplest species of a genus may enable us to deduce the
properties of the more complex species. In b25-9756 he points
out how the method of division, which, considered as an all-
sufficient method, he has criticized in ch. 5, may be used as a
check on the correctness of the application of his own inductive
method. In 9757-29 he points out the importance of defining
species before we define the genus to which they belong.
96720-2. Πῶς μὲν οὖν... πρότερον. The reference is to chs. 8
and 9. πῶς τὸ τί ἐστιν εἰς τοὺς ὅρους ἀποδίδοται (‘is distributed
among the terms’) refers to the doctrine stated in ch. 8 about the
definition of attributes, like eclipse. In the demonstration which
enables us to reach a complete causal definition of an attribute,
the subject which owns the attribute appears as minor term, the
attribute as major term, the cause as middle term; ‘the moon
suffers eclipse because it suffers the interposition of the earth.’
28-9. ὥσπερ τὸ dv... ἀριθμῷ is an illustration of the kind of
ἐπὶ πλέον ὑπάρχειν which A. does not mean, ie. extension not
merely beyond the species but beyond the genus; this is merely
preliminary to his illustration of the kind of ἐπὶ πλέον ὑπάρχειν
he does mean (429-32).
36-7. τὸ πρῶτον... .. ἀριθμῶν, i.e. three is primary both in the
sense that it is not a product of two numbers and in the sense
that it is not a sum of two numbers; for in Greek mathematics
1 is not a number, but ἀρχὴ ἀριθμοῦ. Cf. Heath, Mathematics in
Anstotle, 83-4.
IT. 13. 96*20 — "25 657
by-5. ἐπεὶ δὲ... ταῦτα. The MSS. have in >2 ὅτι ἀναγκαῖα μέν.
With this reading τὰ καθόλου δὲ ἀναγκαῖα spoils the logic of the
passage, since without it we have the syllogism ‘Elements in
the '*what" are necessary, The attributes we have ascribed to the
number three are elements in its "what", Therefore they are
necessary to it’; rà καθόλου δὲ ἀναγκαῖα contributes nothing to
the proof. The ancient commentators saw this, and say that δέ
must be interpreted as if it were yáp. Then we get a prosyllogism
to support the major premiss above: 'Universal attributes are
necessary, (Elements in the "what" are universal,» Therefore
elements in the ''what'" are necessary.’ δέ cannot be interpreted
as ydp; but we might read γάρ for δέ. This, however, would not
cure the sentence; for it is not true that τῇ τριάδι... λαμβανόμενα
has been proved previously (ἐν τοῖς ἄνω ^2). What the structure of
the sentence requires is (1) two general principles that have been
proved already, distinguished by μέν and δέ, and (2) the applica-
tion of these to the case in hand. The sentence can be cured only
by reading καθόλου for ἀναγκαῖα in 52 and supposing the eye of
the writer of the archetype to have been caught by ἀναγκαῖα in
the line below. We then get : ‘(1) We have proved (a) that elements
in the "what" are universal, (b) that universal elements are
necessary. (2) The attributes we have ascribed to the number
three are elements in its "what". Therefore (3) these elements
are necessary to the number three.'
The reference in ἐν τοῖς ἄνω is to 73*34—7, >25-8.
I2. ἐπὶ rots ἀτόμοις. The ταῖς of the MSS. is due to a mechani-
cal repetition of the ταῖς in Pro. E. 189. 17 has τοῖς.
ἔσχατος τοιάυτη κατηγορία. The form ἔσχατος as nom. sing.
fem. is unusual, but occurs in Arat. 625, 628.
15-25. Χρὴ δέ... ἐκεῖνα. Most of the commentators hold
that while in 424-14 A. describes the inductive method of 'hunt-
ing’ the definition of an imfima species, he here describes its use
in hunting the definition of a subaltern genus, i.e. of a class inter-
mediate between the categories (Prg-20) and the infima species.
They take A. to be describing the obtaining of such a definition
inductively, by first dividing the genus into its smfima species
(615-17), then obtaining inductively the definitions of the infimae
spectes (17-19), then discovering the category to which the genus
belongs (19-20), and finally discovering the differentiae proper
to the genus (i.e. characterizing the whole of it) by noting those
common to the species (b2o-1); the last step being justified by
the remark that the attributes of the genus composed of certain
infimae species follow from the definitions of the species, and
4985 vu
658 COMMENTARY
belong to the genus because they belong directly to the species
(b21-5). There are great difficulties in this interpretation. (1) The
interpretation put upon τὰ ἴδια πάθη θεωρεῖν διὰ τῶν κοινῶν
πρώτων (20-1) is clearly impossible. The words suggest much
rather the deducing of the peculiar consequential attributes of
different species (πάθη suggests these rather than differentiae)
from certain attributes common to all the species. (2) The inter-
pretation of rots συντιθεμένοις ἐκ τῶν ἀτόμων (P21) as meaning the
genera, and of rots ἁπλοῖς (623) as meaning the species, while not
impossible, is very unlikely; A. would be much more likely to
call the genus simple and the species complex (cf. 1oob2 n.).
συμβαίνοντα, like πάθη, suggests properties rather than differentiae,
and the contrast A. expresses is one between συμβαίνοντα and
ὁρισμοί, not between the ὁρισμός of a genus and the ὁρισμοί of
its species. It might be objected that a reference to the deduction
of properties would be out of place in a chapter that is concerned
only with the problem of definition ; the answer is that while the
chapter as a whole is concerned with definition, this particular
section concerns itself with the question what method of approach
to the problem of definition is the best prelude to the scientific
study of a subject-genus (Prs)— which study will of course aim
(on A.'s principles) at deducing the properties of the genus from
its definition. (3) the immediately following section on the utility
of division (25-976) is relevant to the defining of infimae species
(ἄνθρωπος, 96534), not of genera.
Maier (2 a. 404 n. 2) takes τοῖς συντιθεμένοις ἐκ τῶν ἀτόμων (921)
to mean the individuals, the συνθεταὶ οὐσίαι, composed of the
infima species - matter ; but this again is unlikely.
Pacius provides the correct interpretation. He supposes rà
ἄτομα τῷ εἴδει τὰ πρῶτα (16) to mean not the znfimae species of
the genus, in general, but the primary tnfimae species. His sug-
gestion is that A. has in mind the fact that in certain genera
some species are definitely simpler than others, and is advocating
the study of the definitions of these as an element in the study
of a whole genus—in the attempt to deduce the properties of the
other species from the primary attributes common to the primary
and the complex species (rà ἴδια πάθη θεωρεῖν διὰ τῶν κοινῶν
πρώτων, 20-1). A.’s examples agree with this view. Of the
infimae species of number (i.e. the cardinal numbers) he names
only 2 and 3, precisely the two that are designated as πρῶτα
in ?35-^r. Of the species of line he takes the two simplest, the
straight line (that out of which all crooked lines may be said to
be compounded (συντιθεμένοις, 521)) and the circle, which A.
II. 13. 96526 — 97411 659
doubtless thought of as the prototype of all curved lines. Of the
species of angle he names only the right angle, by reference to
which the acute and the obtuse angle are defined. His idea would
then be, for instance, that by studying the definition of the
number two and that of the number three we shall be able to
deduce the properties of the number six as following from the
definitions of its two factors. A better example for his purpose
would be the triangle, which is the simplest of rectilinear figures,
and from whose definition the properties of all other rectilinear
figures are derived.
26. εἴρηται ἐν rois πρότερον, i.e. in ch. 5 and in An. Pr. i. 31.
32-5. εἰ yap... αἰτεῖσϑαι. This sentence is difficult. In b28-
3o A. has pointed out the objection to the Platonic method of
definition by division which he has stated at length in ch. 5—that
it has at each stage to take for granted which of two alternative
differentiae belongs to the subject. In b3o-2 he points out that
division is nevertheless useful as securing that the elements in
a definition are stated in proper order, passing continuously from
general to particular. In 532-5, though the sentence is introduced
by ydp, he seems to be harking back to the objection stated in
b28-30, and the commentators interpret him so; yet he can
scarcely be so inconsequent as this. We must give a different
turn to the meaning of the sentence, by interpreting it as follows:
‘if everything consists of a generic and a differential element,
and "animal, tame", as well as containing two such elements, is
a unity, and out of this and a further differentia man (or whatever
else is the resultant unity) is formed, to get a correct definition
we must assume its elements not higgledy-piggledy (ὥσπερ dv
εἰ ἐξ ἀρχῆς ἐλάμβανέ τις ἄνευ τῆς διαιρέσεως, P29) but on the basis
of division.’ The stress in fact is on διελόμενον, not on αἰτεῖσθαι.
9776-11. οὐδὲν δὲ... τούτου. T. 58. 4, P. 4o5. 27, E. 202. 17
refer the implicit objection ('you cannot define by the help of
division without knowing all existing things’) to Speusippus. An.
584. 17 does the same, and quotes Eudemus as his authority. The
objection may be interpreted in either of two ways. Let A be
the thing we wish to define, and B, C, D the things it is to be
distinguished from. The argument may be (1) 'We cannot know
the differences between 4 and B, C, D without first knowing
B, C, D; but we cannot know B, C, D without first knowing the
differences between them and A’, so that there is a problem like
that of the hen and the egg. Or (2) it may be 'We cannot know
the differences between A and B,C, D without knowing B,C, D;
and we cannot know A without knowing its differences from
660 COMMENTARY
B,C, D; therefore we cannot know A without knowing B, C, D.'
The first interpretation has the advantage that it makes ἕκαστον
throughout refer to B, C, D, while the other makes it refer to
B, C, D in *g and to A in bro. On the other hand, the second
interpretation relates the argument more closely to the thesis
mentioned in 56—, that you cannot know one thing without
knowing everything else.
P. and E. interpret Speusippus’ argument as a sceptical attack
on the possibility of definition and of division; but Zeller
(ii. a^. 996 n. 2) remarks truly that an eristic attack of this kind
is not in keeping with what we know about Speusippus. His point
seems rather to have been an insistence on the unity of knowledge
and the necessity for a wide knowledge of facts as a basis of
theory. As Cherniss remarks (Ar.’s Criticism of Plato and the
Academy, i. 60), ‘for Plato . . . the independent existence of the
ideas furnished a goal for the search conducted by means of
“‘division’’ which Speusippus no longer had, once he had aban-
doned those entities. Consequently, the essential nature of any
one concept must for him exist solely in its relations of likeness
and difference to every other concept, relations which, while for
the believer in ideas they could be simply necessary implications
of absolute essences, must with the loss of the ideas come to con-
stitute the essential nature of each thing. The principle of ὁμοιότης,
the relations expressed by ταὐτόν and ἕτερον, changed then from an
heuristic method to the content of existence itself.’ Cf. the whole
passage ib. 59-63 for the difference between the attitudes of Plato,
Speusippus, and A. to the process of division.
II-14. οὐ yap... αὑτά, i.e. there are many separable acci-
dents which belong to some members of a species and not to
others, while leaving their definable essence the same.
22. εἴπερ ἐκείνου διαφορά éors.* The sense demands not ἔσται
but ἐστι, which seems to have been read by P. (408. 20) and E.
(207. 19): ‘if the differentiation is a differentiation of the genus
in question, not of a subordinate genus’.
26-8. ἔστι δὲ... κατασκευάσαι. A. has shown that a defini-
tion cannot be scientifically proved to be correct (chs. 4, 7), which
follows from the fact that the connexion between a term and its
definition is immediate. But just as an accident can be estab-
and this can be done διὰ τοῦ γένους, i.e. by using the τόποι proper
to the establishment of the genus to which the subject belongs
(for which see Top. iv); for the differentiae are to be established
by the same τόποι as the genus (Top. 101^17-19).
II. 13. 97*11 —533 661
37-9. τοῦ δὲ τελευταίου... τοῦτο. The first clause is mis-
leading, since it suggests that in defining any species we must
reach a complex of genus and differentiae that is not further
differentiable. This would be untrue; for it is only if the species
is an infima species that this condition must be fulfilled. The
second clause supplies the necessary correction.
by-2, πάντα yap... τούτων. πάντα τούτων seems to be used,
as E. 212. 32-3 says, in the sense of ἕκαστον τούτων, as we say ‘all
of these’. The lexicons and grammars, so far as I know, quote
no parallels to this.
3-4. γένος μὲν οὖν... προσλαμβανόμενον, i.e. we may treat
as the genus to which the species belongs either the widest genus,
with which we started, or the genus next above the species, got
by combining the widest genus with the subsequently discovered
differentiae.
9-10. αὑτοῖς μὲν ταὐτά. The sense requires αὑτοῖς, which is
presupposed by E.’s πρὸς ἄλληλα (213. 32).
15-25. olov λέγω... μεγαλοψυχίας. A.’s classical description
of μεγαλοψυχία is in E.N. 1123*34-1125*35. He does not there dis-
tinguish two types; but the features of his account which repel
modem sympathies correspond roughly to τὸ μὴ ἀνέχεσθαι ὑβριζό-
μενοι, and those which attract us to τὸ ἀδιάφοροι εἶναι εὐτυχοῦντες
xai ἀτυχοῦντες.
17-18. olov εἰ ᾿Αλκιβιάδης... ὁ Αἴας. This is a nice example
of Fitzgerald’s Canon (W. Fitzgerald, A Selection from the Nic.
Eth. of A. 163-4), which lays it down that it is A.’s general prac-
tice to use the article before proper names only when they are
names of characters in a book. ὁ AyiAdeds xai ὁ Alas means
‘Homer’s Achilles and Ajax’. Cf. I. Bywater, Cont. to the Textual
Criticism of A.’s Nic. Eth. 52, and my edition of the Metaphysics,
i, pp. xxxix-xli.
26—7. αἰεὶ δ᾽... ἀφορίσας. This goes closely with what has
gone before. Every definition applies universally to its subject ;
therefore a definition that applies only to some μεγαλόψυχοι is
not the definition of μεγαλοψυχία.
28-39. ῥᾷόν re... μεταφοραῖς. In b7-27 A. has shown the
advantage of working from particular instances upwards, in our
search for definition, viz. that it enables us to detect ambiguities
in the word we are seeking to define. Here he makes a similar
point by saying it is easier to work from the definition of the
species (τὸ καθ᾽ ἕκαστον, P28) to that of the genus, rather than
vice versa.
33. διὰ τῶν καθ᾽ ἕκαστον εἰλημμένων. In view of hr2 we should
662 COMMENTARY
read εἰλημμένων, which seems to have been read by E. (220. 33,
221. II, 222. 14, 18, 25, 36, 223. 13, 21, 22). In the MSS. the com-
moner word replaced the rarer.
34-5. olov τὸ ὅμοιον... . . σχήμασι. ‘Like’ does not mean the
same when applied to colours and when applied to figures
(99*11—15).
CHAPTER 14
The use of division (b) for the orderly discussion of problems
g8*1. In order to formulate the propositions to be proved, we
must pick out the divisions of our subject-matter, and do it in
this way: we must assume the genus common to the various
subjects (e.g. animal), and discover which of the attributes belong
to the whole genus. Then we must discover which attributes
belong to the whole of a species immediately below the genus
(e.g. bird), and so on. Thus if A is animal, B the attributes com-
mon to every animal, C, D, E, the species of animal, we know why
B belongs to D, viz. through A. So too with the connexion of
C or E with B. And so too with the attributes proper to classes
lower than A.
13. We must pick out not only common nouns like ‘animal’
but also any common attributes such as ‘horned’, and ask (1)
what subjects have this attribute, and (2) what other attributes
accompany this one. Then the subjects in (1) will have the
attributes in (2) because these subjects are horned.
20. Another method of selection is by analogy. There is no
one name for a cuttle-fish's pounce, a fish's spine, and an animal's
bone, but they have common properties which imply the posses-
sion of a common nature.
Zabarella maintains that this chapter is concerned with advice
not as to the solution of προβλήματα (with which chs. 15-18 are
concerned), but as to their proper formulation; his reason being
that if you say (19-11) Ὁ is B because A is B and C is an A’,
you are not giving a scientific demonstration because in your
minor premiss and your conclusion the predicate is wider than the
subject. You have not solved the real problem, viz. why B belongs
to A, but have only reduced the improper question why C is B
to the proper form ‘why is A B?'
This interpretation might seem to be an ultra-refinement ; but
it is justified by A.’s words, πρὸς τὸ ἔχειν τὰ προβλήματα. The
object in view is not that of solving the problems, but that of
II. 13. 97534— 14. 9821 663
having them in their truly scientific form. What he is doing
in this chapter is to advise the scientific inquirer to have in his
mind a 'Porphyry's tree' of the genera and species included in
his subject-matter, and to discover the widest class, of the whole
of which a certain attribute can be predicated—this widest class
then serving to mediate the attribution of the attribute to classes
included in the widest class. He further points out that some-
times (21—12) ordinary language furnishes us with a common name
for the subject to which the attribute strictly belongs, sometimes
(413-19) it has only a phrase like ‘having horns’, and sometimes
(320-3) where several subjects have an attribute in common, we
cannot descry and name the common nature on which this depends
but can only divine its presence. The chapter expresses, though
in very few words, a just sense of the extent to which language
helps us, and of the point at which it fails us, in our search for the
universals on which the possession of common properties depends.
I. Düring points out in Aristotle’s De Partibus Animalium:
Critical and Literary Commentaries, 109-14, that Aristotle's four
main discussions of the problem of classification— Tof. vi. 6,
An. Post. ii. 14, Met. Z. 12, and De Part. An. 1. 2-4—show a
gradual advance from the Platonic method of a prtort dichotomy
to one based on empirical study of the facts.
9871-2. Πρὸς δὲ τὸ ἔχειν... ἐκλέγειν. In *1 λέγειν, and in *2
διαλέγειν, is the reading with most MS. support. But A. seems
nowhere else to use διαλέγειν, while he often uses ἐκλέγειν (e.g. in
the similar passage An. Pr. 43511) ; and ἐκλέγειν derives some sup-
port from 320. Further, ἐκλέγειν... οὕτω δὲ ἐκλέγειν would be
an Aristotelian turn of phrase. I therefore read éxAéyew in both
places, with Bekker.
I. τάς Te ἀνατομὰς καὶ τὰς διαιρέσεις. A. does not elsewhere
use ἀνατομή or ἀνατέμνειν metaphorically, and Plato does not use
the words at all. But A. once (Met. 1038428), and Plato once,
(Polit. 2613) use τομή of logical division, and that is probably
what is meant here, there being no real distinction between
dvarouds and διαιρέσεις. Mure suggests that ἀνατομή means ‘that
analysis of a subject, for the purpose of eliciting its properties,
which would precede the process of division exhibiting the true
generic character in virtue of which the subject possesses those
properties’. But if A. had meant this, he would probably have
devoted some words to explaining the distinction between the
two things.
T. 59. 15-16, 25-6, P. 417. 6-17, E. 224. 21-5 suppose the reference
to be to literal dissection (in which sense A. uses dvaréuvew and
664 COMMENTARY
ἀνατομή elsewhere). But such a reference would not be natural
in a purely logical treatise; it would apply only to biological
problems, not to problems in general, and it is ruled out by the
fact that the words which follow describe a purely logical pro-
cedure.
I2. ἐπὶ τῶν κάτω. n's reading κάτω is clearly preferable to
ἄλλων, which has crept in by repetition from the previous clause.
16-17. olov τοῖς κέρατα ἔχουσι... εἶναι. In Part. An. 663b31-
664*3 A. explains the fact that animals with horns have no front
teeth in the upper jaw (that is what μὴ ἀμφώδοντ᾽ εἶναι means;
cf. H.A. so1312-13) as due to the ‘law of organic equivalents’
(Ogle, Part. An. ii. 9 n. 9), later formulated by Goethe in the words
"Nature must save in one part in order to spend in another.' In
Pari. An. 674222-'15 he explains the fact that horned animals
have a third stomach (ἐχῖνος) by the principle of compensation.
Because they have horns they have not front teeth in both jaws;
and because of this, nature gives them an alternative aid to
digestion.
CHAPTER 15
One middle term will often explain several properties
98*24. (1) Problems are identical in virtue of having the same
middle term. In some cases the causes are the same only in
genus, viz. those that operate in different subjects or in different
ways, and then the problems are the same in genus but different
in species.
29. (2) Other problems differ only in that the middle term of
one falls below that of the other in the causal chain; e.g. why does
the Nile rise in the second half of the month? Because this half
is the stormier. But why is it the stormier? Because the moon
is waning. The stormy weather falls below the waning of the
moon in the causal chain.
In the previous chapter A. has shown that problems of the
form ‘why is C B?', ‘why is D B?’, ‘why is E B?' may be reduced
to one by finding a genus A of which C, D, and E are species,
and the whole of which has the attribute B. Here various
problems have a common predicate. In the present chapter he
points out that problems with different predicates (and sometimes
with different subjects) may meet through being soluble (1) by
means of the same middle term, or (2) by means of middle terms
of which one is ‘under’ the other. (1) (324-9) ἀντιπερίστασις (defined
11. 14. 98412 — 15. 984832 665
thus by Simpl. Phys. 1350. 31--ντιπερίστασις δέ ἐστιν ὅταν é£o-
θουμένου τινὸς σώματος ὑπὸ σώματος ἀνταλλαγὴ γένηται τῶν τόπων,
καὶ τὸ μὲν ἐξωθῆσαν ἐν τῷ τοῦ ἐξωθηθέντος στῇ τόπῳ, τὸ δὲ ἐξωθηθὲν
τὸ προσεχὲς ἐξωθῇ καὶ ἐκεῖνο τὸ ἐχόμενον, ὅταν πλείονα 4, ἕως av τὸ
ἔσχατον ἐν τῷ τόπῳ γένηται τοῦ πρώτου ἐξωθήσαντος) might be used
to explain the flight of projectiles (Phys. 215*15, 266927—267219),
the action of heat and cold on each other (Meteor. 34852—349*9),
the mutual succession of rain and drought (ib. 36o0b30—361*3),
the onset of sleep (De Somno 457*33-b2, 458*25-8); cf. also
Probl. 867^31—3, 909322—6, 962%1-4, 963*5-12. In certain cases, A.
adds (9825-9), as in that of ἀνάκλασις (and the remark would no
doubt apply also to ἀντιπερίστασις), the middle term, and there-
fore the problem, is only generically identical, while specifically
different. (2) (529-34) (à) Why does the rising of the Nile (A)
accompany the second half of the month (D)? Because the Nile's
rising (4) accompanies stormy weather (B), and stormy weather
(B) accompanies the second half of the month (D). (b Why
does stormy weather (B) accompany the second half of the
month (D)? Because stormy weather (B) accompanies a waning
moon (C), and a waning moon (C) accompanies the second half
of the month (D).
98'29-30. τὰ δὲ... προβλημάτων. τὰ δέ answers to rà μέν in
424, and we therefore expect A. to mention a second type of case
in which two problems ‘are the same’. He actually mentions a
type of case in which two problems differ. But the carelessness
is natural enough, since in fact the two problems are partly the
same, partly different.
It will be seen from the formulation given above that the
middle term used in solving the first problem (B) is in the chain
of predication 'above' that used in solving the second (C), i.e.
predicable of it (τὸ B ὑπάρχει τῷ I, A. would say). But when A.
says (329—30) τῷ τὸ μέσον ὑπὸ τὸ ἕτερον μέσον εἶναι he is probably
thinking of the μέσον of the first problem as falling below that of
the second. ὑπὸ τὸ ἕτερον μέσον means not ‘below the other
middle term in the chain of predication’ but ‘below it in the chain
of causation’; a waning moon produces stormy weather.
32. ὁ pets. This form, which n has here, is apparently the
only form of the nominative singular that occurs in A. (G.A.
77723) or in Plato (Crat. 409 c 5, Tim. 39 € 3).
666 COMMENTARY
CHAPTER 16
Where there 1s an attribute commensurate with a certain subject,
there must be a cause commensurate with the attribute
98*35. Must the cause be present when the effect is (since if the
supposed cause is not present, the cause must be something else) ;
and must the effect be present when the cause is?
b4. If each entails the other, each can be used to prove the
existence of the other. If the effect necessarily accompanies the
cause, and the cause the subject, the effect necessarily accom-
panies the subject. And if the effect accompanies the subject,
and the cause the effect, the cause accompanies the subject.
16. But since two things cannot be causes of each other (for
the cause is prior to the effect ; e.g. the interposition of the earth
is the cause of lunar eclipse and not vice versa), then since proof
by means of the cause is proof of the reasoned fact, and proof
by means of the effect is proof of the brute fact, one who uses the
latter knows that the cause is present but not why it is. That
eclipse is not the cause of the interposition of the earth, but vice
versa, is shown by the fact that the latter is included in the
definition of the former, so that evidently the former is known
through the latter and not vice versa.
25. Or can there be more than one cause of the same thing?
If the same thing can be asserted immediately of more than one
thing, e.g. A of B and of C, and B of D, and C of E, then A will
belong to D and E, and the respective causes will be B and C.
Thus when the cause is present the effect must be, but when the
effect is present a cause of it but not every cause of it must be
present.
32. No: since a problem is always universal, the cause must
be a whole and the effect commensurately universal. E.g. the
shedding of leaves is assigned to a certain whole, and if there are
species of this, it is assigned to these universally, to plants or to
plants of a certain kind, and therefore the middle term and the
effect must be coextensive. If trees shed their leaves because of
the congealing of the sap, then if a tree sheds its leaves there must
be congealing, and if there is congealing (sc. in a tree) the leaves
must be shed.
98*35-54. Περὶ δ᾽ αἰτίου... φυλλορροεῖ. This passage is re-
duced to order by treating ὥσπερ εἰ... αὐτῶν as parenthetical,
and the rest of the sentence as asking two questions, Does effect
II. 16. 98435 — "38 667
entail cause? and Does cause entail effect? If both these things
are true, it follows that the existence of each can be proved from
the existence of the other (54-5).
br6-2r. εἰ δὲ... οὔ. Bonitz (Ar. Stud. ii, iii, 79) isright in
pointing out that this is one sentence, with a colon or dash (not,
as in the editions, a full stop) before εἰ in Pig. The parenthesis
ends with ἐκλείπειν (19), not with αἴτιον (17).
17. τὸ yàp atriov . . . αἴτιον. πρότερον means ‘prior in nature’,
not ‘prior in time’; for A. holds that there are causes that are
simultaneous with their effects ; cf. 9514-24.
22-3. ἐν yàp τῷ Àóyo . . . μέσῳ, cf. 9353-7.
25-31. Ἤ ἐνδέχεται... οὐ μέντοι wav. A. raises here the pro-
blem whether there can be plurality of causes, and tentatively
answers it in the affirmative. xai γὰρ εἰ (P25) does not mean ‘for
even if'; it means 'yes, and if', as in examples from dialogue
quoted in Denniston, The Greek Particles, 1og-1o. The content of
525-31, summarized, is ‘Can there be more than one cause of
one effect? Yes, and if the same predicate can be affirmed im-
mediately of more than one subject, this must be so.'
32-8. ἢ εἰ ἀεὶ... φυλλορροεῖν. This is A.'s real answer to the
question whether there can be plurality of causes. A 'problem',
ie. a proposition such as science seeks to establish, is always
universal, in the sense explained in i. 4, viz. that the predicate
is true of the subject κατὰ παντός, καθ᾽ αὑτό, and ἧ αὐτό (in virtue
of the subject's being precisely what it is). It follows that the
premisses must be universal; the cause, which is the subject of
the major premiss, must be ὅλον τι, the whole and sole cause of
the effect, which must in turn attach to it καθόλου (32-3). E.g.
if we ask what is the cause of deciduousness, we imply that there
is a class of things the whole of which, and nothing but which,
suffers this effect, and therefore that there is a cause which ex-
plains the suffering of this effect by this whole class and by noth-
ing else, and must therefore be coextensive with the effect (635-6).
Thus a system of propositions such as is suggested in ?26—9 cannot
form a scientific demonstration. A cannot be a commensurately
universal predicate of B and I’, but only of something that in-
cludes them both, say Z; and this will not be a commensurately
universal predicate of 4 and E, but only of that which includes
them both, say H; the demonstration will be ‘All Z and nothing
else is A, All H and nothing else is Z, Therefore all H and nothing
else is A’; and we shall have proved not only that but also pre-
cisely why all H and nothing else is A.
668 COMMENTARY
CHAPTERS 17, 18
Different causes may produce the same effect, but not in things
specifically the same
9951. Can there be more than one cause of the occurrence of
an attribute in all the subjects in which it occurs? If there is
scientific proof, there cannot; if the proof is from a sign or fer
accidens, there can. We may connect the attribute with the
subject by means of a concomitant of either; but that is not
regarded as scientific. If we argue otherwise than from a con-
comitant, the middle term will correspond to the major: (a) If
the major is ambiguous, so is the middle term. (b) If the major
is a generic property asserted of one of the species to which it
belongs, so is the middle term.
8. Example of (δ).
11. Example of (a).
15. (c) If the major term is one by analogy, so is the middle
term.
16. The effect is wider than each of the things of which it can
be asserted, but coextensive with all together; and so is the
middle term. The middle term is the definition of the major
(which is why the sciences depend on definition).
25. The middle term next to the major is its definition. For
there will bea middle term next to the particular subjects, assigning
a certain characteristic to them, and a middle connecting this
with the major.
30. Schematic account. Suppose A to belong to B, and B to
belong to all the species of D but extend beyond each of them.
Then B will be universal in relation to the several species of D
(for an attribute with which a subject is not convertible may be
universal to it, though only one with which the subject as a whole
is convertible is a primary universal to it), and the cause of their
being A. So A must be wider than B; else A might as well be
the cause of the species of D being B.
37. If now all the species of E have the attribute A, there will
be a term C which connects them with it. Thus there may be
more than one term explaining the occurrence of the same
attribute, but not its occurrence in subjects specifically the same.
by, If we do not come forthwith to immediate propositions—
if there are consecutive middle terms—there will be consecutive
causes. Which of these is the cause of the particular subject's
having the major as an attribute? Clearly the cause nearest to
II. 17, 18 669
the subject. If you have four terms D, C, B, A (reading from
minor to major), C is the cause of D’s having B, and therefore of
its having A; B is the cause of C’s having A and of its own
having A.
The question raised and answered in this chapter is the same
that has been raised and answered in 98525-38, and it would seem
that the two passages are alternative drafts, of which the second
is the fuller and more complete. A. answers, as in 9832-8, that
where there is a genuine demonstration of an attribute A as
following from an element B in the nature of a subject C, only
one cause can appear as middle term, viz. that which is the
definition of the attribute ; his meaning may be seen by reference to
ch. 8, where he shows that, for example, the term ‘interposition of
the earth’, which serves to explain the moon’s suffering eclipse,
becomes an element in the definition of lunar eclipse. He admits,
however, that there are arguments in which the subject’s posses-
sion of a single attribute may be proved by means of different
middle terms. An obvious case is proof κατὰ σημεῖον (9973); A
may have several consequences, and any of these may be used
to prove C’s possession of A (though of course it does not explain
it); cf. 93437-63 and Am. Pr. ii. 27. Another case is proof xara
συμβεβηκός ; both the attribute and the subject may be considered
κατὰ συμβεβηκός (*4~5); C may be shown to possess A because it
possesses an inseparable concomitant of A, or because an in-
separable concomitant of C entails A, and of course a variety of
concomitants may be thus used. οὐ μὴν δοκεῖ (A. continues)
προβλήματα εἶναι (‘these, however, are not thought to be scientific
treatments of the problem’). εἰ δὲ μή, ὁμοιώς ἕξει τὸ μέσον. εἰ δὲ
μή is taken by the commentators to mean εἰ δὲ μὴ οὐ δοκεῖ
προβλήματα εἶναι, ‘if such treatments of the problem are admitted’ ;
and what follows in *6-16 is taken to offer various types of argu-
ment κατὰ συμβεβηκός. But if so, the logic of the passage would
require them to be arguments in which a single effect is proved
to exist by the use of more than one middle term. What A. asserts,
however, is that in the three cases he discusses (#7, 7-8, 15-16) the
middle term used has precisely the kind of unity that the effect
proved has. I infer that the three cases are not put forward as
cases of proof κατὰ συμβεβηκός, and that εἰ δὲ μή means ‘if we
study not κατὰ συμβεβηκός the od αἴτιον or the à atrwov'.
The three cases, then, are cases which might seem to show that
there can be more than one cause of the same effect, but do not
really do so. They are as follows: (a) We may be considering not
670 COMMENTARY
one effect but two effects called by the same name, or (b) (ws ἐν
γένει, 31) the major may be predicable of a whole genus, and we
may be asking why it is predicable of various species of the genus.
Case (b) is illustrated first (38-11). All proportions between
quantities are convertible alternando (i.e. if a is to b as c is to d,
aistocas bis to d). If we ask not why all proportions between
quantities are convertible, but why proportions between lines,
and again why proportions between numbers, are convertible (a
procedure which in 74217-25 A. describes as having been followed
by the earlier mathematicians), there is a misfit between subject
and predicate. There is a single reason why all proportions are
convertible, consisting in the attribute, common to all quantities,
of bearing definite ratios to quantities of the same kind (f ἔχον
αὔξησιν τοιανδί, *10). But if we ask why proportions between lines
are convertible, we shall use a middle term following from the
nature of lines, and if we ask why proportions between numbers are
convertible, a middle term following from the nature of numbers.
A. now (*r1) turns to case (2). Similarity between colours is not
the same thing as similarity between figures; they are two things
with a single name; and it is only to be expected that the middle
term used to prove that two colours are similar will be different
from that used to prove that two figures are similar; and if the
two middle terms are called by the same name, that also will be
a case of ambiguity.
Finally (c) (315-16), when two effects are analogous, i.e. when
they are neither two quite different things called by the same
name, nor yet two species of the same genus, but something
between the two—when the resemblance between two things is
one of function or relation, not of inherent nature or structure
(bone, for example, playing the same part in animals that fish-
spine does in fishes, 98220-3), there will naturally be two causes
which also are related by analogy. (For oneness by analogy as
something more than unity of name and less than unity of nature
cf. Met. 1016531—101723, E.N. 1096%25-8.)
A consequential attribute, A. continues (#18), is wider than
each species of its proper subject but equal to all together.
Having external angles equal to four right angles, which has as its
proper subject 'all rectilinear figures', is wider than triangle or
square but coextensive with all rectilinear figures taken together
(for these are just those that have that attribute), and so is the
middle term by which the attribute is proved. In fact the middle
term is the definition of the major (for A.'s proof of this as regards
the middle term by which a physical effect is explained, cf. ch. 8,
II. 17, 18 671
and for his attempt to show that the same is true of the middle
term in a mathematical proof cf. 94?24-35) ; and that is why all
the sciences depend on definitions—viz. since they have to use
the definitions of their major terms as middle terms to connect
their major terms with their minor terms (421-3). (For the part
played by definitions among the ἀρχαί of science cf. 72414-24.)
To the mathematical example A. adds a biological one.
Deciduousness extends beyond the vine or the fig-tree, but is co-
extensive with all the species of deciduous trees taken together.
He adds the further point, that in this case /wo middle terms
intervene between the vine or fig-tree and deciduousness. The
vine and fig-tree shed their leaves because they are both of a
certain class, sc. broad-leaved (9854), but there is a middle term
between ‘broad-leaved’ and ‘deciduous’, viz. ‘having the sap con-
gealed at the junction of the leaf-stalk with the stem'. The latter
is the 'first middle term', counting from the attribute to be ex-
plained, and is its definition; the former is the ‘first in the other
direction’, counting from the particular subjects (99225-8). Thus
there are two syllogisms: (1) All trees in which the sap is con-
gealed, etc., are deciduous, All broad-leaved trees have their sap
congealed, etc., Therefore all broad-leaved trees are deciduous. (2)
All broad-leaved trees are deciduous, The vine is (or the vine,
the fig-tree, etc., are) broad-leaved, Therefore the vine is (or
the vine, the fig-tree, etc., are) deciduous. In syllogism (1) all
the propositions are genuine scientific propositions and their
terms are convertible. In syllogism (2) the minor premiss and the
conclusion, in either of their forms, are not scientific universals ;
for the vine is not the only broad-leaved tree, and 'the vine, the
fig-tree, etc.', are not one species but an aggregate of species;
but if we enumerate all the species of broad-leaved trees both
the minor premiss and the conclusion will be convertible.
A. now (530) proposes to exhibit in schematic form (ἐπὶ τῶν
σχημάτων) the correspondence of cause and effect. But he
actually gives a formula which seems to fit quite a different type
of case, viz. that previously outlined in 98525-31. He envisages
two syllogisms, parallel, not consecutive like the two in 99*23-9.
(1) All B is A, All the species of D are B, Therefore all the species
of D are A. (2) AIL C is A, All the species of E are C, Therefore
all the species of E are A. Thus he omits altogether the single
definitory middle term which he insisted on above. He is taking
for granted two syllogisms which connect B and C respectively
with A through a middle term definitory of A, and is drawing
attention to the later stage only.
672 COMMENTARY
The general upshot of the chapter is that, to explain the occur-
rence of an attribute, wherever it occurs, there must be a single
middle term ‘next’ the attribute, which is the definition of the
attribute and therefore coextensive with it; there may also be
alternative middle terms connecting different subjects with the
definitory middle term and therefore with the attribute to be
explained (*25-8). Thus in a sense there is and in a sense there is
not plurality of causes.
99*13-14. ἔνθα μὲν yap... γωνίας. This is Euclid's definition of
similarity (El. vi, def. 1). As Heiberg remarks (A bh. zur Gesch. d.
Math. Wissensch. xviii. 9), A.’s tentative ἴσως may indicate that
the definition had not found its way into the text-books of his
time.
19-20. olov τὸ τέτταρσιν . . . ἴσον, cf. 85538-8641 n.
20-1. ὅσα yap... ἔξω, ‘for all the subjects taken together are
ex hypothesi identical with all the figures whose external angles
equal four right angles'. This must be printed as parenthetical.
29. ἐν τῇ συνάψει τοῦ σπέρματος. P. 430. 9 says τὸ σπέρμα
means τὸ ἄκρον τοῦ ὀχάνου (presumably = channel for sap, akin
to óxerós—a usage of ὀχάνον not mentioned in L. and S.), καθ᾽
ὃ συνάπτεται TQ φύλλῳ. σπέρμα δὲ λέγεται τὸ ἄκρον διὰ τὸ ἐγκεῖσθαι
ἐν αὐτῷ τὴν σπερματικὴν ἀρχὴν καὶ δύναμιν, ἐξ ἧς φύεται τὸ φύλλον.
E. 248. 16 says ὁ γὰρ ὁπὸς οὗτος ἅμα μὲν τρέφει τὸ φύλλον διὰ τοῦ
ὀχάνου kai θάλλειν ποιεῖ, ἅμα καὶ τῷ δένδρῳ αὐτὸ προσκολλᾷ.
30. ὧδε ἀποδώσει, ‘the thing will work out thus’; cf. the in-
transitive use of ἀποδιδόναι in Meteor. 363*11, H.A. 585532, 58622,
G.A. 72238, Met. 105798.
32-5. τὸ μὲν 8: B . . . παρεκτείνει. B will be καθόλον, predicable
κατὰ παντός and καθ᾽ αὑτό of each of the D's, but πρῶτον καθόλου,
ie. predicable also # αὐτό (to use the language of i. 4) only of
D as a whole.
33. τοῦτο yàp λέγω καθόλου ᾧ μὴ ἀντιστρέφει. d (instead of
the usual reading ó) is required (1) by parallelism with the next
clause, and (2) by the fact that when A. wishes to say ‘the pro-
position ''B is A”’ is convertible’, he says τὸ B ἀντιστρέφει τῷ A,
not vice versa. Cf. Cat. 2521, An. Pr. 31*31, 5144, 5258, 67537. The
first hand of B seems to have had the right reading. So also
E. 251. 7 πρὸς o.
35-6. xai παρεκτείνει.. . ἐπὶ πλέον τοῦ B ἐπεκτείνειν. In 536
the MSS. and P. have παρεκτείνειν, but this is difficult to accept,
because in *35 παρεκτείνει must mean ‘are coextensive’. Zabarella
says that in 335 some MSS. have καὶ μὴ παρεκτείνει, and takes this
to mean ‘and do not extend beyond’. But that does not give the
TI. 17. 99*13— 18. gg>r1 673
right sense ; there is no question of the subspecies of D collectively
extending beyond B—the point is that B does not extend beyond
them. Besides, the natural meaning of παρεκτείνειν is ‘to be co-
extensive’ (L. and S., sense iii). It is παρεκτείνειν in ?36 that is
difficult; L. and S. quote no other example of the sense 'extend
beyond'. To avoid interpreting the word differently in the two
lines, Mure supposes that τοῦτο yàp . . . δὲ ἀντιστρέφει (533-5)
should be read as a parenthesis, and xai παρεκτείνει coupled with
καθόλου dv εἴη τοῖς A (33). But this gives an unnatural sentence;
and we should then expect παρεκτείνει δέ. The passage is
best cured by reading ἐπεκτείνειν (or ὑπερεκτείνειν) in 236; ἐπεκτεί-
νειν ἐπὶ πλέον occurs in 96?24. The corruption is clearly one that
might easily have occurred.
36-7. δεῖ ἄρα. . . ἐκείνου; This is a very careless inference.
A. recognizes causes coextensive with their effects (i.e. the causes
which are definitions of their effects (cf. 98532-8)); and clearly
as between two coextensive events priority of date would suffice
to establish which alone could be the cause of the other.
52. otov [τὸ A]... A. Hayduck's emendations will be found in
his Obs. Crit. in aliquos locos Artst. 15. τὸ A seems to me more
likely to have come in by intrusion from the previous line.
ἀλλ᾽ ἄρα, as Bonitz’s Index says, has the force enunctatt
modeste vel dubttanter affirmantss.
7-8. Ei δὲ... rà αἴτια πλείω. This starts a topic distinct from
that discussed in *3o-57 (though broached in *25-9), and connected
with what follows, which should never have been treated as a
separate chapter. The sentence has been connected with what
precedes by some editor who thought τὸ ἄτομον meant τὸ ἄτομον
εἶδος, and connected it in thought with τοῖς αὐτοῖς τῷ εἴδει (4).
But eis τὸ ἄτομον means ‘to the immediate proposition’, and the
clause means ‘if the διάστημα between the subject and the effect
to be explained cannot be bridged by two immediate propositions’.
II. τὸ ἐγγύτατα should be read, instead of rà ἐγγύτατα, which
is a natural corruption. ἐγγύτατα is the superlative of the adverb;
cf. τῷ ἐγγύτατα, 98°6.
CHAPTER 19
How we come by the apprehension of first principles
99^r5. We have described what syllogism and demonstration
(or demonstrative science) are and how they are produced; we
have now to consider how the first principles come to be known
and what is the faculty that knows them.
4985 xx
674 COMMENTARY
20. We have said that demonstrative science is impossible
without knowledge of the first principles. The questions arise (1)
whether these are objects of science, as the conclusions from them
are, or of some other faculty, and (2) whether such faculty comes
into being or is present from the start without being recognized.
26. (2) It would be strange if we possessed knowledge superior
to demonstration without knowing it. On the other hand, we
cannot acquire it, any more than demonstration, without pre-
existing knowledge. So we can neither possess it all along, nor
acquire it unless we already have some faculty of knowledge. It
follows that we must start with some faculty, but not one
superior to that by which we know first principles and that by
which we know the conclusions from them.
34. Such a faculty all animals have—an innate faculty of dis-
cernment, viz. perception. And in some animals perceptions
persist. There is no knowledge outside the moment of perception,
for animals in which perceptions do not persist, or about things
about which they do not persist ; but in some animals, when they
have perceived, there is a power of retention. And from many
such acts of retention there arises in some animals the forming of
a conception.
10033. Thus from perception arises memory, and from repeated
memory of the same thing experience. And from experience—
ie. when the whole universal has come to rest in the soul—the
one distinct from the many and identical in all its instances—
there comes the beginning of art and science—-of art if the
concern is with becoming, of science if with what is.
xo. Thus these states of knowledge are neither innate in a
determinate form, nor come from more cognitive states of mind,
but from perception; as when after a rout one man makes a
stand and then another, till the rally goes right back to where
the rout started. The soul is so constituted as to be capable of
this.
14. To be more precise: when an injfima species has made
a stand, the earliest universal is present in the soul (for while
what we perceive is an individual, the faculty of perception
is of the universal—of man, not of the man Callias); again a
stand is made among these, till we reach the unanalysable con-
cepts, the true universals—we pass from 'such and such a kind
of animal' to 'animal', and from 'animal' to something higher.
Clearly, then, it is by induction that we come to know the first
principles ; for that is how perception, also, implants the universal
1n us.
II. 19 675
bs. (1) Now (a) of the thinking states by which we grasp truth
some (science and intuitive reason) are always true, while others
(e.g. opinion and calculation) admit of falsity, and no state is
superior to science except intuitive reason ; and (5) the first prin-
ciples are more knowable than the conclusions from them, and
all science involves the drawing of conclusions. From (8) it
follows that it is not science that grasps the first principles; and
then from (a) it follows that it must be intuitive reason that does
so. This follows also from the fact that demonstration cannot be
the source of demonstration, and therefore science cannot be
the source of science; if, then, intuitive reason is the only neces-
sarily true state other than science, it must be the source of
science. It apprehends the first principle, and science as a whole
grasps the whole subject of study.
The ἀρχαί, with the knowledge of which this chapter is con-
cerned, are the premisses from which science or demonstration
starts, and these have been classified in 7214-24. They include
(1) ἀξιώματα or κοιναὶ ἀρχαί. These in turn include (a) principles
which apply to everything that is, ie. the law of contradiction
and that of excluded middle; and (δ) principles valid of every-
thing in a particular category, such as the principle (common to
all quantities) that the whole is greater than the part and equal
to the sum of its parts. (a) and (4) are not distinguished in 72214—
24 but are distinguished elsewhere. Secondly (2) there are θέσεις
or ἔδιαι dpyai, which in turn are subdivided into (a) ὁρισμοί,
nominal definitions of all the terms used in the given science, and
(b) ὑποθέσεις, assumptions of the existence of things corresponding
to the primary terms of the given science.
All of these are propositions, while the process described in
99^35-10c^s seems to be concerned with the formation of universal
concepts (cf. the examples ἄνθρωπος, ζῷον in 100>1-3). It would
not be difficult to argue that the formation of general concepts
and the grasping of universal propositions are inseparably inter-
woven. But A. makes no attempt to show that the two pro-
cesses are so interwoven; and he could hardly have dispensed
with some argument to this effect if he had meant to say that they
are so interwoven. Rather he seems to describe the two processes
as distinct, and alike only in being inductive. δῆλον δὴ ὅτι ἡμῖν
τὰ πρῶτα ἐπαγωγῇ γνωρίζειν ἀναγκαῖον: Kai yàp xai ἡ αἴσθησις
οὕτω τὸ καθόλου ἐμποιεῖ (10053).
The passage describing the advance from appreliension of the
particular to that of the universal should be compared with Met.
4985 XX2
676 COMMENTARY
980*27—981*12, where the formation of universal judgements is
definitely referred to (τὸ μὲν yàp ἔχειν ὑπόληψιν ὅτι Καλλίᾳ κάμνοντι
τηνδὶ τὴν νόσον τοδὶ συνήνεγκε καὶ Σωκράτει καὶ καθ᾽ ἕκαστον οὕτω
πολλοῖς, ἐμπειρίας ἐστίν: τὸ δ᾽ ὅτι πᾶσι τοῖς τοιοῖσδε κατ᾽ εἶδος ἕν
ἀφορισθεῖσι, κάμνουσι τηνδὶ τὴν νόσον, συνήνεγκεν, οἷον τοῖς φλεγμα-
τώδεσιν 7) χολώδεσι [7] πυρέττουσι καύσῳ, τέχνης, 98157--12), while
much of what A. says is equally applicable to the formation of
general concepts.
99°19. προαπορήσασι πρῶτον. This refers to 522-34 below. Of
the questions raised in 522-6 the last, πότερον οὐκ ἐνοῦσαι αἱ ἕξεις
ἐγγίνονται ἢ ἐνοῦσαι λελήθασιν, is discussed in >26-100%5 ; the answers
to the other questions are given in 10o55-17.
21. εἴρηται πρότερον, in i. 2.
24. ἢ οὔ is clearly superfluous, and there is no trace of it in
P. 433. 8-12 or in E. 260. 28-30.
30. ὥσπερ καὶ ἐπὶ τῆς ἀποδείξεως ἐλέγομεν, in 7121—11.
39. αἰσθομένοις seems to be a necessary emendation of αἰσθανο-
μένοις; cf. An. 600. το.
100?2-3. τοῖς μὲν... μονῆς. Presumably A. thinks this true
only of man. But in Met. 98ob21-5 he draws a distinction among
the animals lower than man. Some do not advance beyond
memory, and even these can be φρόνιμα; but those that have
hearing as well go beyond this and are capable of learning from
experience.
4-5. ἐκ δὲ μνήμης... ἐμπειρία. On A.’s conception of memory
I may be allowed to quote from my edition of the Metaphysscs
(i. 116-17). ‘It is not easy to see what Aristotle wants to say
about ἐμπειρία, the connecting link between memory and art or
science. Animais have a little of it; on the other hand it involves
thought (98126). In principle it seems not to differ from memory.
If you have many memories of the same object you will have
ἐμπειρία; those animals, then, which have good memories will
occasionally have it, and men will constantly have it. After
having described it, however, as produced by many memories
of the same object, Aristotle proceeds to describe it as embracing
a memory about Callias and a memory about Socrates. These
are not the same object, but only instances of the same universal ;
say, 'phlegmatic persons suffering from fever'. An animal, or a
man possessing only ἐμπειρία, acts on such memories, and is
unconsciously affected by the identical element in the different
objects. But in man a new activity sometimes occurs, which
never occurs in the lower animals. A man may grasp the universal
of which Callias and Socrates are instances, and may give to a
IT. 19. 99b1r9 — 1oo*r 677
third patient the remedy which helped them, knowing that he is
doing so because the third patient shares their general character.
This is art or science—for here these two are not distinguished
by Aristotle.
"What is revived by memory has previously been experienced
as a unit. Experience, on the other hand, is a coagulation of
memories; what is active in present consciousness in virtue of
experience has not been experienced together. Therefore (a) as
embodying the data of unconsciously selected awarenesses it fore-
shadows a universal; but (b) as not conscious of what in the past
is relevant, and why, it is not aware of it as universal. Ie.
experience is a stage in which there has appeared ability to inter-
pret the present in the light of the past, but an ability which
cannot account for itself; when it accounts for itself it becomes
art.' :
6-7. ἢ ἐκ παντὸς ... Ψυχῇ. The passage contains a remini-
scence of Pl. Phaedo 96 b ὁ δ᾽ ἐγκέφαλός ἐστιν ὁ τὰς αἰσθήσεις
παρέχων... ἐκ τούτων δὲ γίγνοιτο μνήμη καὶ δόξα, ἐκ δὲ μνήμης καὶ
δόξης λαβούσης τὸ ἠρεμεῖν, κατὰ ταῦτα γίγνεσθαι ἐπιστήμην.
4. τοῦ ἑνὸς παρὰ τὰ πολλά, not ‘existing apart from the
many’ (for it is ἐν ἅπασιν ἐκείνοις), but ‘distinct from the many’.
13. ἕως ἐπὶ ἀρχὴν ἦλθεν. It has been much debated whether
ἀρχή here means ‘rule’ (or ‘discipline’) or ‘beginning’. I doubt
whether the words can mean ‘returns to a state of discipline’,
though ὑπ᾽ ἀρχὴν ἦλθεν could well have meant that. P. seems to
be right in thinking (436. 23-9) that the meaning is ‘until the
process of rallying reaches the point at which the rout began';
Zabarella accepts this interpretation, which derives support from
a comparison with Meteor. 341528 (about meteors) ἐὰν μὲν πλέον τὸ
ὑπέκκαυμα ἦ κατὰ TO μῆκος ἢ TO πλάτος, ὅταν μὲν οἷον ἀποσπινθηρίζη
ἅμα καιόμενον (τοῦτο δὲ γίγνεται διὰ τὸ παρεκπυροῦσθαι, κατὰ μικρὰ
μέν, ἐπ᾽ ἀρχὴν δέ), αἷξ καλεῖται, where ἐπ᾽ ἀρχήν seems to mean
‘continuously with that from which the process of taking fire
began’.
14. ὃ δ᾽ ἐλέχθη μὲν πάλαι refers to *6-7. πάλαι can refer to
a passage not much previous to that in which it occurs, e.g. Phys.
25416 referring to 2525-32, Pol. 126229 referring to 424, 1282415
referring to 1281439-11. L. and S. recognize ‘just now’ as a
legitimate sense of πάλαι.
15. τῶν ἀδιαφόρων, 1.6. of the not further differentiable species,
the infimae species ; cf. 97437 τοῦ δὲ reAevratov μηκέτι εἶναι διαφοράν.
16-b1i. kai yàp αἰσθάνεται. . . Καλλίου ἀνθρώπου. These
words serve to explain how it is that the ‘standing still’ of an
678 COMMENTARY
individual thing before the memory is at the same time the first
grasping of a universal; this is made easier to understand by the
fact that even at an earlier stage—that of perception (καὶ yap
aic@dvera)—the awareness of an individual is at the same time
awareness of a universal present in the individual ; we perceive an
individual thing, but what we perceive in it is a set of qualities
each of which can belong to other individual things.
bz. ἕως ἂν... καθόλου. The reaching of rà ἀμερῆ is described
as the culmination of the process, so that rà ἀμερῆ cannot mean
universals in general, but only the widest universals, the cate-
gories, which alone cannot be resolved into the elements of genus
and differentia ; and τὰ καθόλου must be used as synonymous with
τὰ ἀμερῆ, i.e. as standing for the universals par excellence, the
most universal universals. For ἀμερῆ in this sense cf. Met. 101456
ὅθεν ἐλήλυθε τὰ μάλιστα καθόλου στοιχεῖα εἶναι, ὅτι ἕκαστον αὐτῶν ἕν
ὃν καὶ ἁπλοῦν ἐν πολλοῖς ὑπάρχει. .. ἐπεὶ οὖν τὰ καλούμενα γένη
(i.e. the highest γένη) καθόλου καὶ ἀδιαίρετα (οὐ γὰρ ἔστι λόγος
αὐτῶν), στοιχεῖα τὰ γένη λέγουσί τινες, καὶ μᾶλλον ἢ τὴν διαφορὰν
ὅτι καθόλου μᾶλλον τὸ γένος, 1τ023Ρ22 ἔτι τὰ ἐν τῷ λόγῳ τῷ δηλοῦντι
ἕκαστον, καὶ ταῦτα μόρια τοῦ ὅλου" διὸ τὸ γένος τοῦ εἴδους καὶ
μέρος λέγεται, 1084514 ἀλλ᾽ ἀδιαίρετον καὶ τὸ καθόλου. In Met.
994521 τὰ ἄτομα is used of the highest universals.
16-17. ἡ δὲ πᾶσα... πράγμα, i.e. science as a whole grasps
its objects with the same certainty with which intuitive reason
grasps the first principles.
INDEX VERBORUM
ἀγαθόν, dist. τὸ ἀγαθόν 49>10
ἀγένητον 6849
ἀγεωμέτρητοι 77°13 4,
ib. 17, 22
ἄγνοια 77P16-33
λεγομένη 79523
ἀγχίνοια 89>10-20
ἀδιόριστος 24319, 26228, P14, 27520, 28,
28528, 296, 35h11, 43P14
ἀδύνατον εἰς τὸ d. dyew 27415,
36?22 διὰ (ἐκ) τοῦ d. δεικνύναι
2857, 29, 29°35, 3443, 35°40, 379,
ἀποδεῖξαι 28923, P14, 39932 πε-
ραίνεσθαι 29*32, 50%29-38 εἰς τὸ
d. ἀπαγωγή 29°5 διὰ τοῦ ἀ.
συλλογισμός 37235, 61218-6321
τοῦ ἐξ ὑποθέσεως μέρος τὸ διὰ rob
d. 40>25 οἱ εἰς τὸ d. (ἄγοντες)
συλλογισμοί 41322, 4523-520 ἡ
εἰς τὸ d. ἀπόδειξις 77222 X ἀντι-
στροφή 61821 Y( δεικτικὴ ἀπό-
δειξις 62020 63021 X στερητικὴ
ἀπόδειξις 8721-28 )νί κατηγορικὴ
ἀπόδειξις ib. 28-30
dÜeros οὐσία 87336
‘AGnvaios 6941, 94237
ἀθρεῖν 465
αἱρετός.
ἐρώτημα
ἡ κατὰ διάθεσιν
πῶς ἔχουσιν οἱ ὅροι κατὰ τὸ
αἱρετώτεροι εἶναι 68225-b9
αἰσθάνεσθαι 5072
αἰσθήματος μονή 9903]
αἴσθησις 78235, 81338-Ῥο, 86430, 000 34-
100%3, 100917, 55 τῶν καθ᾽ éxaa-
rov 8156 )( ἐπιστήμη ib. 87528-
88917 δύναμις σύμφυτος κριτική
9935
αἰτεῖσθαι τὸ ἐξ ἀρχῆς (τὸ ἐν ἀρχῇ)
41P9, 20, 6428-6537, 91*36, cf.
46433, Prt
αἴτημα 76523, 31-4, 773, 86234
αἰτίαι τέτταρες 94?21
αἰτιατός 76720, 98736
αἴτιον 1022, 76419, 78427, ba, 15,
9325, P21-8, 9458, 95210-537, 98*35-
99514 αἰτιώτερον 85924
ἄκρα, dist. μέσον 25b36, 28415, 46522
d. μεῖζον, ἔλαττον 26422, b37, 28813
τὸ πρῶτον τῶν d. 46°1, syn. τὸ d.
49237, 592, 68534, 35 τὸ ἔσχατον
&, τοῦτο, syn. τὸ d, 48241, 26
ἀκριβεστέρα ἐπιστήμη ἐπιστήμης 87931
ἀκρωτήρια 7oP17
ἀλέγειν 5052
ἀληθεύεσθαι τόδε κατὰ τοῦδε 4056
ἀληθής. πᾶν τὸ d. ἑαυτῷ ὁμολογού-
μενον 4738 coni. τὸ εἶναι 52432,
67520 ἐξ ἀληθῶν οὐκ ἔστι ψεῦδος
συλλογίσασθαι 5357, 11 ἐκ ψευ-
δῶν ἔστιν ἀληθές ib. 8, 26-5717,
6457, οὐ μὴν ἐξ ἀνάγκης 57540
ἐξ ἀντικειμένων οὐκ ἔστιν ἀληθὲς
συλλογίσασθαι 6458
Ἀλκιβιάδης μεγαλόψυχος 97>18
ἄλληλα. τὸ ἐξ d. δείκνυσθαι 5718
ἡ δι’ ἀλλήλων δεῖξις 59232
ἄλυτος γί λύσιμος συλλογισμός 0320
ἄμεσος. dueca 48433 ἀμέσων
ἐπιστήμην ἀναπόδεικτον 72°19 d-
nega καὶ ἀρχαί 93522
ὁρισμός 94*9
7227, 8571
ggb21
ἀμετάπειστος 7253
ἀμφώδοντα 98917
ἀνάγειν sobs—srb2
συλλογισμοὺς εἰς τοὺς ἐν τῷ πρώτῳ
σχήματι καθόλου 2g>r, 41b4, cf.
40°19 πῶς ἀνάξομεν τοὺς ava-
λογισμοὺς εἰς τὰ σχήματα 46940-
47°14 τοὺς ἐξ ὑποθέσεως συλ-
λογισμοὺς οὐ πειρατέον d. 50316
ἀναγκαῖος 2538, 27, 2634, 2929-3014,
35623-36525, 38%13-39%3, 398, 405
4-b16, 45P29, 47°23, 33 6212,
74914, 26 συμβαίνει ποτε τῆς
ἑτέρας προτάσεως d. οὔσης d.
γίνεσθαι τὸν συλλογισμόν 3015-
3214 τούτων ὄντων d., dist.
ἁπλῶς 30432, 39, cf. 3208. Χ). ἐν-
δεχόμενον 32319, 29, 33°17, 22, 3759
ἐξ ἀναγκαίων οὐκ ἔστι συλλογίσασθαι
ἀλλ᾽ 3 ἀποδεικνύντα 74916
ἀνάγκη 24b19, 34°17, 40536, 53617,
57440, 73518, 9403] πρότασις
τοῦ ἐξ d. ὑπάρχειν 2531 συλλο-
γισμὸς τοῦ ἐξ d. ὑπάρχειν 29b29-
ἀμέσων
ἄ. πρότασις 6830,
αἱ πρῶται ἀρχαὶ αἱ ἅ.
> ’ .
a. παντας TOUS
680
30714 ὅταν ἡ μὲν ἐξ d. ὑπάρχειν
ἡ δ᾽ ἐνδέχεσθαι σημαίνῃ τῶν προ-
τάσεων 35b23-36b25, 36631, 38413—
39*3
ἀναγωγή 90737
ἀναίτιον. τὸ d. ὡς αἴτιον τιθέναι 65516
ἀνακάμπτειν 72636
ἀνάκλασις 98929
ἀναλογία 76239, 99915 πολλαπλασία
η831
ἀνάλογον 51524, 98820
ἀναλύειν (1) (v. 4722-5 n.) 4724. robs
διὰ τοῦ ἀδυνάτου περαινομένους
(συλλογισμούς) οὐκ ἔστιν d. 5o*30,
bs — (2) ib. 30-5133, 51322-b4,
182]
ἀνάλυσις (1) (v. 4722-5 n.) 49419,
5038, 88518 (2) 51418, 32
ἀναλυτικῶς 8438, 52
ἀνάμνησις 67322
ἀναπόδεικτος πρότασις 57532
ἀμέσων d. ἐπιστήμη 72°19
ἀνασκευάζειν 4240-43815
ἀνασκευαστικῶς 52337
dvaropai xai διαιρέσεις 9842
"Aváxapots 7830
ἀνεπισκεψία 7926
ἀνομολογούμενον 48221
ἀντεστραμμένος 44731
ἀντίθεσις 32232, 72412
ἀντικείμενος 32922, 51615, 68226 τὰ
ἀ. λαμβάνειν ὀρθῶς 52°15 ἐν τοῖς
διὰ τοῦ ἀδυνάτου συλλογισμοῖς τὸ
d. ὑποθετέον 62>25, cf. 61518, 32,
62411 ἐξ d. προτάσεων συλλο-
γίσασθαι: 63522-64527 d. mpo-
τάσεις τέτταρες 63>24, éEaxds 64338
)( ἐναντίος 63^ 30, 40, 64319, 32. ἐκ
τῶν d. οὐκ ἔστιν ἀληθὲς συλλο-
γίσασθαι Ὁ8 4. συλλογισμοί 69>31
ἀντικειμένως, def. 27429 d. ἣ €vav-
τίως ἀντιστρέφειν τὸ συμπέρασμα
5956
ἀντιπερίστασις πάντα 98425
ἀντιστρεπτέος 51423
ἀντιστρέφειν: (1) (v. 2526 n.) 2546, 8, το,
28, 36935-3731, 53°7, 59730 A
31431, 5174, 5259, s7b32-s8b12,
65215, 67627-68425 (3) 6411, 40
(4) 32430, 36°38 (5) 4556, 5964,
6, 6145, 8ob25 (6) 5961-61716
ἐν μόνοις τοῖς ἀντιστρέφουσι κύκλῳ
INDEX VERBORUM
ἐνδέχεται γίνεσθαι τὰς ἀποδείξεις
58°13
ἀντιστροφὴ ἐπὶ τῶν ἐνδεχομένων 25737-
bas )( διὰ τοῦ ἀδυνάτου συλλο-
γισμός 61522 πῶς ἔχουσιν of
ὅροι κατὰ τὰς d. 6858
ἀντιφάναι 6551
ἀντίφασις — 72*12-14, 73°21, 93°34
ὅταν ἀδύνατόν τι συμβαίνῃ τῆς d.
τεθείσης 41°25, 61219, 62534 συλ-
λογισμὸς ἐξ d. 6411
ἀντίφραξις γῆς 90716, 93b5
dvriópárrew 90*18
ἄνω, dist. κάτω 43736, 65b23, 29,
82322, 23, 8363, 7
ἀξίωμα (1) 62413 (v. n.) (2) 72517,
75*41, 76914
ἀόριστος 32°10, 19
ἀπαγωγή 2821, 69320-36 eig τὸ
ἀδύνατον 29b6, 50?31
ἀπαρνεῖσθαι 4792-4, 09736, 37
ἀπατή 66518-67526, 72 » 145], 19023-
81337 ἐν τῷ παρὰ μικρόν px
ἀπατητικὸς συλλογισμός 8obr5
ἄπειρος. εἰς d. ἰέναι 81533, 8247, 39
ἡ ἄπειρα, οὐκ ἐπιστητά 8675
ἀπλατής 49°36
ἀποδεικτικός. a. πρότασις, dist. δια-
λεκτική 245322, cf. 68>10 συλλο-
γισμὸς d. τῶν ἀορίστων οὐκ ἔστι
32618 — d. ἐπιστήμη 73322, ἸΟΡῚΣ
ἀποδεικτὸς 48437, 76°33, 84°33, 8637,
gobz5, 936
ἀπόδειξις 24311, 4023, 72°17, 25-
73320, 74*1, 12, 32->4, 15-18,
75413, 39-P11, 762225, 83320, 85*1,
20-86430, 94*6 )( συλλογισμός
25°28 περὶ οὐσίας d. xal τοῦ τί
ἐστιν 46236 ἐκ τίνων αἱ d. γίνονται
b38 ἐκ προτέρων ἐστιν 64632
)( διαλεκτικοὶ συλλογισμοί ὅς536
συλλογισμὸς ἐπιστημονικός 71518,
cf. 73424 μὴ πάντων εἶναι ἀπό-
δειξιν 84331, cf. 7255-7, 8238 ἡ
καθόλου τῆς xarà μέρος βελτίων
85312, ἡ δεικτικὴ τῆς στερητικῆς
86432, τῆς εἰς τὸ ἀδύνατον ἀγούσης
8732 d. πλείους τοῦ αὐτοῦ bs-18
ἀπολείπειν 9o?18
ἀπόσβεσις 9356, 10
ἀπόφανσις 72°11
ἀπόφασις 32222, 62914, 72414
INDEX VERBORUM
ἀποφατικῶς Gana
ἀριθμητικός 93°24 ἀριθμητική 752
39, P3, 768, 87234, 35
Ἀριστομένης διανοητός 47^ 22
Aptororédns, refs. to An. Pr. 7338, 14,
15, 77235, 8047, 86b1o, 91513, 964
to An. Post. 24>14, 25627, 232623,
4333] to Top. 24512, 46429, 64237
to Soph. Fl.65516 τὸ Phys. gsbrz
ἁρμονικός 76224 ἁρμονικὴ ὑπ᾽ ἀρι-
θμητικήν 75516, 7838 q re
μαθηματικὴ καὶ ἡ κατὰ τὴν ἀκοήν
7971 τὰ d. 76710
ἄρρυθμον διττόν 77524
ἄρτιος 41427, 50438
ἀρχή 43°21, 536, 5333, 65913, 72836,
17 bs, 885 4, 21 KL gob 24, gg> 17-
100917 τὸ ἐξ d. (ἐν d.) αἰτεῖσθαι
(λαμβάνειν) 40632, 4158, 13, 20,
64028-65337, 91236, Pii αἱ d.
τῶν συλλογισμῶν 46710
ξεως 727 συλλογιστική ib. 14
ἐν ἑκάστῳ γένει 7631
αὐταὶ ἁπάντων 88718
αἱ ἄμεσοι ggb21
ἀρχοειδέστερος 86538
ἄσκεπτος. ἐν d. χρόνῳ ϑοῦτο
ἀστρολογία 7611 3 τε μαθηματικὴ
καὶ ἡ ναυτική 78240
ἀστρολογικὴ ἐμπειρία 46719
ἀσυλλόγιστος 91 23
ἀσυλλογίστως 77940
ἀσύναπτοι of συλλογισμοί 42221
ἄτακτον τὸ μέσον 32°19
ἀτελεῖς οἱ ἐν τῷ δευτέρῳ σχήματι συλ-
λογισμοΐ 2844, of ἐν τῷ τρίτῳ 29715
οἱ ἀ. συλλογισμοὶ τελειοῦνται διὰ τοῦ
πρώτου σχήματος 29730
ἄτομος 91532
ἀτόμως μὴ ὑπάρχειν 79*33-P22
αὐξάνει ἡ σελήνη 7806
αὑτό, καθ᾽ 73°34, P28, 84212
ἀφαίρεσις. ἐξ ἀφαιρέσει λεγόμενα 8155
Ἀχιλλεύς 97°18
ἄχρειοι axépers 44°26
ἀποδεί-
> H
οὐχ αἱ
ε μ᾿
αἱ πρῶται
βροντᾶν 94532
βροντή 93322, P8, 9423-7
Βρύσων 75°40
γέλως οὐ σημεῖον 48533
γένεσις συλλογισμῶν 4732
681
γένος. διὰ τῶν y. διαίρεσις 46231-b37
περὶ γένους συλλογίσασθαι Ῥ2] οὐκ
ἔστιν ἐξ ἄλλου γένους μεταβάντα
δεῖξαι 75438 ἡ ἀπόδειξις οὐκ
ἐφαρμόττει ἐπ᾽ ἄλλο y. 76423, cf. ib. 3
γεωμέτρης 49535 οὐ ψευδῆ ὑπο-
τίθεται 7639-7733
γεωμετρία 7503-20, 7699
γεωμετρικός 7539, 77240->33
γίνεσθαι χ γενέσθαι 95227 τὸ
γεγόνος, ὅτε γέγονεν, ἔστιν 34512
γνωρίζειν 64535, 71317 ἡ γνωρί-
ζουσα ἕξις 99 18
γνωριμώτερα διχῶς 71533-7228
γνωρισμὸς οὐσίας gob16
γνωστὸν δι’ αὑτοῦ 64536, 6538
δεικτικὴ ἀπόδειξις 62529-63b21
)( διὰ τοῦ ἀδυνάτου 29?
)( ἐξ ὑποθέσεως 4ob25
δεικτικῶς
31, 45326
δεικτός 76227
διὰ τί 93939 δι᾽ αὑτό 730ι1᾿΄:2 δι᾽
ἀλλήλων δεῖξις 59332
διαγράμματα 41514
διαγράφειν κατ᾽ ἀλήθειαν 4678
διαιρεῖν 4711 διαιρεῖσθαι 46738,
by, 20
διαίρεσις ἡ διὰ τῶν γενῶν 46931-b37,
gib29, 96b25-97b6 ἡ διὰ τῶν
8. ὁδὸς οὐ συλλογίζεται gtb12, 36
κατασκευάζειν dpov διὰ τῶν 8. 97423
διαιρετικοὶ ὅροι 91030
διαλέγεσθαι πρός τι 50712 ὄρους 92532
διαλεκτικὴ πρότασις 24?22, 25 8.
συλλογισμοί 4649, 65237 ἡ 8.
77229, 31-4 πραγματεία ἡ περὶ
τὴν 8. 46230
διαλεκτικῶς συλλογίζεσθαι 81619, 22
διάλογοι Υ( μαθήματα 78412
διάμετρος 41226, 46629, 50437, 65518
διανοητικὴ μάθησις 7141
διάνοια 89b7 τὰ ἀπὸ διανοίας 9533
διαπορεῖν 90437
διαπορήματα 93°20
διάστημα e 31, 3834, 42b9, 8257,
84435,
διαφορά M 83r, 96525-9756
δίεσις 84039
διότι γί ὅτι 5359, 78*22, 533, 87932,
89316, b24 τὸ δ. ἐπίστασθαι
75°35 κυριώτατον τοῦ εἰδέναι τὸ
8. θεωρεῖν 79223
682
δόξα 43°39, 46710, 8972-4
στήμη 88530-8956
δοξάζειν 67522
δοξαστικῶς
δοξαστόν
YX ἐπι-
)( ἐπίστασθαι 89411
)( κατ᾽ ἀλήθειαν 4358
)( ἐπιστητόν 88530
δυνατός, δυνατόν )( ἐνδεχόμενον
25439 syn. ἐνδεχόμενον 318
8. συλλογισμός 27*2, 28216, 41533
δυσεπιχειρητότερον 42531
ἐγρήγορσις 3128, 41-3234
ἐγχωρεῖ, τωι ἐνδέχεται 3200, 3757
εἰ ἔστιν 8953
εἰδέναι 6786, 7427-39, 76428, 93*20-6
βέλτιον ἔχειν τοῦ εἰ, 8334, 36,
8454, cf. 72533
εἴδη (Platonica) τερετίσματά ἐστι
83733 τὰ μαθήματα περὶ et. ἐστίν
795]
εἰκός )( σημεῖον 7043
εἶναι. μὴ εἶναι τοδί Y εἶναι μὴ
τοῦτο 51>s—52438 ἔστιν ἐπιστά-
μενος, Syn. ἐπίσταται 51513 τὸ
ov 92b14 τὰ μὴ ὄντα ib. 30
εἷς. ἑνός τινος ὄντος οὐδὲν ἔστιν ἐξ
ἀνάγκης 34*17, cf. 40535, 7357, 94224
λόγος «ls διχῶς 93535
ἔκθεσις (1) (v. 28923 n.) 28b14
(2) 48425, 4956
ἐκκεῖσθαι τοὺς ὅρους 4858
ἐκλαμβάνειν προτάσεις 431, 6, 47410
ἐκλείπειν 89526, 903, 30, 98>18
ἔκλειψις 15534, 8871, go*17, 93123, 30,
ἐκτίθεσθαι (1) (v. 28523 n.) 28223,
3059, 11, 12, 49633 (2) 30631,
48*1, 29
ἔλαττον ἄκρον 26222, 538, 28214
ἔλεγχος 6654-17
ἕλκη περιφερῆ 79°15
ἐμβάλλεσθαι 84236, 86518, 88bc
ἐμπειρία 46218, 10045-9
ἐμπίπτειν εἰς τὴν διαίρεσιν
ἐμπίπτοιεν ὅροι 84°12
ἐναλλάξ 74718, 9928
ἐναντίος. ἐναντίον )( ἀντικείμενον
61br7, 24, 62411, 17, 28, 63°28, 41,
64418, 31 ἐ, προτάσεις 63°28,
64831
ἐναντίως
$«v 596
ἐνδέχεσθαι, ἐνδεχόμενον 32216-4016
97*20
X ἀντικειμένως ἀντιστρέ-
INDEX VERBORUM
πολλαχῶς λέγεται VIS37 cf. Pr4,
32420, 3328, 30, 34°27, 35°33, 36°33,
39911 )( δυνατόν 25439 τῷ
ἔστιν ὁμοίως τάττεται 25 "21, 3202
syn. δυνατόν 3108 περὶ τοῦ ἐν-
δέχεσθαι συλλογισμός 32*16-33524,
36526-37^18, 39*4-56 ἐὰν ἡ μὲν
ὑπάρχειν ἡ δ᾽ ἐνδέχεσθαι λαμβάνηται
τῶν προτάσεων 3302 25-3522, 36 36529,
37°19-38812,. 39*7, P7-40*3 — ὅταν
ἡ μὲν ἐξ ἀνάγκης ὑπάρχειν ἡ 8
ἐνδέχεσθαι σημαίνῃ 35%23-3625,
36031, 38413-3973, 40“-Ὁ16 — )(
ἀναγκαῖον 32718, 28, 329, 16, 22,
38735 def. 32718, cf. 33> 23. 28,
30, 34°27, 37°27 συμβαίνει πάσας
τὰς κατὰ τὸ ἐνδέχεσθαι προτάσεις
ἀντιστρέφειν 32229 κατὰ δύο λέ-
γέται τρόπους 54 οὐκ ἀντιστρέφει
τὸ ἐν τῷ ἐνδέχεσθαι στερητικόν 36635,
37933 τὸ μὴ €. μηδενὶ διχῶς
λέγεται 37915, 24
ἕνεκά τινος )( ἐξ ἀνάγκης 9402]
τὸ τίνος ἕνεκα 94723,
ἐνεργεῖν 6753-9
ἐνθύμημα 70*10, 71*10
ἔνστασις 69337—70?2, 73333, 74P18-21,
71534-9
ἐνυπάρχειν Y( ἐνυπάρχεσθαι 73°17
ἐξ ἀλλήλων δείκνυσθαι 57°18, 28
ὁ ἐπάγων gibts, ἃς, 92437
ἐπαχθῆναι 71424, 815 érayó-
μενος 71?21
ἐπαγωγή 42423, 67123, 68b13-37, 72529,
78234, 81358-b9, goPr4, rooh4 γί
συλλογισμός 4233, 6814,
7136, τὸ ἐξ ἁπάντων 68528,
69916, )( παράδειγμα 69216
ἐπακτικὴ πρότασις 77935
ἐπαλλάττειν 79>7
ἐπαναδιπλούμενον 49*11—26
ἐπεκτείνειν 96524
ἕπεσθαι. τὰ ἑπόμενα 4301, ΣΙ
ἐπί τι )( ὅλη 5451, b3, 19, 35, 55*1,
19, P5, 7-9, 23, 28, 31, 36, 38, 5633
Y ἁπλῶς 66b39, 6785 ἐ. τινος
λέγεσθαι 48>10
ἐπιβεβαιοῦσθαι 4756
ἐπίβλεψις 4440, 45217, 19, 23
ἐπιδεικνύναι 50424, 85427
ἐπικατηγορούμενα 49425
ἐπικοινωνεῖν 77226
ἐπάγειν.
INDEX VERBORUM
ἐπιπολάζειν τὰ σίτια 94913
ἐπίστασθαι 71228, 9-33, 74°23, 7644,
83638, 8728-37, 8839, 94*20 λέ-
γεται τριχῶς 67°3
ἐπιστήμη 7133, 15, 7206, 18-25,
Ἰ3521, 75°24, 76411, 78632-79916,
88 h30-89 9, 99 brs-roobry τῶν
ἀορίστων οὐκ ἔστι 32918 ἡ καθό-
λον )( ἡ καθ᾽ ἕκαστον 67°18
ἡ καθόλου )( ἡ οἰκεῖα Ὶ ἡ τῷ
ἐνεργεῖν b4 ἀποδεικτική 71920,
η3322, 745 εἶναι ἐπιστήμην 72
περὶ τρία ἐστίν 76012 ἀκριβε-
στέρα 87331 μία 338-b4 ἑτέρα
820 ἀναπόδεικτος 88536 ἀρχὴ
ἐπιστήμης 10078, 9
ἐπιστημονικός 71518
ἐπιστήμων 74528
ἐπιστητόν. τὸ 6. ἀναγκαῖον 73822, cf.
7456
ἐπιτελεῖν 27°17, 2825, 2956, 20
ἐπιχειρεῖν 66334
᾿Ερετριεῖς 94?1
ἔρως 68440
€pwrüv 42739
ἐρώτημα 64236 συλλογιστικόν 77436
ἐπιστημονικόν ib. 38 yewperpt-
xóv 1b. 40
ἔσχατος 25533. σχῆμα 4ης ἐ.
κατηγορία 96912
εὐεπιχείρητος 42020
εὐστοχία 89>10
ἔχεσθαι. ἐχόμενος 95°3
ἐχῖνος 98417
Ζήνων 65°18
ζητεῖν. ζητοῦμεν τέτταρα 80Ὁ24
ζήτησις τοῦ μέσου 90224
ἢ αὐτό, syn. καθ᾽ αὑτό 73629
ἡδονὴ οὐ γένεσις 48932
ἠρεμίζεσθαι 8759, 13
θέσις 65P14, 6622, 7329-10
μα 72?14-24
8erós — )( ἄθετος 87*36
Θήβαιοι 6941-10
X ἀξίω-
ἰατρικός 77441, 79*14
ἴδιον 4302, 7337, gr*15, 9238 )(
κοινόν 76438
683
Dads 92032, 93536
)( ἄνισον
ἰσοσκελές 41914
ἵστασθαι X eis ἄπειρον ἰέναι 72b11,
81533, 36, 82414
ἱστορία 46224
)( οὐκ ἴσον 51527
*
toov
καθ᾽ αὑτό 73%34-524, 628, 7456-10,
asby διττῶς 8412-17
καθ᾽ ἕκαστον 43°27, 40, 67222, 100817
καθόλου 43726; 73526-7443, 8845 def.
24218 ἐν ἅπαντι συλλογισμῷ Bet
τὸ x, ὑπάρχειν 4156, cf. 47526 τὰ
x. διὰ τῆς κατὰ μέρος ἐπιβλέψεως
συλλογίσασθαι 45°23, cf. 7138 οἱ
x. συλλογισμοὶ ἀεὶ πλείω συλλογί-
ζονται 5334 ἡ κι ἐπιστήμη X
ἡ καθ᾽ ἕκαστον 67318 X 9
οἰκεῖα ib. 27 τῶν δὲ ἅμα λαμ-
βάνοντα τὴν γνῶσιν, οἷον ὅσα
τυγχάνει ὄντα ὑπὸ τὸ x, 7151
πρῶτον κ. 7475, 99734 )( τὰ καθ᾽
ἕκαστον 7975 ἀδύνατον τὰ x.
θεωρῆσαι μὴ δι᾽ ἐπαγωγῆς 8102
Καινεύς 1041.
καιρός 48535
Καλλίας 4332], 7717, 8304, toobr
κατὰ παντός 2402], 73328
καταπυκνοῦσθαι 79230
κατασκευαστικῶς 52431
κατασυλλογίζεσθαι 66225
κατάφασις 32422, 72713, 86635
καταφατικός )( στερητικός 2712,
28b2
κατηγορεῖν 24b16, 43*25-40, 47b1,
48341, 49°16, 7351] τὰ κατη-
γορούμενα οὐκ ἄπειρα 82°17
κατηγορίαι. 4951, 83516
κατηγορικόν )( στερητικόν 26:18, kh
κατηγορικῶς Ὶ στερητικῶς 26522,
27327
κάτω 65523, 82423
κεῖσθαι 92717
88430, 92*14
κεκλάσθαι 7699
κίνησις 48>31
Κλέων 43426
κλήσεις τῶν ὀνομάτων
48541
κοινά Ἰ6537- 52, 77%26-31
8836-53
Κορίσκος 85324
τὰ κείμενα 47°24, 32,
Ὶ πτώσεις
κ᾿ ἀρχαί
684
κρύσταλλος 95316
κύκλῳ δείκνυσθαι 57518-59241, 72>25
γένεσις 95538-9647
λαμβάνειν 24P10, 73224
gt bir
λαμπτήρ 94>28
λέγεσθαι ἀπό τινος
64414
λογικός 86222
λογικῶς θεωρεῖν 8235, 88819 X
ἀναλυτικῶς 8427, 2
λογισμοί 88512
λόγοι ols οὐ κεῖται ὄνομα 48730 ó
ἔξω )( ὃ ἐν τῇ ψυχῇ, 6 ἔσω 16524
ὀνοματώδης 93°30 εἷς διχῶς ib.
35 ἀνὰ A. 85338
Λύσανδρος 97521
λύσιμος συλλογισμός 704831, 34
30$ 09 08
TO ἐν ἀρχῇ
)( κατά τινος
μάθημα 4694 τὰ μ. 7727-33, 1851ι,
79*7-10
μαθηματικός 7143
μάθησις 67421, 7141
μανθάνομεν 3 ἐπαγωγῇ 7 ἀποδείξει
81240
μεγαλοψυχία 9715-25
μεῖζον ἄκρον 26221, 637, 28413
Μένων. ὃ ἐν τῷ M. λόγος 67421 τὸ
ἐν τῷ M. ἀπόρημα 71729
μέρος. ἐν μ. 24417, 25λ1ο, 5355
μέρος 25420, 5334, Bibi κατα-
σκευάζοντι ῥάω τὰ ev μ. 4379 αἱ
κατὰ μέρος ἐπιστῆμαι )( αἱ καθόλου
67238 ὡς μέρος πρὸς ὅλον 69414
μέσον 4133, 44P40, 47238-b14, 74b26-
75°17, 75°11, 76%9, 7808, 81417,
8936-90230, 9377, 95436, 99*4
def. 25635, 26536, 28412 σχῆμα
42534, 35, 39, 4478, 4703, 48415,
5068 ἄνευ p. συλλογισμός οὐ
γίνεται 66328 οἰκεῖον 80>1 7-22
μεταβαίνειν 75238
H
κατα
μεταλαμβάνειν 39427, 41239 τὰς
προτάσεις 37°15 ἃ τὸ αὐτὸ δύνα-
ται 4903 τοὺς λόγους 94022
μετάληψις. κατὰ μετάληψιν συλλογισ-
pos 4517
μεταφοραί 97°37
μὴ τινὶ ὑπάρχειν 24219, 26632, 32335,
cf. 59°10
Μηδικὸς πόλεμος 94436
INDEX VERBORUM
μήνισκοι 69933
μηχανικός 76224, 78537
Μίκκαλος μουσικός 47°30
μνήμη 10043-6
μονάς 72°22
Νεῖλος 98731
νεύειν 769
νοεῖν 88416
νόησις 8847
νοῦς 85%1, 8008 ἀρχὴ ἐπιστήμης
88b36,100b5-17 ἀληθὴς ἀεί 10058
νῦν. τὰ v. ἀρχὴ τοῦ χρόνου 95518
ὁδὸς ἐπὶ τὰς ἀρχάς 840 24
οἰκεῖος 71023, 7236, 74526, cf. 75538,
γό36 oi. ἐπιστήμη )( καθόλου
67727
ὁλόπτερος 9639
ὅλος. ἐν 6. εἶναι 2426, 25533, 30*2,
53921 ὅλον )( μέρος 42710, 16,
49°37, 64*17, P12, 69414
ὁμόγονος 95°37
ὁμοιοσχήμονες προτάσεις 27°11, 34;
32637, 33237, 36°7
ὁμωνυμία 85°11, τό, 97536
ὁμώνυμος 9947
ἀὀνοματώδης λόγος 93531
ὅπερ 49518, by, 837, 14, 24-30, 89435,
4
ὁπός 99*29
ὀπτικός 76424
75516, 7837
ὀρείχαλκος 92b22
ὁρισμός 4352, 72421, 75P31, go*3s-
9111, 9254-9320, 93^529-94?10,
96522, 97513, 99422 πρὸς ὁρισμὸν
λόγοι 50411 )( ἀπόδειξις goP2, 30
x συλλογισμός g2>35
ὅρος 76535-7734, 9338, 97526, 32
def. 24516 Aaeivó.27b20 δεῖ
κατηγορικόν twa τῶν 6. εἶναι 4156
πᾶσα ἀπόδειξις διὰ τριῶν 6. ib.
36-42331, cf. 4456, 53619 μέσος
47°38 διαψεύδεσθαι παρὰ τὸ μὴ
καλῶς ἐκτίθεσθαι τοὺς ὅ. ὕ4ο-48328
οὐ δεῖ τοὺς ὅ. ἀεὶ ζητεῖν ὀνόματι
ἐκτίθεσθαι 48429-39 τοὺς ὅρους
θετέον κατὰ τὰς κλήσεις τῶν ὀνο-
μάτων P40
6. ὅταν ἁπλῶς τι συλλογισθῇ καὶ
ὅταν τόδε τι ἣ πῇ 3] πώς 49227-52
eos "
τὰ ὁ. ὑπο γεωμετρίαν
οὐχ ἡ αὐτὴ θέσις τῶν
INDEX VERBORUM
ὅτι, τό 75916, 76*11, 78322-79116,
8732, 89415, 523-35,93*317-20 τὸ
6. διαφέρει xai τὸ διότι ἐπίστασθαι
78422
οὐ παρὰ τοῦτο 65438-66415
οὐσία 96334, Ὀ12 περὶ οὐσίας ἀπό-
δειξιν γίνεσθαι 46236 coni. τόδε
τι 7357 οὐσίαν ἔστιν ὁρίσασθαι
83Ὁ 5
παθήματα φυσικά 70>7~38
παράδειγμα 6808. ὅ9519, 71210 X
ἐπαγωγή 69716
παράλληλοι 77522
παραλογισμός 64b13, 7720, 28
παρεῖναι 44*4, 5, 45210
παρεκτείνειν 99*35
παρεμπίπτειν 4298, 23, 95923
nds. πᾶν 74?30-2 κατὰ παντός
24028, 25537, 3023 )( καθ᾽ αὐτό
( καϑόλου 73*26-34
xew 3457
περαΐνειν 41721, 42530
πέρας 74>1
περιπατεῖν 9459
περιττά 41727, 50338
πιστεύειν 68 13
Πίττακος 70°16, 26
πλάνητες ov στίλβουσιν 78430
πλατύφυλλος 9857
Πλάτων, ref. to Meno 67?21, 71*29,
Theael. 76525
ποιότης. συλλογισμὸς κατὰ ποιότητα
45517
πολιοῦσθαι 3256, 17
πολύ. ὡς ἐπὶ τὸ m. 2514, 87523
πραγματεύεσθαι 96>r5
πρόβλημα 88712, 9821-34
)( εὐεπιχείρητον 4229
προγινώσκειν διχῶς ἀναγκαῖον 7171 1-58
προδιομολογεῖσθαι 50333
προεπίστασθαι 67?22
προομολογεῖσθαι 61224
mpocavatpeiv 6243
προσδηλοῦν 92023, 34
πρόσθεσις. ἐκ προσθέσεως 87735
προσλαμβάνειν 42434, 58527, 59212, 22
[πρόσληψις 5889]
πρόσρησις 2533
προσυλλογίζεσθαι 66735
προσυλλογισμός 4205
πρότασις 24>16, 43b1-46?3o, 714,
εν
παντὶ ὑπαρ-
χαλεπόν
685
77736, 84b22, 36-85*1, 87b19-27,
92312 def. 24*16 ἀποδεικ-
τική, διαλεκτική, συλλογιστική, 248
22-by2, cf. 72410, 77639 τοῦ
ὑπάρχειν, τοῦ ἐξ ἀνάγκης ὑπάρχειν,
τοῦ ἐνδέχεσθαι ὑπάρχειν 2531
φατικαί, ἀποφατικαί ib. 2 ὁμοία
32411 κατὰ τὸ ἐνδέχεσθαι ib. 30,
bas, 3392, 3575 ἐνδεχομένη 32>
36, 33>19 ἐνδέχεσθαι λαμβανο-
μένη 33038, 35226, 27, λαμβάνουσα
35°15, σημαίνουσα 39921 5 ἀμ-
φοτέρας 3j τὴν ἑτέραν ὁμοίαν ἀνάγκη
γίνεσθαι τῷ συμπεράσματι 41Ὁ28
ἐκ δύο π. πᾶσα ἀπόδειξις 42332, cf.
40636, 4406, 53520, 66217
ἐκλαμβάνειν 4351, 47310
κείμεναι m. 63922 δὶς ταὐτὸν ἐν
ταῖς m. 66727 ἄμεσος 722] ἕἔν-
δοξος 74022 ἐπακτική 7734
προτείνειν τὴν καθόλου 47415
πρότερον τῇ φύσει )( πρὸς ἡμᾶς
71633-7245
προὔπάρχουσα γνῶσις 7171
προὔπολαμβάνειν 62536, 71412
πρῶτον 71°21 Twi πρώτῳ ὑπάρχειν
66620, 81531, 35, 98527
ἀρχή ταὐτόν 7236 X
82b2 T. ἀμφοτέρως 96736
πρώτως τινὶ ὑπάρχειν 79438, b25, 38
πτῶσις 42630
Πυθαγόρειοι 94°33
πυκνοῦται τὸ μέσον 84>35
κατα-
τὰς T.
avre-
T. xai
ὕστατον
ῥητορικός 68°11, 7130
Σάρδεις 94>1
σελήνη 784
σημεῖον 70*3-P38, 75733, 993 πρό-
τασις ἀποδεικτικὴ ἀναγκαία ἣ ἔνδοξος
7097 λαμβάνεται τριχῶς ib. 11
γ(συλλογισμός ib. 24
σήπιον 98221
ailew 94°33
σκαληνός 8457
Σκύθαι 78930
σοφία 8958
σοφισταί 74023
σοφιστικὸς τρόπος 71>10, 74228
στερεομετρία 7838
στέρησις 73921 )( κατηγορία 52415
στερητικὸς 37220, 38414, 39522
686
στιγμή δ μονάς 87836
στίλβειν 8330
στοιχεῖον 84921
στόμα κοιλίας g4P15
συλλογίζεσθαι )( ἀποδεικνύναι 243
27, cf. 81518—23
συλλογισμός def. 24518 τέλειος
)( ἀτελής ib. 22, 25535, 26529, 27416,
28215, 33320, 34%2 Y( ἀπόδειξις
25>27,71523 δυνατός 2742, 28216,
41933 of ἀτελεῖς τελειοῦνται διὰ τοῦ
πρώτον σχήματος 29930 ἔστιν ἀνα-
γαγεῖν πάντας εἰς τοὺς ἐν τῷ πρώτῳ
σχήματι καθόλου 291, cf. 40°18, 4153
a. δεικτικοί )( of ἐξ ὑποθέσεως 40°27
διὰ τριῶν ὅρων μόνον 41036-42
a31,81b10 εἰς τὸ ἀδύνατον 41522,
45323, bg, διὰ τοῦ ἀδυνάτου 61518
πότ᾽ ἧσται o. 41b6-42b26 δεῖ
κατηγορικόν τινα τῶν ὅρων εἶναι
4156, cf. 81bro-14 δεῖ τὸ xa0ó-
Àov ὑπάρχειν 4107 ἐκ δύο προ-
τάσεων 42532-40 πῶς εὐπορή-
σομεν συλλογισμῶν 43320-45322
κατὰ μεταλῆψιν ἢ κατὰ ποιότητα
45h17 πῶς ἀνάξομεν τοὺς c.
4640 πολλάκις ἀπατᾶσθαι συμ-
βαίνει περὶ τοὺς σ. διὰ τὸ ἀναγκαῖον
47*22-516 ἐνίοτε δὲ παρὰ τὴν
ὁμοιότητα τῆς τῶν ὅρων θέσεως
b16-48228 διὰ τῆς ἀντιστροφῆς
63>17 ἐξ ἐπαγωγῆς 68>15 γί
ἐπαγωγή ib. 31 ἐπιστημονικός
71518 ἀποδεικτικός 74>11 τοῦ
διότι 79422 στερητικοί 85%3
συλλογιστικὸς λόγος 42236 σ. πρότα-
σις 24°28 a. ἐρώτημα 17336-Ὁ33
συμβεβηκός 4308, 4602], 75218-22, br,
83227, bat, 26 ( καθ' αὑτό
7354, 9 (δύ αὐτό 0.1: κατὰ
σ. 43734, 7110, 8124, 83216, 20
συμπέρασμα 3075, 3238-14, 41b36-
4226, 53*17, 75922 τὶ κατά
τινος 5338
συμφωνία 90%18
συνακολουθεῖν gu
συνεπιφέρειν 5257
σχῆμα 29*19-P28, 39*3, 4obr7-41bs,
42b27-43*19, goP5-5192 πρῶτον
25>26-26633 δεύτερον 26b34-28a
9 τρίτον 28*10-29*18 TÓ dva-
λύειν εἰς ἄλληλα τὰ o. 51722, by
INDEX VERBORUM
> , . "T" "
ἐν ποίῳ oc. ἔστιν ἐξ ἀντικειμένων
προτάσεων συλλογίσασθαι 63622
ἐπιστημονικὸν μάλιστα τὸ πρῶτον
1951]
ταὐτότης 45222
τεκμήριον Jo>2
τέλειος συλλογισμός 25534, 26920, bag
οὐδαμῶς ἐν τῷ δευτέρῳ σχήματι
27*1, cf. 2854
τερετίσματα τὰ εἴδη 83?33
τετραγωνίζειν 69731
τετραγωνισμός 75°41
τέχνη 4634, 8008
10038
τί ἐστι 43b7, 82637, 89524, 90*31, 36,
bs, gaba, 9ó*20
τὶ ἦν εἶναι 91425, P8, 10, 26, 9251, 9, τό,
24, 25, 93*12, 19, 94°21, 34, 35
τόδε τι 1301, 87529
τομὴ ἄπειρος 95030
Τοπικά 24>12, 64237, 65>16
τραγέλαφος 4924, 9257
τριάς 96235
τρίγωνον 67317, 71714, 73°31, 76735,
85br1, 9331
τριχοῦσθαι 96710
τύχη 87>19-27, 95*5
τέχνης ἀρχή
ὕαλος τετρυπημένη 88714
ὑπάρχειν Y ἐξ ἀνάγκης ὑπάρχειν
2541, 29%29, 33b9 ὑπάρχουσα
πρότασις 32536 ἐὰν ἡ μὲν ὑπάρ-
xew ἡ δ᾽ ἐνδέχεσθαι λαμβάνηται τῶν
προτάσεων 33925-3522, 3629, 37>
19-38712, 3957, °7-40%3
Ümeprelvew 33730, 68>24, 70>34, 8425
ὑπέχειν λόγον 66232, 7753, 5
ὑπόθεσις 7220-4, 76523-7794 ἐξ
ὕ, 41524, 72>15, 83039, 9236-33
ἐξ ὑ. )( δεικτικῶς δεικνύναι 40P25,
45°16 συλλογισμοὶ ἐξ ὕ. 50°16
ὑποκείμενον 79*9, 8336, 13, 522, grrr
γένος $. 75742, 76912
ὑποληπτόν 49b6
ὑπόληψις 6429, 66619, 79b28
φαινόμενα. τὰ $. ὑπ᾽ ἀστρολογικήν
78°39
φάναι )( ἀποφάναι 71714, 73523,
77710, 22, 30
INDEX VERBORUM
φάσις )( ἀπόφασις 32428, 51620,
33, 62414
φθαρτόν 75b24
φθίνειν. φθίνοντος τοῦ μηνός 98931
φρόνησις 8908
φύεσθαι. πεφυκέναι, coni. ἐνδέχεσθαι
25914 πεφυκὸς ὑπάρχειν (elvat)
3257, 16
φυλλορροεῖν 98437, 38
φυσικός 7058
φυσιογνωμονεῖν 70>7~38
Φωκεῖς 6942
687
χειμεριώτερος 98232
ψευδὴς ἐπί τι )( ὅλη 54*1, P19
ψεῦδος 88225—30 )( ἀδύνατον 34425
ἐξ ἀληθῶν οὐκ ἔστι ψ, συλλογίσασθαι
5357, 11-25, 6285, ἐκ ψευδῶν ἔστιν
ἀληθές 538, 26-57>17, 64> τὸ
πρῶτον ψ. 66416
ψυχή 7625
ὡς ἐπὶ τὸ πολύ 25>14, 43533, 87b23
coni. εἰκός 7034
INDEX
Abstract science superior to con-
crete 596-7
Adrastus I
Affirmative proof better than nega-
tive 592-3
Alexander of Aphrodisias 1, 2,
32 n., 41-2, 45, 9I
Alternative terms 477, 479-80
Ammonius 2, 91
Anacharsis 554
Analysis 545, 548-50
Analytics, title and plan 1-5 rela-
tion of Prior to Posterior 6—22
date 22-3 ^ purpose24-5 text
87-93 MSS. 93-5
Anonymus 2, 9I
Antiphanes 548
Antisthenes 514
Apodeictic syllogism 40-3, 316-18
premisses of 325 semi-apodeictic
syllogism 318-25
Apollonius of Perga 539
Aristomenes 401
Aristotle, De Interpretatione 23, 28
Topics 6, 8, 20, 23-5, 27 Sophi-
stici Elenchi 6,8,23 Physics 59,
81 De Partibus Animalium 81
Metaphysics 15, 23, 24, 59, 64
Nicomachean Ethics 23 Eude-
mian Ethics 23 Politics 7, 8
Rhetoric 23 Protrepticus 14
Assertoric syllogism 300-13, 325
Assos 22
Autolycus 289
Axiom 508, 510-II, 542-3
Becker, A. 294, 296, 299, 327-8,
331, 336, 338-41, 349
Boethius 90
Bonitz, H. 301, 521, 534, 546, 582,
613, 618, 621, 623-4, 667
Bryson 536
Bywater, I. 661
Caeneus 548
Case, T. 421
Cases, nominative and oblique 405-8
Causes, the four 78-80 can func-
tion as middle terms 637-47
plurality of 82-4, 666—73
Chance conjunctions not demon-
strable 598
Cherniss, H. 514, 605, 622, 660
Circular proof 512-19
Consbruch, M. 485
Conspectus of contents 280-5
Contingency 326-30
Conversion of propositions 29-30,
292-300 of syllogisms 445-9
Convertible terms 477-80
Coriscus 22, 590
Cross-references 8-11
Definition 75-8, 81-2, 415, 508,
510-II, 538-9, 653-62 and
demonstration 613-36
Demonstrative science 51-75
Denniston, J. D. 368, 457, 585, 613,
615, 620, 667
Dialectic 542-3
Dictum de omni et nullo 28-9, 33
Diels, H. 491
Diodorus 337
Diogenes Laertius 1
Division, Platonic 7, 25-6, 397-9,
618-20 utility of division 653-
64
Diimmler, F. 514
Düring, I. 663
Ecthesis 29, 32, 311
Einarson, B. 290-1, 301, 311, 380,
400, 540, 556
Enthymeme 498-502
Error, types of 65-7, 544—50, 558-64
Euclid 52, 56—9, 372, 375, 468, 505-
6, 511, 525, 531—2, 541, 590, 635,
640-1, 672 ps.-Euclid 375
Eudemus 41, 45, 525
Eudoxus 623
Eustratius 2
Ewing, A. C. 39
Example, argument from 487-8
Extrapolation 66
False cause 465-8
Figures of syllogism 33-5, 300-16,
369-82, 556
First principles 18-19, 673-8
Fitzgerald, W. 548, 661
Forms, Platonic 14-17; criticized
542, 578, 581
Furlani, G. 9o
Geminus 525
George, Bishop of the Arabs 89
Gomperz, T. M. 372
Gorgias 599, 645
Grote, G. 485
INDEX
Hayduck, M. 540, 615, 673
Heath, T. 56, 463, 467, 491, 506,
511, 525, 537, 540-1, 555. 591,
641, 656
Heiberg, J. L. 375, 463, 468, 591,
672
Hermippus 1
Hesychius 1
Hippocrates of Chios 56, 491
Hoffmann, J. G. E. 91
Hypothesis 18-19, 508, 510-11,
538-40
Hypothetical argument 30-2, 392,
394-5, 415-17
Immediate premisses, necessity of
68—73 immediate negative
premisses 556-8
Induction 37, 47-51, 481-7
Interpolation 66
Jaeger, W. i 582) 584, 590
Joseph, H. W. Β. 38
Kalbfleisch, K. go
Kant, I. 59
Kühner, R. 288, 415, 534, 541, 572,
604, 627
Lee, H. D. P. 511
Leon 56
Limitation of chains of reasoning
566-83
Maier, H. 3, 6, 7, 26, 288, 298-300,
303. 314, 317, 320-1, 337. 354.
356, 373. 395, 397-8, 412-13,
416, 421, 437. 441, 472, 494-5,
497, 500-1, 514, 529, 594, 622,
658
Mansion, A. 63
Mathematics 14-16, 75, 504-5,
545 mathematical reasoning
35. 52-3, 55-9 mathematical
allusions 370, 466-7, 489-91,
503-6, 508-11, 517-21, 523-6,
530-2, 536-7, 539-41, 544-7.
551-2, 564-6, 588-91, 596-8,
606-8, 611, 613-15, 625, 627,
637, 640-2, 653, 656, 672
Megarian philosophers 337
Meiser, K. 91
Miccalus 401-2
Middle term,
664-5
Milhaud, G. 491
Miller, J. M. gon. 1
Minio, L. 89-91
search for 610-13,
689
Modal syllogisms 40-7, 392, 395
Mure, G. R. G. 529, 582, 618, 627,
636, 663, 673
Objection 491-7
Ogle, W. 664
Opinion 605-8
Oppermann 539
Opposite premisses, reasoning from
457-61
Ostensive proof 454-7 better
than reductio ad impossibile 594-5
Pacius, J. 414, 469, 479, 486, 548,
610, 615, 622, 624, 632, 658
Past and future events, inference
of 648
Petitio principii 38-9, 461-5
Philo 337
Philoponus 2, 91
Physiognomonics 498-9, 501-2
Plato 14-20, 22-3, 25-7, 64, 290,
373, 398-9, 460, 474, 483, 490,
503, 506, 528, 537, 543, 585, 632,
660, 663, 677
Platonists 384, 414
Plurality of causes 82-4, 666-73
Porphyry 8
Postulate 538-41
Potential )( actual knowledge
470-6, 506
Predication per accidens 566-8,
573, 576-7
Premiss 287-9 of demonstrative
science 55-65, 84-6, 507—12, 517-
23, 526-32, 535-43
Principles, first 673-8
Proba 89
Problematic syllogism 43-7 — prob-
lematic and semi-problematic
syllogism 330-69
Proper predication 70-1
Protagoras 599
Pythagoreans 308, 525, 590, 596,
613
Quick wit 609
Reciprocal proof 438-44
Reductio ad impossibile 29-32, 37,
42-3. 392-5, 449-57
Reduction of problems 489-91
of syllogisms 417-18
Robinson, R. 550
Schüler, S. 9o
Scientific knowledge 507-12
Sense-perception the foundation of
scientific knowledge 564-6 — can-
not give demonstration 598-9
690 INDEX
Sextus Empiricus 39
Shorey, P. 26-27, 373
Signs 498-502
Socrates 460, 482
Solmsen, F. 6-22
Sophonias 2
Speusippus 605, 623, 660
Stoics 291
Syllogism, assertoric 23-40 de-
finition of 35, 287, 291
Syriac translations 89
Term 16, 287, 290
Themistius 2, 91
Theophrastus 30 n. 3, 41, 45-7, 395,
441
Thesis 508, 510-11
Theudius 42, 46, 635
Thiel, N. M. 372
Thouvenez, E. 314
Tredennick, H. 403, 486
Trendelenburg, F. A. 47
True conclusion from false premisses
428-37
Universal 16, 518, 523 universal
)( particular demonstration 588—
92
Valid moods 286
Waitz, T. 90
Wallies, M. 2, 303
Wilson, J. Cook 71, 496-7
Xenocrates 514, 618
Zabarella, J. 64, 512, 520, 529, 533,
537. 542, 547. 549, 569, 591, 596,
604, 610, 613, 646, 662, 672, 677
Zeno 467
Zeuthen, H. G. 539
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PRINTER
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